In this paper, a predictive sliding mode control (PSMC) strategy for the quadrotors tracking trajectory problem is proposed. This strategy aims to combine the advantages of sliding mode control (SMC) and non-linear model predictive control (NMPC) to improve the tracking control performance for quadrotors in terms of optimality, inputs/states constraints satisfaction, and strong robustness against disturbances. A comparative study of three popular controllers: the SMC, NMPC, and the integral backstepping control (IBC) is performed with different criteria. Accordingly, IBC and SMC show less computational time and strong robustness, while NMPC has minimum control effort. The discrete Dryden turbulence model is used as a benchmark model to represent the wind effect on the trajectory tracking accuracy. The effectiveness of the proposed method PSMC has been proven and compared with discrete-time sliding mode control (DSMC) and NMPC in several scenarios. Simulation results show that under both wind turbulence and time-variant uncertainties, the PSMC outperforms the other controllers by providing simultaneously disturbance rejection and guarantee that the control inputs are within bounded constraints.
We focus a modern methodology in this paper for adding the fuzzy logic control as well as sliding model control. This combination can enhance the MLS position control robustness and enhanced performance of it.In the start, for an application in an area to control the loops placement and position for the synchronous motor what has permanent magnetic linearity we tend to control the fuzzy sliding mode control. To resolve the chattering issues a designed controller is investigated and, in this way, steady state motion in sliding with higher accuracy is obtained. In this case, method of online tuning with the help of fuzzy logic is used in order to adjust the thickness of boundary layer and switching gains.For the suggested scheme technique, the outcomes of simulation suggest that with the classical SMC the accurate state and good dynamic performance is compared due to force chattering resistance, response by quick dynamic force and external disturbance elements and robustness against them.
The aim of this research is the speed tracking of the permanent magnet synchronous motor (PMSM) using an intelligent Neural-Network based adapative backstepping control. First, the model of PMSM in the Park synchronous frame is derived. Then, the PMSM speed regulation is investigated using the classical method utilizing the field oriented control theory. Thereafter, a robust nonlinear controller employing an adaptive backstepping strategy is investigated in order to achieve a good performance tracking objective under motor parameters changing and external load torque application. In the final step, a neural network estimator is integrated with the adaptive controller to estimate the motor parameters values and the load disturbance value for enhancing the effectiveness of the adaptive backstepping controller. The robsutness of the presented control algorithm is demonstrated using simulation tests. The obtained results clearly demonstrate that the presented NN-adaptive control algorithm can provide good trackingperformances for the speed trackingin the presence of motor parameter variation and load application.
Adaptive proportional integral derivative deep feedforward network for quadr...IJECEIAES
When the controlled system is subject to parameter variations and external disturbances, a fixed-parameter proportional integral derivative (PID) controller cannot ensure its stabilization. In this case, its control requires online parameter adjustment. Specifically, as the quadrotor is a multi-input multi-output, nonlinear, and underactuated system, robust control is necessary to ensure efficient trajectory tracking flights. In this paper, an adaptive proportional integral derivative (APID) controller is proposed to control the quadrotor systems. This APID-based control strategy uses a two hidden layer deep feedforward network (DFN), where the one-step secant algorithm is chosen for initializing the DFN parameters. All the design steps of the proposed adaptive controller are described. The multidimensional particle swarm optimization (PSO) algorithm is used for tuning the DFN parameters. Then, using two simulation efficiency tests, a comparison between the proposed PSO-based APID-DFN, the (non-optimized) APID-DFN, the feedforward network APID, and the fixed-parameter PID controllers proves much efficiency of the proposed adaptive controller. The results illustrate that the proposed PSO-based APID-DFN controller can ensure good quadrotor system stabilization and achieve minimum overshoot and faster convergence speed for all quadrotor motions. Thus, the proposed control strategy could be considered an additional intelligent method-based adaptive control for unmanned aerial vehicles.
Model Validation and Control of an In-Wheel DC Motor Prototype for Hybrid El...Scientific Review SR
In this paper, a mathematical model and a controller for a DC motor are developed for the
construction of an in-wheel motor. In-wheel motors can be used in hybrid electric vehicles to provide traction
force of front or rear wheels. The model identification is achieved using a simple and low cost data acquisition
system. An Arduino Uno embedded board system is used to collect data from sensors to a computer and for
control purposes. Data processing is performed using Matlab/Simulink. Validations of the devel oped
mathematical model and controller performance are carried out by comparing simulation and experimental results.
The results obtained show that the mathematical model is accurate enough to assist in speed controller design and
implementation.
Evaluation of the stability enhancement of the conventional sliding mode cont...nooriasukmaningtyas
The proposed work is an attempt to investigate the stability of the nonlinear
system by using a whale optimization algorithm as of one of the metaheuristic optimization methods, and this investigation was conducted on a
single inverted pendulum as a study model. The evaluation measures which
were used in this article values of gain and sliding surface of the
conventional sliding mode controller to illustrate the extent of the system`s
stability. Furthermore, control action, the relationship between error and its
derivative, desired, and actual position in addition to sliding response
graphically showed the feasibility of the proposed solution. The attained
results illustrated considerable improvement in the settling time and
minimizing the impact of chattering behavior.
Optimal backstepping control of quadrotor UAV using gravitational search opti...journalBEEI
Quadrotor unmanned aerial vehicle (UAV) has superior characteristics such as ability to take off and land vertically, to hover in a stable air condition and to perform fast maneuvers. However, developing a high-performance quadrotor UAV controller is a difficult problem as quadrotor is an unstable and underactuated nonlinear system. The effort in this article focuses on designing and optimizing an autonomous quadrotor UAV controller. First, the aerial vehicle's dynamic model is presented. Then it is suggested an optimal backstepping controller (OBC). Traditionally, backstepping controller (BC) parameters are often selected arbitrarily. The gravitational search algorithm (GSA) is used here to determine the BC parameter optimum values. In the algorithm, the control parameters are calculated using an integral absolute error to minimize the fitness function. As the control law is based on the theorem of Lyapunov, the asymptotic stability of the scheme can be ensured. Finally, several simulation studies are conducted to show the efficacy of the suggested OBC.
Induction motors are work-horse of the industry and major element in energy conversion. The replacement of the existing non-adjustable speed drives with the modern variable frequency drives would save considerable amount of electricity. A proper control scheme for variable frequency drives can enhance the efficiency and performance of the drive. This paper attempt to provide a rigorous review of various control schemes for the induction motor control and provides critical analysis and guidelines for the future research work. A detailed study of sensor based control schemes and sensor-less control schemes has been investigated. The operation, advantages, and limitations of the various control schemes are highlighted and different types of optimization techniques have been suggested to overcome the limitations of control techniques.
In this paper, a novel adaptive control approach for Unmanned Aerial Manipulators (UAMs) is proposed. The UAMs are a new configuration of the Unmanned Arial Vehicles (UAVs) which are characterized by several inhered nonlinearities, uncertainties and coupling. The studied UAM is a Quadrotor endowed with two degrees of freedom robotic arm. The main objectives of our contribution are to achieve both a tracking error convergence by avoiding any singularity problem and also the chattering amplitude attenuation in the presence of perturbations. Therefore, the proposed Adaptive Nonsingular Terminal Super-Twisting controller (ANTSTW) consists of the hybridization of a Nonsingular Terminal Sliding Mode Control and an Adaptive Super Twisting. The adaptive law, which adjust the Super-Twisting’s parameters, is obtained by using stability Lyapunov theorem. Simulation experiments in trajectory tracking mode were realized and compared with Nonsingular Terminal Super-twisting control to prove the superiority and the effectiveness of the proposed approach.
We focus a modern methodology in this paper for adding the fuzzy logic control as well as sliding model control. This combination can enhance the MLS position control robustness and enhanced performance of it.In the start, for an application in an area to control the loops placement and position for the synchronous motor what has permanent magnetic linearity we tend to control the fuzzy sliding mode control. To resolve the chattering issues a designed controller is investigated and, in this way, steady state motion in sliding with higher accuracy is obtained. In this case, method of online tuning with the help of fuzzy logic is used in order to adjust the thickness of boundary layer and switching gains.For the suggested scheme technique, the outcomes of simulation suggest that with the classical SMC the accurate state and good dynamic performance is compared due to force chattering resistance, response by quick dynamic force and external disturbance elements and robustness against them.
The aim of this research is the speed tracking of the permanent magnet synchronous motor (PMSM) using an intelligent Neural-Network based adapative backstepping control. First, the model of PMSM in the Park synchronous frame is derived. Then, the PMSM speed regulation is investigated using the classical method utilizing the field oriented control theory. Thereafter, a robust nonlinear controller employing an adaptive backstepping strategy is investigated in order to achieve a good performance tracking objective under motor parameters changing and external load torque application. In the final step, a neural network estimator is integrated with the adaptive controller to estimate the motor parameters values and the load disturbance value for enhancing the effectiveness of the adaptive backstepping controller. The robsutness of the presented control algorithm is demonstrated using simulation tests. The obtained results clearly demonstrate that the presented NN-adaptive control algorithm can provide good trackingperformances for the speed trackingin the presence of motor parameter variation and load application.
Adaptive proportional integral derivative deep feedforward network for quadr...IJECEIAES
When the controlled system is subject to parameter variations and external disturbances, a fixed-parameter proportional integral derivative (PID) controller cannot ensure its stabilization. In this case, its control requires online parameter adjustment. Specifically, as the quadrotor is a multi-input multi-output, nonlinear, and underactuated system, robust control is necessary to ensure efficient trajectory tracking flights. In this paper, an adaptive proportional integral derivative (APID) controller is proposed to control the quadrotor systems. This APID-based control strategy uses a two hidden layer deep feedforward network (DFN), where the one-step secant algorithm is chosen for initializing the DFN parameters. All the design steps of the proposed adaptive controller are described. The multidimensional particle swarm optimization (PSO) algorithm is used for tuning the DFN parameters. Then, using two simulation efficiency tests, a comparison between the proposed PSO-based APID-DFN, the (non-optimized) APID-DFN, the feedforward network APID, and the fixed-parameter PID controllers proves much efficiency of the proposed adaptive controller. The results illustrate that the proposed PSO-based APID-DFN controller can ensure good quadrotor system stabilization and achieve minimum overshoot and faster convergence speed for all quadrotor motions. Thus, the proposed control strategy could be considered an additional intelligent method-based adaptive control for unmanned aerial vehicles.
Model Validation and Control of an In-Wheel DC Motor Prototype for Hybrid El...Scientific Review SR
In this paper, a mathematical model and a controller for a DC motor are developed for the
construction of an in-wheel motor. In-wheel motors can be used in hybrid electric vehicles to provide traction
force of front or rear wheels. The model identification is achieved using a simple and low cost data acquisition
system. An Arduino Uno embedded board system is used to collect data from sensors to a computer and for
control purposes. Data processing is performed using Matlab/Simulink. Validations of the devel oped
mathematical model and controller performance are carried out by comparing simulation and experimental results.
The results obtained show that the mathematical model is accurate enough to assist in speed controller design and
implementation.
Evaluation of the stability enhancement of the conventional sliding mode cont...nooriasukmaningtyas
The proposed work is an attempt to investigate the stability of the nonlinear
system by using a whale optimization algorithm as of one of the metaheuristic optimization methods, and this investigation was conducted on a
single inverted pendulum as a study model. The evaluation measures which
were used in this article values of gain and sliding surface of the
conventional sliding mode controller to illustrate the extent of the system`s
stability. Furthermore, control action, the relationship between error and its
derivative, desired, and actual position in addition to sliding response
graphically showed the feasibility of the proposed solution. The attained
results illustrated considerable improvement in the settling time and
minimizing the impact of chattering behavior.
Optimal backstepping control of quadrotor UAV using gravitational search opti...journalBEEI
Quadrotor unmanned aerial vehicle (UAV) has superior characteristics such as ability to take off and land vertically, to hover in a stable air condition and to perform fast maneuvers. However, developing a high-performance quadrotor UAV controller is a difficult problem as quadrotor is an unstable and underactuated nonlinear system. The effort in this article focuses on designing and optimizing an autonomous quadrotor UAV controller. First, the aerial vehicle's dynamic model is presented. Then it is suggested an optimal backstepping controller (OBC). Traditionally, backstepping controller (BC) parameters are often selected arbitrarily. The gravitational search algorithm (GSA) is used here to determine the BC parameter optimum values. In the algorithm, the control parameters are calculated using an integral absolute error to minimize the fitness function. As the control law is based on the theorem of Lyapunov, the asymptotic stability of the scheme can be ensured. Finally, several simulation studies are conducted to show the efficacy of the suggested OBC.
Induction motors are work-horse of the industry and major element in energy conversion. The replacement of the existing non-adjustable speed drives with the modern variable frequency drives would save considerable amount of electricity. A proper control scheme for variable frequency drives can enhance the efficiency and performance of the drive. This paper attempt to provide a rigorous review of various control schemes for the induction motor control and provides critical analysis and guidelines for the future research work. A detailed study of sensor based control schemes and sensor-less control schemes has been investigated. The operation, advantages, and limitations of the various control schemes are highlighted and different types of optimization techniques have been suggested to overcome the limitations of control techniques.
In this paper, a novel adaptive control approach for Unmanned Aerial Manipulators (UAMs) is proposed. The UAMs are a new configuration of the Unmanned Arial Vehicles (UAVs) which are characterized by several inhered nonlinearities, uncertainties and coupling. The studied UAM is a Quadrotor endowed with two degrees of freedom robotic arm. The main objectives of our contribution are to achieve both a tracking error convergence by avoiding any singularity problem and also the chattering amplitude attenuation in the presence of perturbations. Therefore, the proposed Adaptive Nonsingular Terminal Super-Twisting controller (ANTSTW) consists of the hybridization of a Nonsingular Terminal Sliding Mode Control and an Adaptive Super Twisting. The adaptive law, which adjust the Super-Twisting’s parameters, is obtained by using stability Lyapunov theorem. Simulation experiments in trajectory tracking mode were realized and compared with Nonsingular Terminal Super-twisting control to prove the superiority and the effectiveness of the proposed approach.
Robust design of a 2 dof gmv controller a direct self-tuning and fuzzy schedu...ISA Interchange
This paper presents a study on self-tuning control strategies with generalized minimum variance control in a fixed two degree of freedom structure–or simply GMV2DOF–within two adaptive perspectives. One, from the process model point of view, using a recursive least squares estimator algorithm for direct self-tuning design, and another, using a Mamdani fuzzy GMV2DOF parameters scheduling technique based on analytical and physical interpretations from robustness analysis of the system. Both strategies are assessed by simulation and real plants experimentation environments composed of a damped pendulum and an under development wind tunnel from the Department of Automation and Systems of the Federal University of Santa Catarina.
DUAL NEURAL NETWORK FOR ADAPTIVE SLIDING MODE CONTROL OF QUADROTOR HELICOPTER...ijistjournal
An adaptive sliding mode control based on two neural networks is proposed in this paper for Quadrotor stabilization. This approach presents solutions to conventional control drawbacks as chattering phenomenon and dynamical model imprecision. For that reason two ANN for each quadrotor helicopter subsystem are implemented in the control loop, the first one is a Single Hidden Layer network used to approximate on line the equivalent control and the second feed-forward Network is used to estimate the ideal corrective term. The main purpose behind the use of ANN in the second part of SMC is to minimize the chattering phenomena and response time by finding optimal sliding gain and sliding surface slope. The learning algorithms of the two ANNs (equivalent and corrective controller) are obtained using the direct Lyapunov stability method. The simulation results are given to highlight the performances of the proposed control scheme.
DUAL NEURAL NETWORK FOR ADAPTIVE SLIDING MODE CONTROL OF QUADROTOR HELICOPTER...ijistjournal
An adaptive sliding mode control based on two neural networks is proposed in this paper for Quadrotor stabilization. This approach presents solutions to conventional control drawbacks as chattering phenomenon and dynamical model imprecision. For that reason two ANN for each quadrotor helicopter subsystem are implemented in the control loop, the first one is a Single Hidden Layer network used to approximate on line the equivalent control and the second feed-forward Network is used to estimate the ideal corrective term. The main purpose behind the use of ANN in the second part of SMC is to minimize the chattering phenomena and response time by finding optimal sliding gain and sliding surface slope. The learning algorithms of the two ANNs (equivalent and corrective controller) are obtained using the direct Lyapunov stability method. The simulation results are given to highlight the performances of the proposed control scheme.
A two-wheeled self-balancing robot (TWSBR) is an underactuated system that
is inherently nonlinear and unstable. While many control methods have been
introduced to enhance the performance, there is no unique solution when it comes to hardware implementation as the robot’s stability is highly dependent on accuracy of sensors and robustness of the electronic control systems. In
this study, a TWSBR that is controlled by an embedded NI myRIO-1900 board with LabVIEW-based control scheme is developed. We compare the performance between proportional-integral-derivative (PID) and linear quadratic regulator (LQR) schemes which are designed based on the TWSBR’s model that
is constructed from Newtonian principles. A hybrid PID-LQR scheme is then proposed to compensate for the individual components’ limitations. Experimental results demonstrate the PID is more effective at regulating the tilt angle of the robot in the presence of external disturbances, but it necessitates a higher velocity to sustain its equilibrium. The LQR on the other hand outperforms PID
in terms of maximum initial tilt angle. By combining both schemes, significant
improvements can be observed, such as an increase in maximum initial tilt angle
and a reduction in settling time.
An efficient application of particle swarm optimization in model predictive ...IJECEIAES
Despite all the model predictive control (MPC) based solution advantages such as a guarantee of stability, the main disadvantage such as an exponential growth of the number of the polyhedral region by increasing the prediction horizon exists. This causes the increment in computation complexity of control law. In this paper, we present the efficiency of particle swarm optimization (PSO) in optimal control of a two-tank system modeled as piece- wise affine. The solution of the constrained final time-optimal control problem (CFTOC) is derived, and then the PSO algorithm is used to reduce the computational complexity of the control law and set the physical parameters of the system to improve performance simultaneously. On the other hand, a new combined algorithm based on PSO is going to be used to reduce the complexity of explicit MPC-based solution CFTOC of the two-tank system; consequently, that the number of polyhedral is minimized, and system performance is more desirable simultaneously. The proposed algorithm is applied in simulation and our desired subjects are reached. The number of control law polyhedral reduces from 42 to 10 and the liquid height in both tanks reaches the desired certain value in 189 seconds. Search time and apply control law in 25 seconds.
Optimal Design of Super Twisting Control with PSO Algorithm for Robotic Manip...CSCJournals
Robotic manipulators are nonlinear and coupling systems exposing to external disturbance. They are used in wide industrial applications; the suitable selection of a nonlinear robust controller is required. Sliding Mode Controller (SMC) was designed to achieve these requirements, but unfortunately the chattering phenomenon was the main drawback of the conventional SMC. It leads to destructive of some components of a real system and subsequent loss in its accuracy. Hence, the design of Super-Twisting Controller (STC) is suggested for chattering elimination. In previous literatures, the accomplishment of the manual adjustment for the parameters of STC was a large burden and time consuming process. Therefore, a new combination of Particle Swarm Optimization (PSO) algorithm with STC is proposed for optimal tuning of STC parameters. The simulation results demonstrate the superiority of the super twisting technique for chattering mitigation comparing to the conventional SMC. Also, STC tuned via PSO proves its effectiveness and robustness to different types of external disturbances without the needs for the knowledge of their upper boundary values. Besides, the performance of the controlled system is faster and more accurate in the criteria of overshoot, settling time and rise time compared to the manual adjusting of super twisting controllers.
The main objective of this paper is to continue the development of activities of basic and applied research related to wind energy and to develop methods of optimal control to improve the performance and production of electrical energy from wind. A new control technique of Double fed induction generator for wind turbine is undertaken through a robust approach tagged nonlinear sliding mode control (SMC) with exponential reaching law control (ERL). The SMC with ERL proves to be capable of reducing the system chattering phenomenon as well as accelerating the approaching process. A nonlinear case numerical simulation test is employed to verify the superior performance of the ERL method over traditional power rate reaching strategy. Results obtained in Matlab/Simulink environment show that the SMC with ERL is more robust, prove excellent performance for the control unit by improving power quality and stability of wind turbine.
This paper presents a novel structure combining the port-controlled Hamiltonian (PCH) and Backstepping (BS) nonlinear control for the vector control of the six-phase induction motor (SPIM). In this new scheme, to improve the outer loop’s robustness, the BS technique using the integral tracking errors action is proposed in the speed and flux controllers design. The advantage of this proposed control law is not to increase the complexity of differential equation resolution due to being not increased system states numbers. To enhance more the performance of SPIM drives (SPIMD), port-controlled Hamiltonian (PCH) scheme is used in the inner current loop controllers. In this proposed PCH current controller, the stabilization of controller is achieved via system passivity. In that, the interconnection and damping matrix functions of PCH system are shaped so that the physical (Hamiltonian) system structure is preserved at the closed loop level and the closed loop energy function is equal to the difference between the physical energy of the system and the energy supplied by the controller. The proposed control design is based on combination PCH and BS techniques improve significantly performance and robustness. The proposed speed control scheme is validated by Matlab-Simulink software.
Robust second order sliding mode control for a quadrotor considering motor dy...ijctcm
In this paper, a robust second order sliding mode control (SMC) for controlling a quadrotor with uncertain
parameters presented based on high order sliding mode control (HOSMC). A controller based on the
HOSMC technique is designed for trajectory tracking of a quadrotor helicopter with considering motor
dynamics. The main subsystems of quadrotor (i.e. position and attitude) stabilized using HOSMC method.
The performance and effectiveness of the proposed controller are tested in a simulation study taking into
account external disturbances with consider to motor dynamics. Simulation results show that the proposed
controller eliminates the disturbance effect on the position and attitude subsystems efficiency that can be
used in real time applications.
Robust Second Order Sliding Mode Control for A Quadrotor Considering Motor Dy...ijctcm
In this paper, a robust second order sliding mode control (SMC) for controlling a quadrotor with uncertain parameters presented based on high order sliding mode control (HOSMC). A controller based on the HOSMC technique is designed for trajectory tracking of a quadrotor helicopter with considering motor dynamics. The main subsystems of quadrotor (i.e. position and attitude) stabilized using HOSMC method. The performance and effectiveness of the proposed controller are tested in a simulation study taking into account external disturbances with consider to motor dynamics. Simulation results show that the proposed controller eliminates the disturbance effect on the position and attitude subsystems efficiency that can be used in real time applications.
Robust Second Order Sliding Mode Control for A Quadrotor Considering Motor Dy...ijctcm
In this paper, a robust second order sliding mode control (SMC) for controlling a quadrotor with uncertain parameters presented based on high order sliding mode control (HOSMC). A controller based on the HOSMC technique is designed for trajectory tracking of a quadrotor helicopter with considering motor dynamics. The main subsystems of quadrotor (i.e. position and attitude) stabilized using HOSMC method. The performance and effectiveness of the proposed controller are tested in a simulation study taking into account external disturbances with consider to motor dynamics. Simulation results show that the proposed controller eliminates the disturbance effect on the position and attitude subsystems efficiency that can be used in real time applications.
Nonlinear control of WECS based on PMSG for optimal power extraction IJECEIAES
This paper proposes a robust control strategy for optimizing the maximum power captured in Wind Energy Conversion Systems (WECS) based on permanent magnet synchronous generators (PMSG), which is integrated into the grid. In order to achieve the maximum power point (MPPT) the machine side converter regulates the rotational speed of the PMSG to track the optimal speed. To evaluate the performance and effectiveness of the proposed controller, a comparative study between the IBC control and the vector control based on PI controller was carried out through computer simulation. This analysis consists of two case studies including stochastic variation in wind speed and step change in wind speed.
An Overview of Adaptive Approaches in Flight ControlIJERA Editor
Multi-mode switching between controllers corresponding to different modes of operation is needed in those cases when the transition from one mode to another results in substantial flight-critical variations in the aircraft dynamics. To address this problem, a general framework for multi-modal flight control is proposed. The framework is based on the Multiple Models, Switching and Tuning (MMST) methodology, combined with Model-Predictive Control (MPC), and the use of different robust mechanisms for switching between the multi-modal controllers. It was shown that many different switching control strategies can be naturally derived from the basic framework, which demonstrates the generality of the proposed approach.
Damping of Inter-Area Low Frequency Oscillation Using an Adaptive Wide-Area D...Power System Operation
This paper presents an adaptive wide-area damping controller (WADC) based on
generalized predictive control (GPC) and model identification for damping the inter-area low
frequency oscillations in large-scale inter-connected power system. A recursive least-squares algorithm
(RLSA) with a varying forgetting factor is applied to identify online the reduced-order linearlized
model which contains dominant inter-area low frequency oscillations. Based on this linearlized model,
the generalized predictive control scheme considering control output constraints is employed to obtain
the optimal control signal in each sampling interval. Case studies are undertaken on a two-area fourmachine
power system and the New England 10-machine 39-bus power system, respectively.
Simulation results show that the proposed adaptive WADC not only can damp the inter-area
oscillations effectively under a wide range of operation conditions and different disturbances, but also
has better robustness against to the time delay existing in the remote signals. The comparison studies
with the conventional lead-lag WADC are also provided.
Bibliometric analysis highlighting the role of women in addressing climate ch...IJECEIAES
Fossil fuel consumption increased quickly, contributing to climate change
that is evident in unusual flooding and draughts, and global warming. Over
the past ten years, women's involvement in society has grown dramatically,
and they succeeded in playing a noticeable role in reducing climate change.
A bibliometric analysis of data from the last ten years has been carried out to
examine the role of women in addressing the climate change. The analysis's
findings discussed the relevant to the sustainable development goals (SDGs),
particularly SDG 7 and SDG 13. The results considered contributions made
by women in the various sectors while taking geographic dispersion into
account. The bibliometric analysis delves into topics including women's
leadership in environmental groups, their involvement in policymaking, their
contributions to sustainable development projects, and the influence of
gender diversity on attempts to mitigate climate change. This study's results
highlight how women have influenced policies and actions related to climate
change, point out areas of research deficiency and recommendations on how
to increase role of the women in addressing the climate change and
achieving sustainability. To achieve more successful results, this initiative
aims to highlight the significance of gender equality and encourage
inclusivity in climate change decision-making processes.
Voltage and frequency control of microgrid in presence of micro-turbine inter...IJECEIAES
The active and reactive load changes have a significant impact on voltage
and frequency. In this paper, in order to stabilize the microgrid (MG) against
load variations in islanding mode, the active and reactive power of all
distributed generators (DGs), including energy storage (battery), diesel
generator, and micro-turbine, are controlled. The micro-turbine generator is
connected to MG through a three-phase to three-phase matrix converter, and
the droop control method is applied for controlling the voltage and
frequency of MG. In addition, a method is introduced for voltage and
frequency control of micro-turbines in the transition state from gridconnected mode to islanding mode. A novel switching strategy of the matrix
converter is used for converting the high-frequency output voltage of the
micro-turbine to the grid-side frequency of the utility system. Moreover,
using the switching strategy, the low-order harmonics in the output current
and voltage are not produced, and consequently, the size of the output filter
would be reduced. In fact, the suggested control strategy is load-independent
and has no frequency conversion restrictions. The proposed approach for
voltage and frequency regulation demonstrates exceptional performance and
favorable response across various load alteration scenarios. The suggested
strategy is examined in several scenarios in the MG test systems, and the
simulation results are addressed.
More Related Content
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Robust design of a 2 dof gmv controller a direct self-tuning and fuzzy schedu...ISA Interchange
This paper presents a study on self-tuning control strategies with generalized minimum variance control in a fixed two degree of freedom structure–or simply GMV2DOF–within two adaptive perspectives. One, from the process model point of view, using a recursive least squares estimator algorithm for direct self-tuning design, and another, using a Mamdani fuzzy GMV2DOF parameters scheduling technique based on analytical and physical interpretations from robustness analysis of the system. Both strategies are assessed by simulation and real plants experimentation environments composed of a damped pendulum and an under development wind tunnel from the Department of Automation and Systems of the Federal University of Santa Catarina.
DUAL NEURAL NETWORK FOR ADAPTIVE SLIDING MODE CONTROL OF QUADROTOR HELICOPTER...ijistjournal
An adaptive sliding mode control based on two neural networks is proposed in this paper for Quadrotor stabilization. This approach presents solutions to conventional control drawbacks as chattering phenomenon and dynamical model imprecision. For that reason two ANN for each quadrotor helicopter subsystem are implemented in the control loop, the first one is a Single Hidden Layer network used to approximate on line the equivalent control and the second feed-forward Network is used to estimate the ideal corrective term. The main purpose behind the use of ANN in the second part of SMC is to minimize the chattering phenomena and response time by finding optimal sliding gain and sliding surface slope. The learning algorithms of the two ANNs (equivalent and corrective controller) are obtained using the direct Lyapunov stability method. The simulation results are given to highlight the performances of the proposed control scheme.
DUAL NEURAL NETWORK FOR ADAPTIVE SLIDING MODE CONTROL OF QUADROTOR HELICOPTER...ijistjournal
An adaptive sliding mode control based on two neural networks is proposed in this paper for Quadrotor stabilization. This approach presents solutions to conventional control drawbacks as chattering phenomenon and dynamical model imprecision. For that reason two ANN for each quadrotor helicopter subsystem are implemented in the control loop, the first one is a Single Hidden Layer network used to approximate on line the equivalent control and the second feed-forward Network is used to estimate the ideal corrective term. The main purpose behind the use of ANN in the second part of SMC is to minimize the chattering phenomena and response time by finding optimal sliding gain and sliding surface slope. The learning algorithms of the two ANNs (equivalent and corrective controller) are obtained using the direct Lyapunov stability method. The simulation results are given to highlight the performances of the proposed control scheme.
A two-wheeled self-balancing robot (TWSBR) is an underactuated system that
is inherently nonlinear and unstable. While many control methods have been
introduced to enhance the performance, there is no unique solution when it comes to hardware implementation as the robot’s stability is highly dependent on accuracy of sensors and robustness of the electronic control systems. In
this study, a TWSBR that is controlled by an embedded NI myRIO-1900 board with LabVIEW-based control scheme is developed. We compare the performance between proportional-integral-derivative (PID) and linear quadratic regulator (LQR) schemes which are designed based on the TWSBR’s model that
is constructed from Newtonian principles. A hybrid PID-LQR scheme is then proposed to compensate for the individual components’ limitations. Experimental results demonstrate the PID is more effective at regulating the tilt angle of the robot in the presence of external disturbances, but it necessitates a higher velocity to sustain its equilibrium. The LQR on the other hand outperforms PID
in terms of maximum initial tilt angle. By combining both schemes, significant
improvements can be observed, such as an increase in maximum initial tilt angle
and a reduction in settling time.
An efficient application of particle swarm optimization in model predictive ...IJECEIAES
Despite all the model predictive control (MPC) based solution advantages such as a guarantee of stability, the main disadvantage such as an exponential growth of the number of the polyhedral region by increasing the prediction horizon exists. This causes the increment in computation complexity of control law. In this paper, we present the efficiency of particle swarm optimization (PSO) in optimal control of a two-tank system modeled as piece- wise affine. The solution of the constrained final time-optimal control problem (CFTOC) is derived, and then the PSO algorithm is used to reduce the computational complexity of the control law and set the physical parameters of the system to improve performance simultaneously. On the other hand, a new combined algorithm based on PSO is going to be used to reduce the complexity of explicit MPC-based solution CFTOC of the two-tank system; consequently, that the number of polyhedral is minimized, and system performance is more desirable simultaneously. The proposed algorithm is applied in simulation and our desired subjects are reached. The number of control law polyhedral reduces from 42 to 10 and the liquid height in both tanks reaches the desired certain value in 189 seconds. Search time and apply control law in 25 seconds.
Optimal Design of Super Twisting Control with PSO Algorithm for Robotic Manip...CSCJournals
Robotic manipulators are nonlinear and coupling systems exposing to external disturbance. They are used in wide industrial applications; the suitable selection of a nonlinear robust controller is required. Sliding Mode Controller (SMC) was designed to achieve these requirements, but unfortunately the chattering phenomenon was the main drawback of the conventional SMC. It leads to destructive of some components of a real system and subsequent loss in its accuracy. Hence, the design of Super-Twisting Controller (STC) is suggested for chattering elimination. In previous literatures, the accomplishment of the manual adjustment for the parameters of STC was a large burden and time consuming process. Therefore, a new combination of Particle Swarm Optimization (PSO) algorithm with STC is proposed for optimal tuning of STC parameters. The simulation results demonstrate the superiority of the super twisting technique for chattering mitigation comparing to the conventional SMC. Also, STC tuned via PSO proves its effectiveness and robustness to different types of external disturbances without the needs for the knowledge of their upper boundary values. Besides, the performance of the controlled system is faster and more accurate in the criteria of overshoot, settling time and rise time compared to the manual adjusting of super twisting controllers.
The main objective of this paper is to continue the development of activities of basic and applied research related to wind energy and to develop methods of optimal control to improve the performance and production of electrical energy from wind. A new control technique of Double fed induction generator for wind turbine is undertaken through a robust approach tagged nonlinear sliding mode control (SMC) with exponential reaching law control (ERL). The SMC with ERL proves to be capable of reducing the system chattering phenomenon as well as accelerating the approaching process. A nonlinear case numerical simulation test is employed to verify the superior performance of the ERL method over traditional power rate reaching strategy. Results obtained in Matlab/Simulink environment show that the SMC with ERL is more robust, prove excellent performance for the control unit by improving power quality and stability of wind turbine.
This paper presents a novel structure combining the port-controlled Hamiltonian (PCH) and Backstepping (BS) nonlinear control for the vector control of the six-phase induction motor (SPIM). In this new scheme, to improve the outer loop’s robustness, the BS technique using the integral tracking errors action is proposed in the speed and flux controllers design. The advantage of this proposed control law is not to increase the complexity of differential equation resolution due to being not increased system states numbers. To enhance more the performance of SPIM drives (SPIMD), port-controlled Hamiltonian (PCH) scheme is used in the inner current loop controllers. In this proposed PCH current controller, the stabilization of controller is achieved via system passivity. In that, the interconnection and damping matrix functions of PCH system are shaped so that the physical (Hamiltonian) system structure is preserved at the closed loop level and the closed loop energy function is equal to the difference between the physical energy of the system and the energy supplied by the controller. The proposed control design is based on combination PCH and BS techniques improve significantly performance and robustness. The proposed speed control scheme is validated by Matlab-Simulink software.
Robust second order sliding mode control for a quadrotor considering motor dy...ijctcm
In this paper, a robust second order sliding mode control (SMC) for controlling a quadrotor with uncertain
parameters presented based on high order sliding mode control (HOSMC). A controller based on the
HOSMC technique is designed for trajectory tracking of a quadrotor helicopter with considering motor
dynamics. The main subsystems of quadrotor (i.e. position and attitude) stabilized using HOSMC method.
The performance and effectiveness of the proposed controller are tested in a simulation study taking into
account external disturbances with consider to motor dynamics. Simulation results show that the proposed
controller eliminates the disturbance effect on the position and attitude subsystems efficiency that can be
used in real time applications.
Robust Second Order Sliding Mode Control for A Quadrotor Considering Motor Dy...ijctcm
In this paper, a robust second order sliding mode control (SMC) for controlling a quadrotor with uncertain parameters presented based on high order sliding mode control (HOSMC). A controller based on the HOSMC technique is designed for trajectory tracking of a quadrotor helicopter with considering motor dynamics. The main subsystems of quadrotor (i.e. position and attitude) stabilized using HOSMC method. The performance and effectiveness of the proposed controller are tested in a simulation study taking into account external disturbances with consider to motor dynamics. Simulation results show that the proposed controller eliminates the disturbance effect on the position and attitude subsystems efficiency that can be used in real time applications.
Robust Second Order Sliding Mode Control for A Quadrotor Considering Motor Dy...ijctcm
In this paper, a robust second order sliding mode control (SMC) for controlling a quadrotor with uncertain parameters presented based on high order sliding mode control (HOSMC). A controller based on the HOSMC technique is designed for trajectory tracking of a quadrotor helicopter with considering motor dynamics. The main subsystems of quadrotor (i.e. position and attitude) stabilized using HOSMC method. The performance and effectiveness of the proposed controller are tested in a simulation study taking into account external disturbances with consider to motor dynamics. Simulation results show that the proposed controller eliminates the disturbance effect on the position and attitude subsystems efficiency that can be used in real time applications.
Nonlinear control of WECS based on PMSG for optimal power extraction IJECEIAES
This paper proposes a robust control strategy for optimizing the maximum power captured in Wind Energy Conversion Systems (WECS) based on permanent magnet synchronous generators (PMSG), which is integrated into the grid. In order to achieve the maximum power point (MPPT) the machine side converter regulates the rotational speed of the PMSG to track the optimal speed. To evaluate the performance and effectiveness of the proposed controller, a comparative study between the IBC control and the vector control based on PI controller was carried out through computer simulation. This analysis consists of two case studies including stochastic variation in wind speed and step change in wind speed.
An Overview of Adaptive Approaches in Flight ControlIJERA Editor
Multi-mode switching between controllers corresponding to different modes of operation is needed in those cases when the transition from one mode to another results in substantial flight-critical variations in the aircraft dynamics. To address this problem, a general framework for multi-modal flight control is proposed. The framework is based on the Multiple Models, Switching and Tuning (MMST) methodology, combined with Model-Predictive Control (MPC), and the use of different robust mechanisms for switching between the multi-modal controllers. It was shown that many different switching control strategies can be naturally derived from the basic framework, which demonstrates the generality of the proposed approach.
Damping of Inter-Area Low Frequency Oscillation Using an Adaptive Wide-Area D...Power System Operation
This paper presents an adaptive wide-area damping controller (WADC) based on
generalized predictive control (GPC) and model identification for damping the inter-area low
frequency oscillations in large-scale inter-connected power system. A recursive least-squares algorithm
(RLSA) with a varying forgetting factor is applied to identify online the reduced-order linearlized
model which contains dominant inter-area low frequency oscillations. Based on this linearlized model,
the generalized predictive control scheme considering control output constraints is employed to obtain
the optimal control signal in each sampling interval. Case studies are undertaken on a two-area fourmachine
power system and the New England 10-machine 39-bus power system, respectively.
Simulation results show that the proposed adaptive WADC not only can damp the inter-area
oscillations effectively under a wide range of operation conditions and different disturbances, but also
has better robustness against to the time delay existing in the remote signals. The comparison studies
with the conventional lead-lag WADC are also provided.
Similar to A predictive sliding mode control for quadrotor’s tracking trajectory subject to wind gusts and uncertainties (20)
Bibliometric analysis highlighting the role of women in addressing climate ch...IJECEIAES
Fossil fuel consumption increased quickly, contributing to climate change
that is evident in unusual flooding and draughts, and global warming. Over
the past ten years, women's involvement in society has grown dramatically,
and they succeeded in playing a noticeable role in reducing climate change.
A bibliometric analysis of data from the last ten years has been carried out to
examine the role of women in addressing the climate change. The analysis's
findings discussed the relevant to the sustainable development goals (SDGs),
particularly SDG 7 and SDG 13. The results considered contributions made
by women in the various sectors while taking geographic dispersion into
account. The bibliometric analysis delves into topics including women's
leadership in environmental groups, their involvement in policymaking, their
contributions to sustainable development projects, and the influence of
gender diversity on attempts to mitigate climate change. This study's results
highlight how women have influenced policies and actions related to climate
change, point out areas of research deficiency and recommendations on how
to increase role of the women in addressing the climate change and
achieving sustainability. To achieve more successful results, this initiative
aims to highlight the significance of gender equality and encourage
inclusivity in climate change decision-making processes.
Voltage and frequency control of microgrid in presence of micro-turbine inter...IJECEIAES
The active and reactive load changes have a significant impact on voltage
and frequency. In this paper, in order to stabilize the microgrid (MG) against
load variations in islanding mode, the active and reactive power of all
distributed generators (DGs), including energy storage (battery), diesel
generator, and micro-turbine, are controlled. The micro-turbine generator is
connected to MG through a three-phase to three-phase matrix converter, and
the droop control method is applied for controlling the voltage and
frequency of MG. In addition, a method is introduced for voltage and
frequency control of micro-turbines in the transition state from gridconnected mode to islanding mode. A novel switching strategy of the matrix
converter is used for converting the high-frequency output voltage of the
micro-turbine to the grid-side frequency of the utility system. Moreover,
using the switching strategy, the low-order harmonics in the output current
and voltage are not produced, and consequently, the size of the output filter
would be reduced. In fact, the suggested control strategy is load-independent
and has no frequency conversion restrictions. The proposed approach for
voltage and frequency regulation demonstrates exceptional performance and
favorable response across various load alteration scenarios. The suggested
strategy is examined in several scenarios in the MG test systems, and the
simulation results are addressed.
Enhancing battery system identification: nonlinear autoregressive modeling fo...IJECEIAES
Precisely characterizing Li-ion batteries is essential for optimizing their
performance, enhancing safety, and prolonging their lifespan across various
applications, such as electric vehicles and renewable energy systems. This
article introduces an innovative nonlinear methodology for system
identification of a Li-ion battery, employing a nonlinear autoregressive with
exogenous inputs (NARX) model. The proposed approach integrates the
benefits of nonlinear modeling with the adaptability of the NARX structure,
facilitating a more comprehensive representation of the intricate
electrochemical processes within the battery. Experimental data collected
from a Li-ion battery operating under diverse scenarios are employed to
validate the effectiveness of the proposed methodology. The identified
NARX model exhibits superior accuracy in predicting the battery's behavior
compared to traditional linear models. This study underscores the
importance of accounting for nonlinearities in battery modeling, providing
insights into the intricate relationships between state-of-charge, voltage, and
current under dynamic conditions.
Smart grid deployment: from a bibliometric analysis to a surveyIJECEIAES
Smart grids are one of the last decades' innovations in electrical energy.
They bring relevant advantages compared to the traditional grid and
significant interest from the research community. Assessing the field's
evolution is essential to propose guidelines for facing new and future smart
grid challenges. In addition, knowing the main technologies involved in the
deployment of smart grids (SGs) is important to highlight possible
shortcomings that can be mitigated by developing new tools. This paper
contributes to the research trends mentioned above by focusing on two
objectives. First, a bibliometric analysis is presented to give an overview of
the current research level about smart grid deployment. Second, a survey of
the main technological approaches used for smart grid implementation and
their contributions are highlighted. To that effect, we searched the Web of
Science (WoS), and the Scopus databases. We obtained 5,663 documents
from WoS and 7,215 from Scopus on smart grid implementation or
deployment. With the extraction limitation in the Scopus database, 5,872 of
the 7,215 documents were extracted using a multi-step process. These two
datasets have been analyzed using a bibliometric tool called bibliometrix.
The main outputs are presented with some recommendations for future
research.
Use of analytical hierarchy process for selecting and prioritizing islanding ...IJECEIAES
One of the problems that are associated to power systems is islanding
condition, which must be rapidly and properly detected to prevent any
negative consequences on the system's protection, stability, and security.
This paper offers a thorough overview of several islanding detection
strategies, which are divided into two categories: classic approaches,
including local and remote approaches, and modern techniques, including
techniques based on signal processing and computational intelligence.
Additionally, each approach is compared and assessed based on several
factors, including implementation costs, non-detected zones, declining
power quality, and response times using the analytical hierarchy process
(AHP). The multi-criteria decision-making analysis shows that the overall
weight of passive methods (24.7%), active methods (7.8%), hybrid methods
(5.6%), remote methods (14.5%), signal processing-based methods (26.6%),
and computational intelligent-based methods (20.8%) based on the
comparison of all criteria together. Thus, it can be seen from the total weight
that hybrid approaches are the least suitable to be chosen, while signal
processing-based methods are the most appropriate islanding detection
method to be selected and implemented in power system with respect to the
aforementioned factors. Using Expert Choice software, the proposed
hierarchy model is studied and examined.
Enhancing of single-stage grid-connected photovoltaic system using fuzzy logi...IJECEIAES
The power generated by photovoltaic (PV) systems is influenced by
environmental factors. This variability hampers the control and utilization of
solar cells' peak output. In this study, a single-stage grid-connected PV
system is designed to enhance power quality. Our approach employs fuzzy
logic in the direct power control (DPC) of a three-phase voltage source
inverter (VSI), enabling seamless integration of the PV connected to the
grid. Additionally, a fuzzy logic-based maximum power point tracking
(MPPT) controller is adopted, which outperforms traditional methods like
incremental conductance (INC) in enhancing solar cell efficiency and
minimizing the response time. Moreover, the inverter's real-time active and
reactive power is directly managed to achieve a unity power factor (UPF).
The system's performance is assessed through MATLAB/Simulink
implementation, showing marked improvement over conventional methods,
particularly in steady-state and varying weather conditions. For solar
irradiances of 500 and 1,000 W/m2
, the results show that the proposed
method reduces the total harmonic distortion (THD) of the injected current
to the grid by approximately 46% and 38% compared to conventional
methods, respectively. Furthermore, we compare the simulation results with
IEEE standards to evaluate the system's grid compatibility.
Enhancing photovoltaic system maximum power point tracking with fuzzy logic-b...IJECEIAES
Photovoltaic systems have emerged as a promising energy resource that
caters to the future needs of society, owing to their renewable, inexhaustible,
and cost-free nature. The power output of these systems relies on solar cell
radiation and temperature. In order to mitigate the dependence on
atmospheric conditions and enhance power tracking, a conventional
approach has been improved by integrating various methods. To optimize
the generation of electricity from solar systems, the maximum power point
tracking (MPPT) technique is employed. To overcome limitations such as
steady-state voltage oscillations and improve transient response, two
traditional MPPT methods, namely fuzzy logic controller (FLC) and perturb
and observe (P&O), have been modified. This research paper aims to
simulate and validate the step size of the proposed modified P&O and FLC
techniques within the MPPT algorithm using MATLAB/Simulink for
efficient power tracking in photovoltaic systems.
Adaptive synchronous sliding control for a robot manipulator based on neural ...IJECEIAES
Robot manipulators have become important equipment in production lines, medical fields, and transportation. Improving the quality of trajectory tracking for
robot hands is always an attractive topic in the research community. This is a
challenging problem because robot manipulators are complex nonlinear systems
and are often subject to fluctuations in loads and external disturbances. This
article proposes an adaptive synchronous sliding control scheme to improve trajectory tracking performance for a robot manipulator. The proposed controller
ensures that the positions of the joints track the desired trajectory, synchronize
the errors, and significantly reduces chattering. First, the synchronous tracking
errors and synchronous sliding surfaces are presented. Second, the synchronous
tracking error dynamics are determined. Third, a robust adaptive control law is
designed,the unknown components of the model are estimated online by the neural network, and the parameters of the switching elements are selected by fuzzy
logic. The built algorithm ensures that the tracking and approximation errors
are ultimately uniformly bounded (UUB). Finally, the effectiveness of the constructed algorithm is demonstrated through simulation and experimental results.
Simulation and experimental results show that the proposed controller is effective with small synchronous tracking errors, and the chattering phenomenon is
significantly reduced.
Remote field-programmable gate array laboratory for signal acquisition and de...IJECEIAES
A remote laboratory utilizing field-programmable gate array (FPGA) technologies enhances students’ learning experience anywhere and anytime in embedded system design. Existing remote laboratories prioritize hardware access and visual feedback for observing board behavior after programming, neglecting comprehensive debugging tools to resolve errors that require internal signal acquisition. This paper proposes a novel remote embeddedsystem design approach targeting FPGA technologies that are fully interactive via a web-based platform. Our solution provides FPGA board access and debugging capabilities beyond the visual feedback provided by existing remote laboratories. We implemented a lab module that allows users to seamlessly incorporate into their FPGA design. The module minimizes hardware resource utilization while enabling the acquisition of a large number of data samples from the signal during the experiments by adaptively compressing the signal prior to data transmission. The results demonstrate an average compression ratio of 2.90 across three benchmark signals, indicating efficient signal acquisition and effective debugging and analysis. This method allows users to acquire more data samples than conventional methods. The proposed lab allows students to remotely test and debug their designs, bridging the gap between theory and practice in embedded system design.
Detecting and resolving feature envy through automated machine learning and m...IJECEIAES
Efficiently identifying and resolving code smells enhances software project quality. This paper presents a novel solution, utilizing automated machine learning (AutoML) techniques, to detect code smells and apply move method refactoring. By evaluating code metrics before and after refactoring, we assessed its impact on coupling, complexity, and cohesion. Key contributions of this research include a unique dataset for code smell classification and the development of models using AutoGluon for optimal performance. Furthermore, the study identifies the top 20 influential features in classifying feature envy, a well-known code smell, stemming from excessive reliance on external classes. We also explored how move method refactoring addresses feature envy, revealing reduced coupling and complexity, and improved cohesion, ultimately enhancing code quality. In summary, this research offers an empirical, data-driven approach, integrating AutoML and move method refactoring to optimize software project quality. Insights gained shed light on the benefits of refactoring on code quality and the significance of specific features in detecting feature envy. Future research can expand to explore additional refactoring techniques and a broader range of code metrics, advancing software engineering practices and standards.
Smart monitoring technique for solar cell systems using internet of things ba...IJECEIAES
Rapidly and remotely monitoring and receiving the solar cell systems status parameters, solar irradiance, temperature, and humidity, are critical issues in enhancement their efficiency. Hence, in the present article an improved smart prototype of internet of things (IoT) technique based on embedded system through NodeMCU ESP8266 (ESP-12E) was carried out experimentally. Three different regions at Egypt; Luxor, Cairo, and El-Beheira cities were chosen to study their solar irradiance profile, temperature, and humidity by the proposed IoT system. The monitoring data of solar irradiance, temperature, and humidity were live visualized directly by Ubidots through hypertext transfer protocol (HTTP) protocol. The measured solar power radiation in Luxor, Cairo, and El-Beheira ranged between 216-1000, 245-958, and 187-692 W/m 2 respectively during the solar day. The accuracy and rapidity of obtaining monitoring results using the proposed IoT system made it a strong candidate for application in monitoring solar cell systems. On the other hand, the obtained solar power radiation results of the three considered regions strongly candidate Luxor and Cairo as suitable places to build up a solar cells system station rather than El-Beheira.
An efficient security framework for intrusion detection and prevention in int...IJECEIAES
Over the past few years, the internet of things (IoT) has advanced to connect billions of smart devices to improve quality of life. However, anomalies or malicious intrusions pose several security loopholes, leading to performance degradation and threat to data security in IoT operations. Thereby, IoT security systems must keep an eye on and restrict unwanted events from occurring in the IoT network. Recently, various technical solutions based on machine learning (ML) models have been derived towards identifying and restricting unwanted events in IoT. However, most ML-based approaches are prone to miss-classification due to inappropriate feature selection. Additionally, most ML approaches applied to intrusion detection and prevention consider supervised learning, which requires a large amount of labeled data to be trained. Consequently, such complex datasets are impossible to source in a large network like IoT. To address this problem, this proposed study introduces an efficient learning mechanism to strengthen the IoT security aspects. The proposed algorithm incorporates supervised and unsupervised approaches to improve the learning models for intrusion detection and mitigation. Compared with the related works, the experimental outcome shows that the model performs well in a benchmark dataset. It accomplishes an improved detection accuracy of approximately 99.21%.
Developing a smart system for infant incubators using the internet of things ...IJECEIAES
This research is developing an incubator system that integrates the internet of things and artificial intelligence to improve care for premature babies. The system workflow starts with sensors that collect data from the incubator. Then, the data is sent in real-time to the internet of things (IoT) broker eclipse mosquito using the message queue telemetry transport (MQTT) protocol version 5.0. After that, the data is stored in a database for analysis using the long short-term memory network (LSTM) method and displayed in a web application using an application programming interface (API) service. Furthermore, the experimental results produce as many as 2,880 rows of data stored in the database. The correlation coefficient between the target attribute and other attributes ranges from 0.23 to 0.48. Next, several experiments were conducted to evaluate the model-predicted value on the test data. The best results are obtained using a two-layer LSTM configuration model, each with 60 neurons and a lookback setting 6. This model produces an R 2 value of 0.934, with a root mean square error (RMSE) value of 0.015 and a mean absolute error (MAE) of 0.008. In addition, the R 2 value was also evaluated for each attribute used as input, with a result of values between 0.590 and 0.845.
A review on internet of things-based stingless bee's honey production with im...IJECEIAES
Honey is produced exclusively by honeybees and stingless bees which both are well adapted to tropical and subtropical regions such as Malaysia. Stingless bees are known for producing small amounts of honey and are known for having a unique flavor profile. Problem identified that many stingless bees collapsed due to weather, temperature and environment. It is critical to understand the relationship between the production of stingless bee honey and environmental conditions to improve honey production. Thus, this paper presents a review on stingless bee's honey production and prediction modeling. About 54 previous research has been analyzed and compared in identifying the research gaps. A framework on modeling the prediction of stingless bee honey is derived. The result presents the comparison and analysis on the internet of things (IoT) monitoring systems, honey production estimation, convolution neural networks (CNNs), and automatic identification methods on bee species. It is identified based on image detection method the top best three efficiency presents CNN is at 98.67%, densely connected convolutional networks with YOLO v3 is 97.7%, and DenseNet201 convolutional networks 99.81%. This study is significant to assist the researcher in developing a model for predicting stingless honey produced by bee's output, which is important for a stable economy and food security.
A trust based secure access control using authentication mechanism for intero...IJECEIAES
The internet of things (IoT) is a revolutionary innovation in many aspects of our society including interactions, financial activity, and global security such as the military and battlefield internet. Due to the limited energy and processing capacity of network devices, security, energy consumption, compatibility, and device heterogeneity are the long-term IoT problems. As a result, energy and security are critical for data transmission across edge and IoT networks. Existing IoT interoperability techniques need more computation time, have unreliable authentication mechanisms that break easily, lose data easily, and have low confidentiality. In this paper, a key agreement protocol-based authentication mechanism for IoT devices is offered as a solution to this issue. This system makes use of information exchange, which must be secured to prevent access by unauthorized users. Using a compact contiki/cooja simulator, the performance and design of the suggested framework are validated. The simulation findings are evaluated based on detection of malicious nodes after 60 minutes of simulation. The suggested trust method, which is based on privacy access control, reduced packet loss ratio to 0.32%, consumed 0.39% power, and had the greatest average residual energy of 0.99 mJoules at 10 nodes.
Fuzzy linear programming with the intuitionistic polygonal fuzzy numbersIJECEIAES
In real world applications, data are subject to ambiguity due to several factors; fuzzy sets and fuzzy numbers propose a great tool to model such ambiguity. In case of hesitation, the complement of a membership value in fuzzy numbers can be different from the non-membership value, in which case we can model using intuitionistic fuzzy numbers as they provide flexibility by defining both a membership and a non-membership functions. In this article, we consider the intuitionistic fuzzy linear programming problem with intuitionistic polygonal fuzzy numbers, which is a generalization of the previous polygonal fuzzy numbers found in the literature. We present a modification of the simplex method that can be used to solve any general intuitionistic fuzzy linear programming problem after approximating the problem by an intuitionistic polygonal fuzzy number with n edges. This method is given in a simple tableau formulation, and then applied on numerical examples for clarity.
The performance of artificial intelligence in prostate magnetic resonance im...IJECEIAES
Prostate cancer is the predominant form of cancer observed in men worldwide. The application of magnetic resonance imaging (MRI) as a guidance tool for conducting biopsies has been established as a reliable and well-established approach in the diagnosis of prostate cancer. The diagnostic performance of MRI-guided prostate cancer diagnosis exhibits significant heterogeneity due to the intricate and multi-step nature of the diagnostic pathway. The development of artificial intelligence (AI) models, specifically through the utilization of machine learning techniques such as deep learning, is assuming an increasingly significant role in the field of radiology. In the realm of prostate MRI, a considerable body of literature has been dedicated to the development of various AI algorithms. These algorithms have been specifically designed for tasks such as prostate segmentation, lesion identification, and classification. The overarching objective of these endeavors is to enhance diagnostic performance and foster greater agreement among different observers within MRI scans for the prostate. This review article aims to provide a concise overview of the application of AI in the field of radiology, with a specific focus on its utilization in prostate MRI.
Seizure stage detection of epileptic seizure using convolutional neural networksIJECEIAES
According to the World Health Organization (WHO), seventy million individuals worldwide suffer from epilepsy, a neurological disorder. While electroencephalography (EEG) is crucial for diagnosing epilepsy and monitoring the brain activity of epilepsy patients, it requires a specialist to examine all EEG recordings to find epileptic behavior. This procedure needs an experienced doctor, and a precise epilepsy diagnosis is crucial for appropriate treatment. To identify epileptic seizures, this study employed a convolutional neural network (CNN) based on raw scalp EEG signals to discriminate between preictal, ictal, postictal, and interictal segments. The possibility of these characteristics is explored by examining how well timedomain signals work in the detection of epileptic signals using intracranial Freiburg Hospital (FH), scalp Children's Hospital Boston-Massachusetts Institute of Technology (CHB-MIT) databases, and Temple University Hospital (TUH) EEG. To test the viability of this approach, two types of experiments were carried out. Firstly, binary class classification (preictal, ictal, postictal each versus interictal) and four-class classification (interictal versus preictal versus ictal versus postictal). The average accuracy for stage detection using CHB-MIT database was 84.4%, while the Freiburg database's time-domain signals had an accuracy of 79.7% and the highest accuracy of 94.02% for classification in the TUH EEG database when comparing interictal stage to preictal stage.
Analysis of driving style using self-organizing maps to analyze driver behaviorIJECEIAES
Modern life is strongly associated with the use of cars, but the increase in acceleration speeds and their maneuverability leads to a dangerous driving style for some drivers. In these conditions, the development of a method that allows you to track the behavior of the driver is relevant. The article provides an overview of existing methods and models for assessing the functioning of motor vehicles and driver behavior. Based on this, a combined algorithm for recognizing driving style is proposed. To do this, a set of input data was formed, including 20 descriptive features: About the environment, the driver's behavior and the characteristics of the functioning of the car, collected using OBD II. The generated data set is sent to the Kohonen network, where clustering is performed according to driving style and degree of danger. Getting the driving characteristics into a particular cluster allows you to switch to the private indicators of an individual driver and considering individual driving characteristics. The application of the method allows you to identify potentially dangerous driving styles that can prevent accidents.
Hyperspectral object classification using hybrid spectral-spatial fusion and ...IJECEIAES
Because of its spectral-spatial and temporal resolution of greater areas, hyperspectral imaging (HSI) has found widespread application in the field of object classification. The HSI is typically used to accurately determine an object's physical characteristics as well as to locate related objects with appropriate spectral fingerprints. As a result, the HSI has been extensively applied to object identification in several fields, including surveillance, agricultural monitoring, environmental research, and precision agriculture. However, because of their enormous size, objects require a lot of time to classify; for this reason, both spectral and spatial feature fusion have been completed. The existing classification strategy leads to increased misclassification, and the feature fusion method is unable to preserve semantic object inherent features; This study addresses the research difficulties by introducing a hybrid spectral-spatial fusion (HSSF) technique to minimize feature size while maintaining object intrinsic qualities; Lastly, a soft-margins kernel is proposed for multi-layer deep support vector machine (MLDSVM) to reduce misclassification. The standard Indian pines dataset is used for the experiment, and the outcome demonstrates that the HSSF-MLDSVM model performs substantially better in terms of accuracy and Kappa coefficient.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
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A predictive sliding mode control for quadrotor’s tracking trajectory subject to wind gusts and uncertainties
1. International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 5, October 2022, pp. 4861∼4875
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i5.pp4861-4875 ❒ 4861
A predictive sliding mode control for quadrotor’s tracking
trajectory subject to wind gusts and uncertainties
Dounia Meradi1
, Zoubir Abdeslem Benselama1
, Ramdane Hedjar2
1Department of Electronics, Saad Dahlab University, Blida, Algeria
2Department of Computer Engineering, King Saud University, Riyadh, Saudi Arabia
Article Info
Article history:
Received Jul 27, 2021
Revised May 28, 2022
Accepted Jun 12, 2022
Keywords:
Discrete-time sliding mode
control
Non-linear model predictive
control
Predictive sliding mode
control
Quadrotor
Wind gusts
ABSTRACT
In this paper, a predictive sliding mode control (PSMC) strategy for the quadrotors
tracking trajectory problem is proposed. This strategy aims to combine the advan-
tages of sliding mode control (SMC) and non-linear model predictive control (NMPC)
to improve the tracking control performance for quadrotors in terms of optimality,
inputs/states constraints satisfaction, and strong robustness against disturbances. A
comparative study of three popular controllers: the SMC, NMPC, and the integral
backstepping control (IBC) is performed with different criteria. Accordingly, IBC and
SMC show less computational time and strong robustness, while NMPC has minimum
control effort. The discrete Dryden turbulence model is used as a benchmark model
to represent the wind effect on the trajectory tracking accuracy. The effectiveness of
the proposed method PSMC has been proven and compared with discrete-time sliding
mode control (DSMC) and NMPC in several scenarios. Simulation results show that
under both wind turbulence and time-variant uncertainties, the PSMC outperforms the
other controllers by providing simultaneously disturbance rejection and guarantee that
the control inputs are within bounded constraints.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Dounia Meradi
Department of Electronics, Signal Processing and Image Laboratory, Saad Dahlab University
Blida 1, BP 270, Route de soumaa, Ouled Yaı̈ch, Blida, Algeria
Email: dounia.meradi@g.enp.edu.dz
1. INTRODUCTION
With the technological advancements in the field of unmanned aerial vehicles (UAVs), the quadrotor
has aroused particular interest in vertical take-off and landing vehicles (VTOL) and has become a popular re-
search platform for testing numerous control techniques. Unlike the conventional helicopters and due to its
small size, payload capability, simple mechanical structure, and smooth maneuverability, the quadrotor is al-
lowed to fly in indoor or outdoor environments, as well as near obstacles. Because of the numerous physicals
phenomena that affect the quadrotor dynamics such as the aerodynamic effect, the gravity center, and the gyro-
scopes effects. Thus, the quadrotor can be considered among the most complex flying systems. Consequently,
the exact modeling of the quadrotor is required in order to design a suitable flight controller. There are various
ways of expressing the motion dynamics, which mainly depend on the rotation parametrization. The most
common attitude parametrizations are: Euler angles, axis-angle, rotation matrix [1], Rodrigues parameters [2] ,
and unit quaternion [3]. Euler angles are widely used to present the quadrotor’s orientation, it is simple, unique,
and can be easily understood. It suffers however from gimbal lock phenomena.
The proportional integral derivative (PID), linear quadratic regulator (LQR), H∞ [4], and gain schedul-
Journal homepage: http://ijece.iaescore.com
2. 4862 ❒ ISSN: 2088-8708
ing [5] are the common linear controllers used to command the quad-rotors due to their simplicity. However,
they can guarantee the closed-loop stability only around an equilibrium point. Besides, they usually fail to track
aggressive maneuvers. Several non-linear controls have been developed to conquer some of the shortcomings
and limitations of linear control. Among them, fuzzy logic controller [6] , adaptive sliding mode control (SMC)
[7], [8], and neural networks (NN) [9], [10].
The SMC has been significantly used to control the quad-rotor. Because of its attractive finite-time
convergence characteristics and robustness to parametric uncertainties and perturbations. Since the SMC suf-
fers from the chattering phenomena caused by the reaching law and has high control effort, many researchers
have been working on those troubles. One of the proposed solutions is the integral sliding mode control [11].
The integral action added to the sliding manifold has the ability to eliminate the reaching phase and reduce
the chattering on the control inputs. Ahmad et al. [12] applied an improved integral power rate exponential
reaching law (IIPRERL) sliding mode control strategy to deal with the unwanted chattering problem, stability,
and the oscillations in the quadrotor responses in the presence of matched disturbances. The simulation results
of IIPRERL-SMC have shown no chattering on the control inputs compared to SMC. In discrete-time, the
authors in [13] have proposed the discrete-time sliding mode control (DSMC) for quadrotor where the linear
extrapolation method has been employed to obtain the discrete-time model of the quadrotor.
In the realm of optimal control for quadrotor, both of the linear and non-linear model predictive control
(MPC) has been widely used, showing a good tracking ability, handling to input/state constraints [14] and
avoiding obstacles [15]. In [16], a nonlinear and linear MPC have been presented for a quadrotor to track
different references trajectories where the non-linear model predictive control (NMPC) has been made by using
a state-dependent coefficient representation. Moreover, stability analysis of Unconstrained/constrained for both
controllers has been provided. The simulation results in the case of with or without disturbances showed that
the NMPC outperformed the linear MPC. Since the MPC depends explicitly on accurate model-plant as well
as that the quadrotor is a strongly constrained coupled non-linear system which is usually prone to parameters
variation on mass and inertia due to payload. For that, any mismatched parameters or disturbances can decrease
the stability of the system when using the conventional MPC approaches.
Many researchers have been combined the SMC and MPC. In [17], the surface parameters of sliding
mode control have been determined and updated using the non-linear model predictive control. In [18], the
sliding mode predictive control has been used to control the boiler-turbine system deal with uncertainties and
system constraints. The adopted control strategy was based on the dual-mode law that is constructed of two-
part: the discrete sliding mode control law where the sliding surface was in the terminal sliding region, and
the receding horizon optimization law where the sliding surface was out from the terminal sliding region. A
comparative study between DSMC with predictive sliding function (PSF) and predictive sliding mode control is
done in [19]. Those strategies are simulated to the linearised isothermal Van de Vussen systems. The simulation
results have shown that both of the combination controllers have outperformed the NMPC and SMC. As well
as, the DSMC with PSF has more ability to eliminate the chattering compared to the PSMC. While this latter
has strong robustness to disturbances.
Upon to the aforementioned discussion and motivated by those works [18], [20], [21], the main contri-
bution of this paper can be encapsulated in the following: i) a discrete sliding mode control is proposed to con-
trol the quadrotor with the calculation of the desired orientation, ii) design an NMPC with the multiple-shooting
concept in order to accelerate and improve the convergence of the optimization control problem (OCP), and
iii) an insensitivity to external disturbances, a robustness to parametric uncertainties, a state/inputs constraints
satisfaction and optimal control are undertaking and ensuring simultaneously by the proposed PSMC.
The roadmap for the remainder of the paper has been organized in the following way: subsection
2.1 develops the quadrotor’s dynamic model and its discrete-time formulation. Subection 2.2 seeks to design
the control law strategy of DSMC, then NMPC, and in the end the PSMC. Simulation results with different
scenarios are shown in section 3 and finally, the conclusion is in section 4.
2. METHOD
2.1. Quadrotor’s model dynamic
The quadrotor is a VTOL vehicle able to perform quasi-stationary flights. It consists of four fixed-
pitch blades coupled with DC brush-less motors fixed to the end of a rigid cross-shaped body as shown in
Figure 1. Indeed, each propeller is rotating at a certain angular speed ωi generates a force Fi and a moment Mi
Int J Elec & Comp Eng, Vol. 12, No. 5, October 2022: 4861–4875
3. Int J Elec & Comp Eng ISSN: 2088-8708 ❒ 4863
that are given by:
Fi = bω2
i , Mi = dω2
i
with i = 1 : 4, and b, d are the thrust and drag coefficients, respectively.
{B}
{I}
M1 M2
M3
M4
F3
F4
F2
F1
bz
bx by
ex
ez
ey
Figure 1. The coordinate system frames
To describe the mathematical model of the quadrotor, we define two reference coordinate frames rep-
resented in Figure 1. The inertial frame {I} is defined by {ex, ey, ez}, and the body-fixed frame {B} attached
to the quadrotor’s gravity center and is defined by {bx, by, bz}. To describe the quadrotor’s rotation, we use
Z-Y-X convention of Euler angles {ϕ, θ, ψ}. Therefore, the attitude of the quadrotor is represented by the rota-
tion matrix R which allows the passage from frame {B} to frame {I} and is defined [22]:
R =
cθcψ −cϕsψ + sϕsθcψ sϕsψ + cϕsθcψ
cθsψ cϕcψ + sϕsθsψ −sϕcψ + cϕsθsψ
−sθ sϕcθ cϕcθ
(1)
where cx (resp. sx) represents the simplified notation of cos(x) (resp.sin(x)).
By applying the fundamental principle of dynamics, we obtain the equations representing the dynamic
behaviour of the quadrotor:
(
mr̈ = RTez + mgez + Kftv + Fdes
JΩ̇ = −Ω×
JΩ + τ + τdes
(2)
where r = [x, y, z]T
represents the position of the quadrotor, Ω = [Ωx, Ωy, Ωz] is the body angular velocity, m,
I = diag(Ix, Iy, Iz) are the total mass of the quadrotor and moments of inertia respectively, T =
P4
i=1 bωi,
τ = [τx, τy, τz]T
represent the thrust force expressed in B-frame and the aerodynamic moments generated
by the propellers respectively. The terms Fdes,τdes ∈ R3
represent the external disturbances applied on the
quadrotor. Finally, The terms Kft = diag(Kftx
, Kfty
, Kftz
) denote the translation drag coefficients and (x)×
represents the skew-matrix of the vector x.
A predictive sliding mode control for quadrotor’s tracking trajectory subject ... (Dounia Meradi)
4. 4864 ❒ ISSN: 2088-8708
The relation between the derivative of Euler angles and the body angular velocities is expressed as (3):
Ωx
Ωy
Ωz
=
1 0 −sθ
0 cθ sϕcθ
0 sθ cϕcθ
×
ϕ̇
θ̇
ψ̇
(3)
The relation between the propellers angular speeds and the generated aerodynamic forces and the moments due
to the propellers is expressed as (4):
u1
u2
u3
u4
=
b b b b
0 −lb 0 lb
−lb 0 lb 0
d −d d −d
×
ω2
1
ω2
2
ω2
3
ω2
4
(4)
From (2), the quadrotor is an under-actuated system with four inputs {T, τx, τy, τz} and six outputs {x, y, z, ϕ, θ,
ψ}. To put the quadrotor equations in state-space form, the state vector of the system x ∈ R12
is chosen as (5):
x =
x, ẋ, y, ẏ, z, ż, ϕ, ϕ̇, θ, θ̇, ψ, ψ̇
T
=
x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12
T
(5)
The physical limitations of the quadrotor’s motors speeds are bounded between minimum angular velocity ω
and maximum angular velocity ω̄. The maximum and minimum of thrust force and torques values providing
by these limitations are:
4bω2
⩽ u1 ⩽ 4bω̄2
bl(ω2
− ω̄2
) ⩽ u2 ⩽ bl(ω̄2
− ω2
)
bl(ω2
− ω̄2
) ⩽ u3 ⩽ bl(ω̄2
− ω2
)
2d(ω2
− ω̄2
) ⩽ u4 ⩽ 2d(ω̄2
− ω2
)
(6)
where [u1, u2, u3, u4]T
= [T, τx, τy, τz]T
for simple notification.
2.1.1. Discrete time quadrotor’s model
According to (2) and (5) the dynamic model can be written in compact form:
ẋ(t) :=
(
x2i−1(t) = x2i(t), i = 1, 2, ..., 6
x2i(t) = fi (x(t)) + ∆fi(x(t)) + (gi (x(t)) + ∆gi(x(t))) u(t) + wi(t)
(7)
Using forward Euler discretization, we obtain the discrete system of (7) as in (8):
x[k] :=
(
x2i−1[k + 1] = x2i−1[k] + hx2i[k] i = 1, 2, ..., 6
x2i[k + 1] = x2i[k] + h (fi (x[k]) + ∆fi(x[k]) + (gi (x[k]) + ∆gi(x[k])) u[k]) + wi[k]
(8)
where h is sampling time, k represents the k-th sampling time, fi (x[k]) and gi (x[k]) are given in Appendix.
∆fi(.) and ∆gi(.) denote the bounded unknown parametric uncertainties, wi[k] is the bounded external distur-
bance, where: ∆fi(.) ⩽ ∆fimax ,∆gi(.) ⩽ ∆gimax and wi[k] ⩽ wimax .
The discrete dynamic system in (8) can be rewritten as (9):
(
x2i−1[k + 1] = x2i−1[k] + hx2i[k], i = 1, 2, ..., 6
x2i[k + 1] = x2i[k] + h (fi (x[k]) + gi (x[k]) u[k]) + d[k]
(9)
where d[k] = h(∆fi(x[k])+∆gi(x[k])u[k])+wi[k]. Let u[k] = [u1[k], u2[k], u3[k], u4[k]]
T
being the control
input. The main objective is to synthesize a non-linear control laws for a quad-rotor in order to track the desired
trajectory {xd, yd, zd, ψd}. In the next section, we assume the case without disturbances, i.e d[k] = 0 and it is
unknown to the controllers.
Int J Elec Comp Eng, Vol. 12, No. 5, October 2022: 4861–4875
5. Int J Elec Comp Eng ISSN: 2088-8708 ❒ 4865
2.2. Control design
In this subsection, we synthesis and describe the different non-linear control laws that have been
used in this paper for the trajectory tracking of the quad-rotor. First, we start the synthesis of the discrete
sliding mode control DSMC. Then, the non-linear model predictive control principle is presented. Finally, the
combined sliding mode with predictive control PSCM is designed.
2.2.1. Design of discrete sliding mode control approach
The objective of the SMC law is to constrain the system state trajectory (9) to be reached and then to
maintain it on the sliding surface even in the presence of uncertainties in the system. Let a second-order Slotine
surface [23] is chosen as (10):
si[k] = e2i[k] + λie2i−1[k], i = 1, 2, ..., 6 (10)
where the λi ∈ R+
are the constants of tuning, e[k] are the tracking error which is the difference between the
actual state x[k] and the desired one r[k] and is defined:
e[k] =
(
e2i−1[k] = r2i−1[k] − x2i−1[k]
e2i[k] = r2i[k] − x2i[k]
(11)
where r[k] is the discrete-time of the desired trajectory r(t) =
h
xd, ẋd, yd, ẏd, zd, żd, ϕd, ϕ̇d, θd, θ̇d, ψd, ψ̇d
i
.
{xd, yd, zd, ψd} and its derivatives are provided from the trajectory generator, while {ϕd, θd} and its derivative
can be deduced from the position controller.
The purpose of the control is to force the system to evolve on the sliding surface and prevent it from
getting out of it,
S = {e[k] | si (e[k]) = 0, i = 1, 2, ..., 6} (12)
We introduce the virtual command vi[k] in such a way that x2i[k + 1] = vi[k], which gives us:
vi[k] = x2i[k] + h (fi(x[k]) + gi(x[k])u[k]) (13)
The dynamic of the surface (10) is:
si[k + 1] = si[k] + e2i[k + 1] + λie2i−1[k + 1]
= si[k] + (r2i[k + 1] − vi[k]) + λie2i−1[k + 1]
(14)
The Gao’s reaching dynamics of the sliding surface are [24]:
si[k + 1] = (1 − hσi) si[k] − hµisign (si[k]) , i = 1, 2, ..., 6 (15)
where σi and µi are tuning parameters and satisfying 0 ⩽ hσi 1 and µi 0.
By equating (15) and (14), the following virtual commands signal are obtained:
vi[k] = σisi[k] + µisign (si[k]) + λie2i−1[k + 1] + r2i[k + 1],
i = 1, 2, ..., 6
(16)
By applying the properties of the rotation matrix [25], we determine the real commands:
u1[k] = m
q
(V1[k])
2
+ (V2[k])
2
+ (V3[k])
2
u2[k] =
V4[k]
g4([xk])
, u3[k] =
V5[k]
g5([xk])
, u4[k] =
V6[k]
g6([xk])
(17)
A predictive sliding mode control for quadrotor’s tracking trajectory subject ... (Dounia Meradi)
6. 4866 ❒ ISSN: 2088-8708
where Vi[k] = vi[k] − fi(x[k]), i = 1, 2, ..., 6.
The desired roll and pitch angles ϕd and θd are generated from:
m (V1[k]cψ + V2[k]sψ) = sθu1[k]
m (V1[k]sψ + V2[k]cψ) = sϕcθu1[k]
mV3[k] = cϕcθu1[k]
(18)
We draw from (18):
ϕd = arctan
V1[k]sψd
− V2[k]cψd
V3[k]
θd = arctan
V1[k]cψd
+ V2[k]sψd
p
(V1[k]sψd
− V2[k]cψd
)2 + V3[k]2
! (19)
To alleviate the chattering problem caused by the discontinuous sign function. We replace this latter by a
pseudo-sign function which is defined:
psign(x, η) =
x
|x| + η
(20)
where 0 η 1 has been chosen equal to 0.05.
2.2.2. Design of non-linear model predictive control NMPC
The predictive control problem consists of determining the control vector u that minimizes the selected
cost function while ensuring the satisfaction of the constraints. It can be summarized as the following steps:
− At each sampling time k, the future system outputs are predicted over a prediction horizon N using the
preceding inputs and outputs. These predictions are noted x[k + j|k], j = 0, 1, . . . , N to indicate the
value of the output at instant k + j, calculated at the instant k
− The sequence of future commands u[k + j|k], j = 0, 1, . . . , N − 1 is calculated by optimizing a cer-
tain determined criterion so that the predicted output x[k + j|k] is as close as possible to the reference
trajectory r[k + j|k], j = 1, . . . N,while minimizing the control effort
− Finally, Only the first component u[k|k] of the optimal control sequence u[k|k + j] is applied to the
system. At the next sampling time k +1, the resolution begins again with step one by taking into account
the new updated measurements of the system x[k + 1] and a new control sequence u[k + 1|k + 1 +
j], j = 0, . . . , N −1 is determined. The control sequence is improved at each sampling period since new
measurements could be taken and consequently the vector of the control signal u[k + 1|k + 1 + j], j =
0, 1, .., N − 1 will be in principle different from u[k + j|k], j = 0, 1, .., N.
Based on the above definition, the discrete-time NMPC formulation with multiple shooting is:
min
u[k+j|k],x[k+j|k]
N−1
X
k=0
Lr (x[k], u[k], r[k]) + Lt (x[N]) (21a)
s.t : x[0] − x0 = 0 (21b)
x[k + 1] − x[k] − fRK4(x[k], u[k]) = 0, j = 0, . . . , N (21c)
x[k] ∈ X, k = 0, . . . , N (21d)
u[k] ∈ U, k = 0, . . . , N − 1 (21e)
where (21d) and (21e) are respectively, the sets of constraint on states (map margins and Euler-angles limita-
tions −π
2 ≺ ϕ ≺ π
2 ,−π
2 ≺ θ ≺ π
2 , −π ≺ ψ ≺ π) and on inputs that were defined in (6). x0 is the current state.
The running cost function denotes Lr (x[k], u[k], r[j]) and is equal to:
Int J Elec Comp Eng, Vol. 12, No. 5, October 2022: 4861–4875
7. Int J Elec Comp Eng ISSN: 2088-8708 ❒ 4867
Lr (x[k], u[k], r[k]) = ∥r[k] − x[k]∥
2
Q + ∥uref [k] − u[k]∥
2
R (22)
and Lt (x[N]) being the terminal cost function and is equal to: L (x[N]) = ∥r[N] − x[N]∥
2
H. Where Q, H
∈ R12×12
, R ∈ R4×4
are a positive-definite tuning matrix.
The control input reference uref is taken to obtain better tracking performance based on desired
trajectory acceleration and defined as: uref =
h
m
p
a2
1 + a2
2 + (a3 + g)2, 0, 0, 0
iT
. Where a1, a2 and a3 are
the discrete time of desired trajectory acceleration {ẍd, ÿd, z̈d}.
Herein (21c), the concept of direct multiple shooting [26] is defined as an equality constraint, where
fRK4(.) is the Runge Kutta 4th
integration and is defined as (23):
k1 = f(x[k], u[k])
k2 = f(x[k] +
h
2
k1, u[k])
k3 = f(x[k] +
h
2
k2, u[k])
k4 = f(x[k] + hk3, u[k])
fRK4(x[k], u[k]) = 1/6 (k1 + 2k2 + 2k3 + k4)
(23)
and, f(x[k], u[k]) = [x2i , fi(x[k]) + gi(x[k])u[k]]
⊤
, i = 1, . . . , 6.
2.2.3. Non-linear predictive sliding mode control
The non-linear predictive sliding mode control (PSMC) control law is used in this work for the quad-
rotor trajectory tracking problems. This hybrid approach is based on the NMPC and the DSMC in order to
provide the best trade-off between minimum effort energy control, tracking trajectory, and rejection of distur-
bance. The main objective of PSMC is to generate the optimum control input where the PSMC concept is
illustrated in Figure 2. Firstly, at each sampling time k, the DSMC part calculates the reference sliding surfaces
sref [k + j|k], j = 0, . . . , N over the horizon N, invoking the (10) and (15) yields:
sref [k] = s[k]
sref [k + 1] = (1 − hσ)sref [k] − hµsref [k]
sref [k + N] = (1 − hσ)sref [k + N − 1] − hµsref [k + N − 1]
(24)
Then, the NMPC computes the control sequence u[k|k + j] using the plant-model. The computations optimize
the tracking of the predicted sliding functions spred[k+j|k], j = 0, . . . , N while minimizing the control effort.
In the end, the first element of the calculated control sequence is applied to the quadrotor model Figure 2.
Optimizer
Nonlinear Model Predictive Control
Model Constraints
Cost
Function
Discrete Sliding Mode
Control (DSMC)
Eq(14),(15)
Desired
Trajectory
Predictive Sliding Mode Control
stochastic disturbance (Wind) disturbance
on inputs δu
∆fi(x[k]) ∆gi(x[k])
u[k + j|k] spred[k + j|k]
x[k + j|k]
r2i−1[k]
r2i[k]
sref (k + j |k)
=
sref (k + 1)
sref (k + 2)
.
.
.
sref (k + N)
u[k|k]
x[k + 1]
+ +
r[k]
Figure 2. Block diagram of predictive sliding mode control strategy
A predictive sliding mode control for quadrotor’s tracking trajectory subject ... (Dounia Meradi)
8. 4868 ❒ ISSN: 2088-8708
The mathematical formulation of the non-linear PSMC can be written:
min
u[k+j|k],x[k+j|k],s[k+j|k]
N−1
X
k=0
Jr (x, s, u, r) + Jt(x[N], s[N]) (25a)
s.t :x[0] − x0 = 0, (25b)
x[k + 1] = x[k] + hf(x[k], u[k]) (25c)
spredi
[k + 1] = spredi
[k] + e2i[k + 1] + λie2i−1[k + 1] (25d)
x[k] ∈ X, k = 0, . . . , N (25e)
u[k] ∈ U, k = 0, . . . , N − 1 (25f)
spred[k] ∈ S, k = 0, . . . , N (25g)
where Jr(.) is the running cost function of PSMC and is defined as (26):
Jr (x, s, u, r) = ∥uref [k] − u[k]∥
2
R + ∥spred[k] − sref [k]∥2
λ (26)
and, Jt(.) = ∥spred[N] − sref [N]∥2
η is the terminal cost function, λ, η ∈ R6×6
are a positive-definite tuning
matrix which penalize the tracking surface functions. X, U are the same specified in 2.2.2, S is the set of
terminal sliding region that is defined as [21], [24]:
S =
6
[
i=1
Si, Si = {x | |si(x)| ≤ ∆i, x ∈ X, u ∈ U, ∆i = hµi} (27)
3. SIMULATION RESULTS AND DISCUSSION
Simulation results using MATLAB/Simulink are developed in this section to corroborate the proposed
controllers’ effectiveness. The quadrotor dynamic model from (2) is used to perform all simulations. The
sampling period of the simulation is set to h = 10 ms, and the initial conditions are set to zero except in the
case 3.1. The quadrotor and controllers parameters are given in Tables 1 and 2, respectively. The OCP in (21)
and (25) are transformed into a nonlinear programming problem (NLP) and simulated using CasADi toolkit
[27]. Furthermore, an interior point optimizer (IPOPT) is used to solve the NLP, using up to 2,000 iterations,
a tolerance of 10−6
, and the horizon prediction N set to 15. In addition, the constraints on inputs, states and
sliding mode band are tacking:
X :=
x1 ∈ ]−∞, +∞[
.
.
.
x6 ∈ ]−∞, +∞[
x7 ∈
h
−
π
2
,
π
2
i
x8 ∈ ]−∞, +∞[
x9 ∈
h
−
π
2
,
π
2
i
x10 ∈ ]−∞, +∞[
x11 ∈ [−π, π]
x12 ∈ ]−∞, +∞[
,
U :=
u1 ∈ [0, 9.3585]
u2 ∈ [−0.5849, 0.5849]
u3 ∈ [−0.5849, 0.5849]
u4 ∈ [−0.0507, 0.0507]
,
S :=
|si[k + 1]|
hµi
1 − hσi
i = 1, . . . , 6.
(28)
Int J Elec Comp Eng, Vol. 12, No. 5, October 2022: 4861–4875
9. Int J Elec Comp Eng ISSN: 2088-8708 ❒ 4869
With the aim of carrying out a comparative study between the SMC, integral backstepping control
(IBC), and NMPC controllers, the following performance indexes are taken into account:
− The control signal energy (CSE) and the control effort energy (CEE):
CSE =
Pn
k=1 u2
[k], CEE =
Pn
k=1 (u[k] − u[k − 1])
2
(29)
− The average computational time.
− The position root mean square error (PRMSE)
PRMSE(cm) =
v
u
u
t
Pn
k=1
(xd[k] − x[k])
2
+ (yd[k] − y[k])
2
+ (zd[k] − z[k])
2
n
(30)
− The attitude root mean square error (ARMSE)
ARMSE(◦
) =
v
u
u
t
Pn
k=1
(ϕd[k] − ϕ[k])
2
+ (θd[k] − θ[k])
2
+ (ψd[k] − ψ[k])
2
n
(31)
Table 1. Quadrotor’s parameters
Symbol Value Unit
m 0.486 kg
g 9.806 m/s2
l 0.25 m
b 2.9842 × 10−5 N/rad/s
d 3.232 × 10−7 N.m/rad/s
I
3.8278 0 0
0 3.8288 0
0 0 7.6566
× 10−3 kg/m2
Kft
5.567 0 0
0 5.567 0
0 0 6.354
× 10−4 N/m/s
ω 0 rad/s
ω̄ 280 rad/s
Results of the comparative study of the three commands are shown in Table 3. The IBC and SMC
have been developed in [28]. Moreover, the disturbances, wind turbulence, and uncertainties used in this
case are the same in the aforementioned paper. Regarding the criteria that indicates the amount of energy
consumed by the controllers, it can be seen that the smallest CSE values with respect to u1, u2, u3, and u4 is
determined based on the NMPC approach for both cases (with or without disturbances) compared to SMC and
IBC. Besides, NMPC provides the lowest fluctuations and smoothness at control inputs which are revealed by
the CEE values. Nevertheless, the NMPC shows a high computational burden compared to other controllers.
As a result of the chattering phenomena, the SMC approach has a high effort (CEE and CSE values) compared
to the other controllers. For the three controllers without disturbances, it can be noticed that the PRMSE and
ARMSE values are less than 0.06 cm and 0.09 deg respectively which are considered tolerable. While, in the
presence of disturbances, the SMC outperforms the IBC and NMPC showing good tracking ability in terms
of ARMSE and PRMSE. To demonstrate the effectiveness of the PSMC control, this latter compared to the
NMPC and DSMC controls with the following different scenarios.
3.1. Case 1: nominal performance comparison
The simulation is done here performed using nominal conditions, to track an inclined 8-shaped tra-
jectory without any considering disturbances or parametric uncertainties, and with an initial condition differ-
ent from the equilibrium point. Simulation results in this case are presented in Figure 3 from Figures 3(a)
to 3(i). As can be shown in Figures 3(a)-3(d) and 3(i), all controllers achieve successful tracking. In con-
trast, the DSMC and PSMC exhibit a response time faster than NMPC. The control efforts are shown in the
Figures 3(e)-3(h). While in Figures 3(g) and 3(h), the DSMC has a large control effort exceeding the control
limits for the pitch and yaw torques in comparison with PSMC and NMPC.
A predictive sliding mode control for quadrotor’s tracking trajectory subject ... (Dounia Meradi)
10. 4870 ❒ ISSN: 2088-8708
Table 2. Controllers’ parameters
Controller Symbol Value
DSMC λi 71 71 18.5 10 10 25
µi 7.9 7.9 0.9 1.9 1.9 6.9
σi 0.02 0.02 0.18 0.2 0.2 0.5
NMPC Q diag
0.5, .05, .5, .05, 60, 20, 20, 3, 20, 3, 65, 53.5
H 10 × Q
R diag
1, 10−2, 10−2, 10−3
PSMC R diag
1, 10−2, 10−2, 10−3
λi 0.05 0.05 18.5 10 10 11
µ diag
0.85, 0.85, 0.005, 0.22, 0.22, 0.35
σ diag
1, 1, 1.5, 0.55, 0.55, 1.85
Table 3. A comparison between SMC, IBC, and NMPC tracking of straight-line trajectory. It is done with
CSE and CEE of {u1, u2, u3, u4}T
, Average time, PRMSE, and ARMS criterions
Controller CSE CEE Average Time [ms] PRMSE [cm] ARMSE [deg]
without IBC 4.5407e+04 2.2729e-04 0.8528 0.0051 0.0718
disturbances 0.0021 8.9765e-05
0.0069 2.3942e-04
4.7647e-04 5.6564e-08
SMC 4.5407e+04 2.3160e-04 0.6636 0.0151 0.0459
0.0074 9.2390e-04
0.0457 0.0022
5.2894e-04 5.7366e-08
NMPC 4.5407e+04 2.1768e-04 16 0.0584 0.0047
4.4816e-04 1.4897e-05
5.7965e-04 1.5780e-05
4.7172e-04 5.5041e-08
with IBC 6.0236e+04 2.9813 1.6 0.8133 1.9414
disturbances 13.2886 1.1165
8.1007 0.6525
3.3047 0.0016
SMC 6.0241e+04 7.9003 1.5 0.1470 0.4943
30.8017 5.1253
21.1184 3.8687
3.3084 0.0021
NMPC 6.0191e+04 0.2527 26.7 4.6709 1.6334
0.8102 9.6626e-04
0.8088 0.0010
3.2275 0.0008
3.2. Case 2: wind gusts rejection ability
In this case, the quadrotor is undergoing sudden wind gusts as external disturbances in the interval
[10, 30] s. The Dryden wind turbulence model [29] is used to generate a stochastic velocities disturbance
added to the dynamics of the quadrotor, as shown in Figure 4. This has had a great influence on the dynamics
of the aircraft, in particular, the linear, and angular velocities. Figures 4(a) and 4(b) illustrate respectively the
linear and angular velocity components of the applied wind turbulence. Figure 5 from Figures 5(a) to 5(i)
depict the quadrotor response to track the square trajectory against wind gusts effect with the three controllers.
The NMPC fails to track the reference trajectory in the presence of wind, in particular in X and Y positions
Figures 5(a) and 5(b) which has a large error that reaches 0.4 m. With the outperforming of DSMC, this
latter and PSMC exhibit strong tracking ability against wind gusts. As for the control effort, the NMPC has a
minimum effort even in the presence of wind Figures 5(e)-5(h). Although, the DSMC’s good tracking, it has
a large control effort; more chattering phenomena and exceeds the control limits Figures 5(f) and 5(g). While,
the PSMC control effort remains within a limits control, and has minimum chattering compared to DSMC.
On the other hand, the DSMC shows some interesting robustness properties, but in the presence of saturation
on inputs, the stability cannot be ensured. Figures 5(a) to 5(d) shows how the quadrotor deviates when it is
controlled via the DSMC with saturation on inputs represented by a blue dash-dotted line. Figure 5(i) shows
3D tracking square trajectory, both of PSMC and DSMC are successfully tracking the desired trajectory even
in the wind presence, while the NMPC cannot follow the desired trajectory and deviate from it.
Int J Elec Comp Eng, Vol. 12, No. 5, October 2022: 4861–4875
11. Int J Elec Comp Eng ISSN: 2088-8708 ❒ 4871
0 5 10 15 20
-0.5
0
0.5
1
(a)
0 5 10 15 20
-1
-0.5
0
0.5
1
(b)
0 5 10 15 20
0.2
0.4
0.6
0.8
1
1.2
(c)
0 5 10 15 20
0
0.5
1
(d)
0 5 10 15 20
3
3.5
4
4.5
5
5.5
(e)
0 1 2 3 4
-0.5
0
0.5
(f)
0 1 2 3 4
-3
-2
-1
0
1
(g)
0 1 2 3 4
-0.15
-0.1
-0.05
0
0.05
(h) (i)
Figure 3. The results of tracking an inclined 8-shaped trajectory in nominal condition with initial condition
x0 = [−15◦
, 0, 35◦
, 0, 40◦
, 0, 1, 0, −0.5, 0, 0.5, 0]T
: (a)-(d) the traking trajectory, (e)-(h) the control
inputs, (i) the 3-D traking trajectory
10 15 20 25 30
-5
-4
-3
-2
-1
0
1
2
(a)
10 15 20 25 30
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
(b)
Figure 4. Velocity components of the applied wind turbulence in the interval [10, 30]s: (a) the linear Vwind
and (b) angular ωwind
A predictive sliding mode control for quadrotor’s tracking trajectory subject ... (Dounia Meradi)
12. 4872 ❒ ISSN: 2088-8708
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 5. Simulation results showing tracking of square references under wind turbulence in the interval
10,30 s: (a)-(d) tracking trajectory, (e)-(h) the control inputs, and (i) 3-D tracking trajectory. The marked area
indicates the turbulence wind period, and the blue dash-dotted line indicates the DSMC with saturation on
inputs
3.3. Case 3: robustness comparison in the presence of model mismatch
In this case, to check the controllers’ robustness, the unmodeled dynamics are included in the mathe-
matical model of the quadrotor. Since the mass m and the inertia matrix I = diag(Ix, Iy, Iz) are time-variant
in the first at interval 10-30 s, 40% variations of these parameters which are unknown to the controllers, and
they are assumed:
m̃ = m (1 + 0.4 sin(0.5t) + γ)
˜
I = I3 × (1 + 0.4 sin(0.5t)) I
where γ = −0.125 + 0.25 × rand(1) and rand(.) is a MATLAB function that generates a random number
between 0 and 1, and I3 is (3 × 3) identity matrix.
In the second period 40-50 s, we assume that there are uncertainties on the drag and thrust coefficients
which are ordinarily difficult to identify. From (4), this variations on d and b parameters induce a disturbances
on the control inputs as follow: ũ = u + δu, where δu is the added disturbances caused by mismatches thrust
and drag coefficients on the control inputs and is equal to δu = [2, 0.5, 0.5, 0.05]T
.
Figure 6 shows the response of the nonlinear controllers under uncertainties. As it can be seen the
PSMC preserves its good tracking performance with small tracking errors Figures 6(a) to 6(d). In
Figures 6(e) to 6(h), it’s observed that DSMC inputs exceeds the limitations on control inputs and has more
chattering compared to PSMC in the presence of mismatched mass and inertia, while NMPC and PSMC pre-
serve the control inputs within bounded constraints.
Int J Elec Comp Eng, Vol. 12, No. 5, October 2022: 4861–4875
13. Int J Elec Comp Eng ISSN: 2088-8708 ❒ 4873
(a) (b) (c)
(d) (e) (f)
(g) (h)
Figure 6. Control performance under parameters uncertainties with helix trajectory (a)-(d) tracking trajectory
error and (e)-(h) the control inputs
4. CONCLUSION
In this paper, the PSMC control strategy is proposed to ensure simultaneously the inputs constraint
and robustness with regard to sudden stochastic disturbances (wind turbulence), and time-variant parametric
uncertainties. This work elaborated from a comparative study between different nonlinear control approaches.
The controllers NMPC, IBC, and SMC have been tested in simulation. The SMC controller exhibited the ro-
bustness against disturbances, while the NMPC has shown lower control effort. These results conduct us to
propose PSMC that merges DSMC and NMPC advantages. The simulation results shown the outperformed
performances of the proposed PSMC with regards to NMPC, IBC, and SMC. Future works comprise the in-
corporation of the adaptive mechanism with PSMC for parameters uncertainties problem to enhance tracking
accuracy in presence of unmodeled dynamics. Further, stability and feasibility analysis will be investigated by
including a nonlinear observer of the state.
APPENDIX
f1(x[k]) =
Kftx
m
x1[k], f4(x[k]) =
(Iy − Iz)
Ix
x10[k]x12[k],
f2(x[k]) =
Kfty
m
x3[k], f5(x[k]) =
(Iz − Ix)
Iy
x8[k]x12[k],
f3(x[k]) =
Kftz
m
x5[k] − g, f6(x[k]) =
(Ix − Iy)
Iz
x8[k]x10[k].
(32)
A predictive sliding mode control for quadrotor’s tracking trajectory subject ... (Dounia Meradi)
14. 4874 ❒ ISSN: 2088-8708
g1(x[k]) =
1
m
(cos (x1[k]) cos (x5[k]) sin(x3[k]) + sin(x1[k]) sin(x5[k])), g4(x[k]) =
l
Ix
,
g2(x[k]) =
1
m
(cos (x1[k]) sin (x3[k]) sin(x5[k]) − sin(x1[k]) cos(x5[k])), g5(x[k]) =
l
Iy
,
g3(x[k]) =
1
m
cos(x1[k]) cos(x3[k]), g6(x[k]) =
1
Iz
.
(33)
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BIOGRAPHIES OF AUTHORS
Dounia Meradi was born in Bordj Bou Arreridj, Algeria in 1992. She received the
Engineer degree in Automatic and Control systems from the National Polytechnic School of Al-
giers (ENP). She is currently a Ph.D. candidate at the Laboratory of Signal Processing and Imaging
(LATSI), Saad Dahlab University in Blida. Her research interests are including optimal control, mod-
eling, and nonlinear control of UAV. She can be contacted at email: dounia.meradi@g.enp.edu.dz.
Zoubir Abdeslem Benselama is in the academic field for the last 30 years. He received
the Engineer degree in 1985, from the Ecole Nationale Polytechnique d'Alger, Algiers, Algeria,
the Master degree in 1997, from the Ecole Nationale Polytechnique d'Alger, Algiers, Algeria, and
the Ph.D. degree in 2007 from the Ecole Nationale Polytechnique d'Alger, Algiers, Algeria, all in
electrical engineering. Currently he is Professor at the Department of Electronics of the University
of Blida, Blida, Algeria. His present interests are in Machine Learning and control process. He can
be contacted at email: benselamaabd@hotmail.com.
Ramdane Hedjar received the B.Sc. and Ph.D. degrees from the University of Science
and Technology Houari Boumediene, Algiers, Algeria, in 1988 and 2002, respectively, and the MSc
degree from the University of Blida in Algeria in 1992 in electronic and electrical engineering. After
obtaining the PhD degree, he joined the Computer Engineering Department at King Saud University
as an assistant professor. From 1992-2000, he was a lecturer with the Electronics Department at
Djelfa University, and from 1994-2000 he was a research assistant with the Electronic Department at
the University of Blida. Currently, he is a professor at King Saud University. His research interests
include robust control, nonlinear predictive control, robotics, neural network control, and networked
control systems. He can be contacted at email: hedjar@ksu.edu.sa.
A predictive sliding mode control for quadrotor’s tracking trajectory subject ... (Dounia Meradi)