An enhanced data driven model-free adaptive yaw control tracking control scheme is proposed for the yaw
channel of an unmanned-aerial-vehicle (UAV) helicopter which is non-affine in the control input in this paper. Through dynamic linearization and observer techniques, the proposed control algorithm is only based on the pseudo-partial derivative (PPD) parameter estimation derived online from the I/O data of the yaw channel of an UAV helicopter, and Lyapunov-based stability analysis is utilized to prove all signals of
close-loop control system are bounded. Compared with the traditional model free adaptive control
(MFAC), the proposed enhanced MFAC algorithm can make the close-loop control system with stronger robustness and better anti-jamming ability. Finally, simulation results of the UAV yaw channel are offered to demonstrate the effectiveness of the proposed novel control technique.
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.
DEVELOPMENT AND IMPLEMENTATION OF A ADAPTIVE FUZZY CONTROL SYSTEM FOR A VTOL ...ijctcm
The studies in aerial vehicles modeling and control have been increased rapidly recently. This paper presents the modeling and control of a four rotor vertical take-off and landing (VTOL) vehicle. The modeling of the VTOL vehicle will be described by using Euler-Newton equations. In order to stable this vehicle and control the attitude of that, classical PID controller and a fuzzy system that adjusts the PID controller gains, have been designed. Although fuzzy control of various dynamical systems has been presented in literature, application of this technology to aerial vehicle control is quite new. This system has nonlinear characteristics where classical control methods are not adequate for stabilize that. On the other hand, fuzzy control is nonlinear and it is thus suitable for nonlinear system control. Matlab Simulink has been used to test, analyze and compare the performance of the controllers in simulations. Finally this
presented controller will be implemented on a real vehicle and performance of that will be showed. This study showed that although, both of the classical PID and the fuzzy self-tuning PID controllers, can control the system properly, the second controller performed better than the classical PID controller
Backstepping linearization controller of the Delta Wing Rock PhenomenaIJERA Editor
This paper deals with the control of the wing rock phenomena of a delta wing aircraft. A control technique is
proposed to stabilize the system. The controller is a BACKSTEPPING controller. It is appeared that the
proposed solution of control guarantee the asymptotic convergence to zero of all the states of the system. To
show the performance of the proposed controller, simulation results are presented and discussed. It is found that
the control scheme work well for the wing rock phenomena of a delta wing aircraft.
Neural Network Control Based on Adaptive Observer for Quadrotor HelicopterIJITCA Journal
A neural network control scheme with an adaptive observer is proposed in this paper to Quadrotor helicopter stabilization. The unknown part in Quadrotor dynamical model was estimated on line by a Single Hidden Layer network. To solve the non measurable states problem a new adaptive observer was proposed. The main purpose here is to reduce the measurement noise amplification caused by conventional high gain observer by introducing some changes in observer’s original structure that can minimize the variance and the amplitude of the noisy signal without increasing tracking error. The stability analysis of the overall closed-loop system/ observer is performed using the Lyapunov direct method. Simulation results are given to highlight the performances of the proposed scheme
Real Time Implementation of Fuzzy Adaptive PI-sliding Mode Controller for Ind...IJECEIAES
In this work, a fuzzy adaptive PI-sliding mode control is proposed for Induction Motor speed control. First, an adaptive PI-sliding mode controller with a proportional plus integral equivalent control action is investigated, in which a simple adaptive algorithm is utilized for generalized soft-switching parameters. The proposed control design uses a fuzzy inference system to overcome the drawbacks of the sliding mode control in terms of high control gains and chattering to form a fuzzy sliding mode controller. The proposed controller has implemented for a 1.5kW three-Phase IM are completely carried out using a dSPACE DS1104 digital signal processor based real-time data acquisition control system, and MATLAB/Simulink environment. Digital experimental results show that the proposed controller can not only attenuate the chattering extent of the adaptive PI-sliding mode controller but can provide high-performance dynamic characteristics with regard to plant external load disturbance and reference variations.
The research of 6-DOF flight simulator washout filter Control MethodIJRES Journal
Electric 6-DOF flight simulator used in large aircraft engineering simulation has great benefits,As a Flight Simulator vector parallel six degree of freedom motion system is a very important part of flight simulator. Feeling is the most important in Flight simulator test while flight.If a flight simulator can feel closer to the real feeling of flying aircraft, in is more better for trainning.According to the question above, In this paper, we will start from the control method,make research on electric 6-DOF flight simulator wash out the filter control method, we will research Longitudinal studies of flight parameters at takeoff position flight simulator. Using MATLAB simulation software to verify washout filter algorithm practicality simulator Simulation.
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.
DEVELOPMENT AND IMPLEMENTATION OF A ADAPTIVE FUZZY CONTROL SYSTEM FOR A VTOL ...ijctcm
The studies in aerial vehicles modeling and control have been increased rapidly recently. This paper presents the modeling and control of a four rotor vertical take-off and landing (VTOL) vehicle. The modeling of the VTOL vehicle will be described by using Euler-Newton equations. In order to stable this vehicle and control the attitude of that, classical PID controller and a fuzzy system that adjusts the PID controller gains, have been designed. Although fuzzy control of various dynamical systems has been presented in literature, application of this technology to aerial vehicle control is quite new. This system has nonlinear characteristics where classical control methods are not adequate for stabilize that. On the other hand, fuzzy control is nonlinear and it is thus suitable for nonlinear system control. Matlab Simulink has been used to test, analyze and compare the performance of the controllers in simulations. Finally this
presented controller will be implemented on a real vehicle and performance of that will be showed. This study showed that although, both of the classical PID and the fuzzy self-tuning PID controllers, can control the system properly, the second controller performed better than the classical PID controller
Backstepping linearization controller of the Delta Wing Rock PhenomenaIJERA Editor
This paper deals with the control of the wing rock phenomena of a delta wing aircraft. A control technique is
proposed to stabilize the system. The controller is a BACKSTEPPING controller. It is appeared that the
proposed solution of control guarantee the asymptotic convergence to zero of all the states of the system. To
show the performance of the proposed controller, simulation results are presented and discussed. It is found that
the control scheme work well for the wing rock phenomena of a delta wing aircraft.
Neural Network Control Based on Adaptive Observer for Quadrotor HelicopterIJITCA Journal
A neural network control scheme with an adaptive observer is proposed in this paper to Quadrotor helicopter stabilization. The unknown part in Quadrotor dynamical model was estimated on line by a Single Hidden Layer network. To solve the non measurable states problem a new adaptive observer was proposed. The main purpose here is to reduce the measurement noise amplification caused by conventional high gain observer by introducing some changes in observer’s original structure that can minimize the variance and the amplitude of the noisy signal without increasing tracking error. The stability analysis of the overall closed-loop system/ observer is performed using the Lyapunov direct method. Simulation results are given to highlight the performances of the proposed scheme
Real Time Implementation of Fuzzy Adaptive PI-sliding Mode Controller for Ind...IJECEIAES
In this work, a fuzzy adaptive PI-sliding mode control is proposed for Induction Motor speed control. First, an adaptive PI-sliding mode controller with a proportional plus integral equivalent control action is investigated, in which a simple adaptive algorithm is utilized for generalized soft-switching parameters. The proposed control design uses a fuzzy inference system to overcome the drawbacks of the sliding mode control in terms of high control gains and chattering to form a fuzzy sliding mode controller. The proposed controller has implemented for a 1.5kW three-Phase IM are completely carried out using a dSPACE DS1104 digital signal processor based real-time data acquisition control system, and MATLAB/Simulink environment. Digital experimental results show that the proposed controller can not only attenuate the chattering extent of the adaptive PI-sliding mode controller but can provide high-performance dynamic characteristics with regard to plant external load disturbance and reference variations.
The research of 6-DOF flight simulator washout filter Control MethodIJRES Journal
Electric 6-DOF flight simulator used in large aircraft engineering simulation has great benefits,As a Flight Simulator vector parallel six degree of freedom motion system is a very important part of flight simulator. Feeling is the most important in Flight simulator test while flight.If a flight simulator can feel closer to the real feeling of flying aircraft, in is more better for trainning.According to the question above, In this paper, we will start from the control method,make research on electric 6-DOF flight simulator wash out the filter control method, we will research Longitudinal studies of flight parameters at takeoff position flight simulator. Using MATLAB simulation software to verify washout filter algorithm practicality simulator Simulation.
Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonl...IJPEDS-IAES
An adaptive fuzzy integral sliding-mode controller using nonlinear sliding surface is designed for the speed regulator of a field-oriented induction motor drive in this paper. Combining the conventional integral sliding surface with fractional-order integral, a nonlinear sliding surface is proposed for the integral sliding-mode speed control, which can overcome the windup problem and the convergence speed problem. An adaptive fuzzy control term is utilized to approximate the uncertainty. The stability of the controller is analyzed by Lyapunov stability theory. The effectiveness of the proposed speed regulator is demonstrated by the simulation results in comparison with the conventional integral sliding-mode controller based on boundary layer.
Analytical Evaluation of Generalized Predictive Control Algorithms Using a Fu...inventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Dynamic modelling and optimal controlscheme of wheel inverted pendulum for mo...ijctcm
Unstable wheel inverted pendulum is modelled and controlled deploying Kane’s method and optimal
partial-state PID control scheme. A correct derivation of nonlinear mathematical model of a wheel inverted
pendulum is obtained using a proper definition of the geometric context of active and inertia forces. Then
the model is decoupled to two linear subsystems namely balancing and heading subsystems. Afterward
partial-state PID controller is proposed and formulated to quadratic optimal regulation tuning method. It
enables partial-state PID to be optimally tuned and guarantees a satisfactory level of states error and a
realistic utilization of torque energy. Simulation and numerical analyses are carried out to analyse
system’s stability and to determine the performance of the proposed controller for mobile wheel inverted
pendulum application.
This article considers different approaches for autopilot controller gain values adjustment. The correct autopilot
performance is tested using modeling methods. A variant of land-based autopilot is considered. Examined are
scenarios of UAV airplanes in level flight. The latter are applicable to tasks such as remote sensing, controlled
area surveillance, etc.
Performance Analysis of a DTC and SVM Based Field- Orientation Control Induct...IJPEDS-IAES
This study presents a performance analysis of two most popular control strategies for Induction Motor (IM) drives: direct torque control (DTC) and space vector modulation (SVM) strategies. The performance analysis is done by applying field-orientation control (FOC) technique because of its good dynamic response. The theoretical principle, simulation results are discussed to study the dynamic performances of the drive system for individual control strategies using actual parameters of induction motor. A closed loop PI controller scheme has been used. The main purpose of this study is to minimize ripple in torque response curve and to achieve quick speed response as well as to investigate the condition for optimum performance of induction motor drive. Depending on the simulation results this study also presents a detailed comparison between direct torque control and space vector modulation based field-orientation control method for the induction motor drive.
A Simplified Speed Control Of Induction Motor based on a Low Cost FPGA IJECEIAES
This paper investigates the development of a simplified speed control of induction motor based on indirect field oriented control (FOC). An original PI-P controller is designed to obtain good performances for speed tracking. Controller coefficients are carried out with analytic approach. The algorithm is implemented using a low cost Field Programmable Gate Array (FPGA). The implementation is followed by an efficient design methodology that offers considerable design advantages. The main advantage is the design of reusable and reconfigurable hardware modules for the control of electrical systems. Experimental results carried on a prototyping platform are given to illustrate the efficiency and the benefits of the proposed approach.
Comparison of Estimated Torques Using Low Pass Filter and Extended Kalman Fil...IAES-IJPEDS
Torque calculation process is one of the major concerns for controlling induction motors in industry, which requires very accurate state estimation of unmeasurable variables of nonlinear models. This can be solved if the variables used for torque calculation is accurately estimated. This paper presents a torque calculation based on a voltage model represented with a low-pass filter (LPF), and an extended Kalman filter (EKF). The experimental results showed that the estimated torque at low speed based on EKF is more accurate in the expense of more complicated and larger computational time.
Mathematical Modeling and Fuzzy Adaptive PID Control of Erection MechanismTELKOMNIKA JOURNAL
This paper describes an application of fuzzy adaptive PID controller to erection mechanism.
Mathematical model of erection mechanism was derived. Erection mechanism is driven by electrohydraulic
actuator system which is difficult to control due to its nonlinearity and complexity. Therefore fuzzy
adaptive PID controller was applied to control the system. Simulation was performed in Simulink software
and experiment was accomplished on laboratory equipment. Simulation and experiment results of erection
angle controlled by fuzzy logic, PID and fuzzy adaptive PID controllers were respectively obtained. The
results show that fuzzy adaptive PID controller can effectively achieve the best performance for erection
mechanism in comparison with fuzzy logic and PID controllers.
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.
A Variable Control Structure Controller for the Wing Rock Phenomenon IJERA Editor
This paper presents the design of a variable structure controller for the model of the wing rock phenomenon of a
delta wing aircraft. It is considered to be a continue study of the last two researches for the same phenomena
"Feedback linearization [15] and back stepping controller [14] ". A control technique is proposed to stabilize the
aircraft phenomena. The solution presented in this paper give a guarantee of asymptotic convergence to zero of
all variables of the system. MATLAB simulation used to show how the proposed control is working well for
such phenomena of a delta wing aircraft. The model of the phenomena in this paper will consider the same
model presented in the last two researches mentioned above.
Hybrid Control Approach to Multi-AUV System in a Surveillance Mission ITIIIndustries
Surveillance missions for multiple autonomous underwater vehicle (AUV) system suggest the use of different modes of operation including organizing and keeping a predefined formation, avoiding obstacles, reaching static and tracking dynamic targets. While exploiting a leader-follower strategy to formation control and the vector Lyapunov function method to controller design, we use discrete-event approach and supervisory control theory to switch between operational modes.
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.
Neural Network Control Based on Adaptive Observer for Quadrotor HelicopterIJITCA Journal
A neural network control scheme with an adaptive observer is proposed in this paper to Quadrotor helicopter stabilization. The unknown part in Quadrotor dynamical model was estimated on line by a
Single Hidden Layer network. To solve the non measurable states problem a new adaptive observer was proposed. The main purpose here is to reduce the measurement noise amplification caused by conventional
high gain observer by introducing some changes in observer’s original structure that can minimize the variance and the amplitude of the noisy signal without increasing tracking error. The stability analysis of the overall closed-loop system/ observer is performed using the Lyapunov direct method. Simulation results are given to highlight the performances of the proposed scheme.
Development of a Customized Autopilot for Unmanned Helicopter Model Using Gen...Ahmed Momtaz Hosny, PhD
The objective of this paper is to develop a customized autopilot system that enables a helicopter model to carry out an autonomous flight using on-board microcontroller. The main goal of this project is to provide a comprehensive controller design methodology, Modeling, simulation, guidance and verification for an unmanned helicopter model. The autopilot system was designed to demonstrate autonomous maneuvers such as flying over the planned waypoints with constant forward speed.
Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonl...IJPEDS-IAES
An adaptive fuzzy integral sliding-mode controller using nonlinear sliding surface is designed for the speed regulator of a field-oriented induction motor drive in this paper. Combining the conventional integral sliding surface with fractional-order integral, a nonlinear sliding surface is proposed for the integral sliding-mode speed control, which can overcome the windup problem and the convergence speed problem. An adaptive fuzzy control term is utilized to approximate the uncertainty. The stability of the controller is analyzed by Lyapunov stability theory. The effectiveness of the proposed speed regulator is demonstrated by the simulation results in comparison with the conventional integral sliding-mode controller based on boundary layer.
Analytical Evaluation of Generalized Predictive Control Algorithms Using a Fu...inventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Dynamic modelling and optimal controlscheme of wheel inverted pendulum for mo...ijctcm
Unstable wheel inverted pendulum is modelled and controlled deploying Kane’s method and optimal
partial-state PID control scheme. A correct derivation of nonlinear mathematical model of a wheel inverted
pendulum is obtained using a proper definition of the geometric context of active and inertia forces. Then
the model is decoupled to two linear subsystems namely balancing and heading subsystems. Afterward
partial-state PID controller is proposed and formulated to quadratic optimal regulation tuning method. It
enables partial-state PID to be optimally tuned and guarantees a satisfactory level of states error and a
realistic utilization of torque energy. Simulation and numerical analyses are carried out to analyse
system’s stability and to determine the performance of the proposed controller for mobile wheel inverted
pendulum application.
This article considers different approaches for autopilot controller gain values adjustment. The correct autopilot
performance is tested using modeling methods. A variant of land-based autopilot is considered. Examined are
scenarios of UAV airplanes in level flight. The latter are applicable to tasks such as remote sensing, controlled
area surveillance, etc.
Performance Analysis of a DTC and SVM Based Field- Orientation Control Induct...IJPEDS-IAES
This study presents a performance analysis of two most popular control strategies for Induction Motor (IM) drives: direct torque control (DTC) and space vector modulation (SVM) strategies. The performance analysis is done by applying field-orientation control (FOC) technique because of its good dynamic response. The theoretical principle, simulation results are discussed to study the dynamic performances of the drive system for individual control strategies using actual parameters of induction motor. A closed loop PI controller scheme has been used. The main purpose of this study is to minimize ripple in torque response curve and to achieve quick speed response as well as to investigate the condition for optimum performance of induction motor drive. Depending on the simulation results this study also presents a detailed comparison between direct torque control and space vector modulation based field-orientation control method for the induction motor drive.
A Simplified Speed Control Of Induction Motor based on a Low Cost FPGA IJECEIAES
This paper investigates the development of a simplified speed control of induction motor based on indirect field oriented control (FOC). An original PI-P controller is designed to obtain good performances for speed tracking. Controller coefficients are carried out with analytic approach. The algorithm is implemented using a low cost Field Programmable Gate Array (FPGA). The implementation is followed by an efficient design methodology that offers considerable design advantages. The main advantage is the design of reusable and reconfigurable hardware modules for the control of electrical systems. Experimental results carried on a prototyping platform are given to illustrate the efficiency and the benefits of the proposed approach.
Comparison of Estimated Torques Using Low Pass Filter and Extended Kalman Fil...IAES-IJPEDS
Torque calculation process is one of the major concerns for controlling induction motors in industry, which requires very accurate state estimation of unmeasurable variables of nonlinear models. This can be solved if the variables used for torque calculation is accurately estimated. This paper presents a torque calculation based on a voltage model represented with a low-pass filter (LPF), and an extended Kalman filter (EKF). The experimental results showed that the estimated torque at low speed based on EKF is more accurate in the expense of more complicated and larger computational time.
Mathematical Modeling and Fuzzy Adaptive PID Control of Erection MechanismTELKOMNIKA JOURNAL
This paper describes an application of fuzzy adaptive PID controller to erection mechanism.
Mathematical model of erection mechanism was derived. Erection mechanism is driven by electrohydraulic
actuator system which is difficult to control due to its nonlinearity and complexity. Therefore fuzzy
adaptive PID controller was applied to control the system. Simulation was performed in Simulink software
and experiment was accomplished on laboratory equipment. Simulation and experiment results of erection
angle controlled by fuzzy logic, PID and fuzzy adaptive PID controllers were respectively obtained. The
results show that fuzzy adaptive PID controller can effectively achieve the best performance for erection
mechanism in comparison with fuzzy logic and PID controllers.
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.
A Variable Control Structure Controller for the Wing Rock Phenomenon IJERA Editor
This paper presents the design of a variable structure controller for the model of the wing rock phenomenon of a
delta wing aircraft. It is considered to be a continue study of the last two researches for the same phenomena
"Feedback linearization [15] and back stepping controller [14] ". A control technique is proposed to stabilize the
aircraft phenomena. The solution presented in this paper give a guarantee of asymptotic convergence to zero of
all variables of the system. MATLAB simulation used to show how the proposed control is working well for
such phenomena of a delta wing aircraft. The model of the phenomena in this paper will consider the same
model presented in the last two researches mentioned above.
Hybrid Control Approach to Multi-AUV System in a Surveillance Mission ITIIIndustries
Surveillance missions for multiple autonomous underwater vehicle (AUV) system suggest the use of different modes of operation including organizing and keeping a predefined formation, avoiding obstacles, reaching static and tracking dynamic targets. While exploiting a leader-follower strategy to formation control and the vector Lyapunov function method to controller design, we use discrete-event approach and supervisory control theory to switch between operational modes.
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.
Neural Network Control Based on Adaptive Observer for Quadrotor HelicopterIJITCA Journal
A neural network control scheme with an adaptive observer is proposed in this paper to Quadrotor helicopter stabilization. The unknown part in Quadrotor dynamical model was estimated on line by a
Single Hidden Layer network. To solve the non measurable states problem a new adaptive observer was proposed. The main purpose here is to reduce the measurement noise amplification caused by conventional
high gain observer by introducing some changes in observer’s original structure that can minimize the variance and the amplitude of the noisy signal without increasing tracking error. The stability analysis of the overall closed-loop system/ observer is performed using the Lyapunov direct method. Simulation results are given to highlight the performances of the proposed scheme.
Development of a Customized Autopilot for Unmanned Helicopter Model Using Gen...Ahmed Momtaz Hosny, PhD
The objective of this paper is to develop a customized autopilot system that enables a helicopter model to carry out an autonomous flight using on-board microcontroller. The main goal of this project is to provide a comprehensive controller design methodology, Modeling, simulation, guidance and verification for an unmanned helicopter model. The autopilot system was designed to demonstrate autonomous maneuvers such as flying over the planned waypoints with constant forward speed.
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.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Optimal FOPI-FOPD controller design for rotary inverted pendulum system using...TELKOMNIKA JOURNAL
The rotary inverted pendulum (RIP) has been used in various control application areas. This system can be represented as two degree of freedom (2-DOF), consisting of a rotating arm and rotating pendulum rod. RIP is an excellent example of designing a single-input multi-output (SIMO) system. Due to unstable RIP system dynamics, and its nonlinear model, multiple control techniques have been used to control this system. This paper uses integer and fractional order proportional integral-proportional derivative (PI-PD) controllers to stabilize the pendulum in the vertical direction. Constrained optimization approaches, such as the grey wolf optimization (GWO) methodology, are utilized to estimate the parametric values of the controllers. The simulation results showed that the fractional order PI-PD controller outperforms the integer order PI-PD controller with and without disturbance signal existence. A multiple results comparison has illustrated the superiority of fractional order controller over a previous work.
PID controller for microsatellite yaw-axis attitude control system using ITAE...TELKOMNIKA JOURNAL
The need for effective design of satellite attitude control (SAC) subsystem for a microsatellite is imperative in order to guarantee both the quality and reliability of the data acquisition. A proportional-integral-derivative (PID) controller was proposed in this study because of its numerous advantages. The performance of PID controller can be greatly improved by adopting an integral time absolute error (ITAE) robust controller design approach. Since the system to be controlled is of the 4th order, it was approximated by its 2nd order version and then used for the controller design. Both the reduced and higher-order pre-filter transfer functions were designed and tested, in order to improve the system performance. As revealed by the results, three out of the four designed systems satisfy the design specifications; and the PD-controlled system without pre-filter transfer function was recommended out of the three systems due to its structural simplicity, which eventually enhances its digital implementation.
Optimal and Pid Controller for Controlling Camera's Position InUnmanned Aeria...Zac Darcy
This paper describes two controllers designed specifically for adjusting camera’s position in a small
unmanned aerial vehicle (UAV). The optimal controller was designed and first simulated by using
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Optimal and pid controller for controlling camera’s position in unmanned aeri...Zac Darcy
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Design of Digital Autopilot for Lateral Motion Control of an Aircraft Based o...IJERA Editor
The optimal digital autopilot needed to control of the roll for an aircraft in the presence of an arbitrary unmeasured disturbances is addressed in this paper. Such autopilot has to achieve a desired lateral motion control of this aircraft via minimizing the upper bound on the absolute value of the difference between the given and true roll angles. It is ensured by means of the two digital controllers. The inner controller is designed as the discrete-time PI controller in order to stabilize a given roll rate. This variable is formed by the external P controller. The necessary and sufficient conditions under which the two-circuit feedback discrete-time control system will be stable are derived. To optimize this control system, the controller parameters are derived utilizing the so-called l1-optimization approach advanced in modern control theory. A numerical example demonstrating the l1-optimization technique and results of some simulation experiments are presented to illustrate the performance of the l1-optimal controller. The robustness properties of this controller are established
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experimental results show that the hybrid controller gave the best performance as it has the smallest overshoot,
oscillation, and setting time.
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ENHANCED DATA DRIVEN MODE-FREE ADAPTIVE YAW CONTROL OF UAV HELICOPTER
1. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
DOI : 10.5121/ijics.2015.5402 13
ENHANCED DATA DRIVEN MODE-FREE ADAPTIVE
YAW CONTROL OF UAV HELICOPTER
Dezhi Xu 1
and Hongcheng Zhou 2
1
Key Laboratory of Advanced Control for Light Industry Processes, Ministry of
Education, Jiangnan University, Wuxi Jiangsu 214122, China
2
Institute of Information, JinLing Institute of Technology, Nanjing 211169, China
ABSTRACT
An enhanced data driven model-free adaptive yaw control tracking control scheme is proposed for the yaw
channel of an unmanned-aerial-vehicle (UAV) helicopter which is non-affine in the control input in this
paper. Through dynamic linearization and observer techniques, the proposed control algorithm is only
based on the pseudo-partial derivative (PPD) parameter estimation derived online from the I/O data of the
yaw channel of an UAV helicopter, and Lyapunov-based stability analysis is utilized to prove all signals of
close-loop control system are bounded. Compared with the traditional model free adaptive control
(MFAC), the proposed enhanced MFAC algorithm can make the close-loop control system with stronger
robustness and better anti-jamming ability. Finally, simulation results of the UAV yaw channel are offered
to demonstrate the effectiveness of the proposed novel control technique.
KEYWORDS
Unmanned-aerial-vehicle helicopter, yaw control, model free adaptive control, internal model
1. INTRODUCTION
The potential use of unmanned-aerial-vehicle (UAV) helicopter can be applied in military and
civilian, although military applications dominate the non-military ones. Military and civilian
applications include power lines inspection, surveillance, national defense, agriculture, disaster
rescue applications and so on [1]. Dynamics of UAV helicopter are strongly nonlinear, seriously
multi-variable coupled, inherently unstable and a non-minimum phase system with time-varying
parameters. So controlling the UAV helicopter is not an easy task. In the control area, to improve
the performance of UAV helicopter has been an important focus [1-2].
As a highly nonlinear and uncertain system, helicopter flight control system design has been
dominated by linear control techniques. In the past few decades, linear control algorithms have
been extensively researched [1, 3-5]. Many linear control technologies were used to design the
UAV helicopter control system [1, 6-10]. However, for the tracking control, the controller based
on fixed linear models may result in an unacceptable response and even the instability of the
closed-loop system. Because linearized models cannot guarantee the global model approximation,
nonlinear control methods have been used in the control system design, such as [2, 11-12].
Furthermore, in a lot of control systems, the nonlinear model of plant dynamics is generally non-
affine in input and is commonly simplified around a trim point, that is, an operating point is
dependent on the current system states [13]. Coupled with the uncertainties under the varying
environment and the changing flight conditions, developing a controller to opportune compensate
for the time varying uncertainties have been a more difficult task [14].
2. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
14
As one of the data-driven control methods, MFAC has been proposed and applied in several areas.
MFAC algorithm based on compact form dynamic linearization (CFDL), partial form dynamic
linearization (PFDL), and full form dynamic linearization (FFDL) have been proposed by Hou for
single-input single-output (SISO), multi-input single-output (MISO), and multi-input multi-output
(MIMO) systems [15-17]. However, the MFAC is still developing. How to prove the stability and
convergence of the tracking problems is one of the open problems in MFAC [20]. We all know
that the Lyapunov function is widely used to analyse the stability of close-loop systems [15].
In this paper, we focus on how to design a data-driven controller based on the Lyapunov method.
Inspired by the work of dynamic linearization technique of Hou [15], we present an enhanced
adaptive observer based on control strategies for nonlinear process systems in which the pseudo-
partial derivative (PPD) theory is used to dynamically linearize the nonlinear system. First, a
novel adaptive strategy for computing the PPD term is designed by using the Lyapunov method.
Then, the internal model approach is used to design the data-driven controller via CFDL. The
stability analysis for tracking error of the proposed algorithm is provided. Last, an application of
the proposed controller design for a small-scale UAV helicopter mounted on an experiment
platform is also given to show the effectiveness of the control algorithm.
The rest of this paper is organized as follows. In Section 2, the yaw dynamic of the helicopter and
the simplified model are given. In Section 3, the main results of internal model approach based on
data-driven control via CFDL are proposed. Simulation results are presented to show the
effectiveness of the proposed technique in Section 4. Finally, some conclusions are given at the
end of this paper.
2. PROBLEM DESCRIPTION
It is clearly known that yaw channel control of controlling small scale UAV helicopters is one of
the most challenging jobs [4, 10]. Due to the small size of small-scale UAV helicopter, the torque
combined with the yaw dynamic is highly sensitive. In order to improve the performance of the
yaw control, a more precise channel model characterizing of UAV is necessary. A framework of
the simulation model for the UAV helicopter (see Fig.1) is set up using rigid body equations of
motion of the helicopter fuselage.
Figure 1: The frame of helicopter
3. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
15
In this way the influence of the aerodynamic forces and moments working on the helicopter are
expressed. The total aerodynamic forces and moments acting on a helicopter can be computed by
summing up the contributions of all parts on the helicopter (including main rotor, fuselage, tail
rotor, vertical fin and horizontal stabilizer). So, the yaw channel dynamic equations are given by:
zz mr tr fus hs vf
r
I r N N N N N
ϕ =
= + + + +
&
&
(1)
where ϕ and r are the yaw angle and angular rate of the helicopter; zzI is the inertia around z-
axis; mrN , trN , hsN , fusN and vfN present the torque of main rotor, tail rotor, horizontal,
fuselage and vertical fin worked on the helicopter respectively.
In hovering and low-velocity flight, the dominant torque is caused by main rotor and tail rotor
[18]. By simplifying the fuselage and vertical fin damping, the yaw channel dynamics can be
rewritten as:
1 2zz mr tr tr
r
I r Q T l b r b
ϕ
ϕ
=
= − + + +
&
&
(2)
where mrQ is the main rotor’s torque, rT is the tail rotor’s thrust, trl is the distance between the
tail rotor and z-axis, 1b and 2b are damping constants.
2 4 4 2
2 0
2 2 2 3 3
2 1 2 2 2 2 0
2 2 2 3 3 2 2
1 2 2 2 1 0 2 1 0
2 2 2 2 4 4
1 0 1 0 2
1
( )
8
+ 8 (2 4 )( )
4 (2 4 )( ) +6 ( )
+6 ( ) 6 ( )
48
mr d mr
d mr mr
mr mr d
mr
d
Q C c R R
C R C C C C C R R
a R C C C C C R R C C R R
c
aC R R C R R R
R
ρ θ
ρπ θ θ
ρπ θ θ
θ
ρπ
π
Ω −
Ω + − + −
+ Ω + − + − +
=
−
− + Ω − +
2 2 2
2 2 2 1 0
2 2 2 2 2 4 4 2 2 2
2 2 1 0 0 0 2 2 0
2 2 2 3 3 2 2 2
1 1 2 2 2 1 0 2 0 2
3 4 ( )
+3 4 ( ) 6 ( ) 3 ( )
+4 (2 4 )( ) 3 ( )
48
d mr
d d
d mr mr
C C C C R R
aC C C R R C R R R C C R R
c
C R C C C C C R R aC R R
R
θ
θ ρπ
ρπ θ θ
π
+ −
+ − + Ω − + −
Ω + − + − + −
(3)
The brief description of the forces and torques computing can be given by using the blade
element method [18]. The torque which is generated by main rotor can be described by:
0
2 2 2 2
2 2
R
l d
mr R
r C c r C c
Q rdr
ρ φ ρ Ω Ω
= +
∫ (4)
with 1 / ( )rφ υ= Ω , lC aα= , 2
0 1 2d d d dC C C Cα α≈ + + , where ρ , a , r , α , c , 1υ , φ and Ω
are density of air, slope of the lift curve, speed radial distance, the angle of attack of the blade
element, chord of the blade, induced speed, inflow angle and rotor speed of the main rotor
respectively. After complete employment with the help of Maple, we obtain (4)
with 2 3 3
1 0
1
( )
6
C abc R Rρ= Ω − , 2 2 2
2 0
1
2 / ( )
8
C abc R R Rρ ρπ= Ω − , where mrθ , R and b are
4. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
16
pitch angle of main rotor, radial and number of the rotor. Similarly, the force which is created by
the tail rotor can be represented by the following form
0
2 2 11
2
tr
tr
R
tr
tr tr tr tr tr tr tr trR
tr
T a b c r r dr
υ
ρ θ
= Ω −
Ω
∫ (5)
1
2
tr
tr
tr
T
A
υ
ρ
= (6)
Combing (5) with (6), we have
( )
0
2 2
2
3 4 4 4 3
1
2 2
1
4
2
tr
tr
R
tr
tr tr tr tr tr tr tr trR
tr tr
tr tr
T r
T a b c r dr
A
C C C C C
ρ θ
ρ
θ θ
= Ω − Ω
= + + +
∫
(7)
with 2 3 3
3 0
1
( )
6
tr tr tr tr tr trC a b c R Rρ= Ω − , 2 2 2
4 0
1
2 / ( )
8
tr tr tr tr tr tr trC a b c R R Rρ ρπ= Ω − . where tra ,
trc , trb , trΩ , trθ , trr , trυ and trA are slope of the lift curve, chord of the blade, number of the
rotor, speed of the tail rotor, pitch angle, radial distance, induced tail rotor’s speed, and the tail
rotor disc’s area, respectively.
Similarly, the force of the main rotor is
( )2
1 2 2 2 1
1
4
2
mr mr mrT C C C C Cθ θ= + + + (8)
The yaw angle ϕ is controlled through the trθ . The trθ is chosen as the control input u . The ϕ
is chosen as the control objective y . By above UAV yaw-channel modeling, we can see that it is
difficult to design a model-based feedback controller to stabilization system (2). Moreover, the
input output relation of UAV yaw-channel modeling can be written in the following Nonlinear
Auto Regressive with eXogenous input (NARX) model:
( 1) ( ( ), , ( ), ( ), , ( )) ( )d ny k f y k y k n u k u k n d t+ = − − +L L (9)
where ( )d t denotes the external disturbance and assumes its slowly time-varying. Currently, in
order to control the yaw-channel of UAV, various control methods are proposed by [6-9], for
example, nonlinear adaptive control, backstepping control, and neural network control and so on.
For the nonlinear system (9), there must exist a parameter ( )kϑ , called PPD, system (9) can be
transformed into the following CFDL description when | ( ) | 0u k∆ ≠ :
( 1) ( ) ( ) ( ) ( ) ( )T
y k u k k d k k kϑ θ∆ + = ∆ + ∆ = Φ (10)
where ( ) ( ) ( 1)d k d k d k∆ = − − , ( ) [ ( ), ( )]T
k k d kθ ϑ= ∆ , ( ) [ ( ),1]T
k u kΦ = ∆ .
5. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
17
3. METHODOLOGY
3.1. Model Parameter Estimation Algorithm
The proposed parameter identification observer has the following structure
ˆˆ ˆ( 1) ( ) ( ) ( ) ( )T
oy k y k k k Ke kθ+ = + Φ + (11)
where ˆ( ) ( ) ( )oe k y k y k= − is the output estimation error, ˆˆ ˆ( ) [ ( ), ( )]T
k k d kθ ϑ= ∆ , and the gain
K is chosen such that 1F K= − in the unit circle.
Hence, in view of (10) and (11), the output estimation error dynamics is given by
( 1) ( ) ( ) ( )T
o oe k k k Fe kθ+ = Φ +% (12)
where ˆ( ) ( ) ( )k k kθ θ θ= −% represents the parameter estimation error. The adaptive update law
for the estimated parameters ( )kθ can be chosen as
ˆ ˆ( 1) ( ) ( ) ( )( ( 1) ( ))o ok k k k e k Fe kθ θ+ = + Φ Γ + − (13)
The gain ( )kΓ is chosen as follows
( )
12
( ) 2 ( )k k µ
−
Γ = Φ +‖ ‖ (14)
where µ is a positive constant, hence, ( )kΓ is positive definite for all k . Notice that, by virtue
of assumption ( )kΦ ≤ Ω‖ ‖ , ( )kΓ can be lower bounded as
2
2
( ) 0k γ
µ
Γ ≥ = >
Ω +
‖ ‖
By taking into account (12) and (13), the estimation error dynamics can be written as
( 1) ( ) ( ) ( )
( 1) ( )
T
o oe k k k Fe k
k H k
θ
θ θ
+ = Φ +
+ =
%
% %
(15)
where cH is given by 2 ( ) ( ) ( )T
H I k k k= − Φ Γ Φ and 2I denotes the (2×2) identity matrix.
Theorem 1: The equilibrium 2 1[ , ] [0, ]T T T T
oe θ ×= 0% of the system (15) is globally uniformly
stable. Furthermore, the estimation error ( )oe k converges asymptotically to 0.
Proof: Consider the Lyapunov function
2
1( ) ( ) ( ) ( )T
oV k Pe k k kλθ θ= + % %
where λ , P are positive constants and P is the solution by 2
P F P Q+ = with Q is positive
constant.
6. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
18
By taking into (15), we have
( )
1 1 1
2 2 2
2
2 2
( ) ( 1) ( )
( ) ( ) ( ) ( ) 2 ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 ( ) ( )
| ( ) | ( ) ( ) ( ) 2 | ( ) | ( )
T T T
o o o
T T T T
o o
T
o o
V k V k V k
P k k k k PF k k e k Pe k PF e k
k H H k Qe k k k k P k PFe k k
Q e k k k P k PF e k k
θ θ θ
θ λ λ θ λµ
λµ
∆ = + −
= Φ Φ + Φ + +
+ − = − − Θ Γ Γ − Θ + Θ
≤ − − Γ Γ − Θ + Θ
≤
% % %
% %
‖ ‖ ‖ ‖
2 2
1 2| ( ) | ( )oc e k c k− − Θ‖ ‖
Where ( ) ( ) ( )T
k k kθΘ = Φ % , 1
1
c Q
ς
= − , 2 2 2
2c P P Fµλγ ς= − − . Hence, 1( ) 0V k∆ ≤
provided that ς , Q and λ satisfy the following inequalities
2 2 21
, 0Q P P Fµλγ ς
ς
> − − >
Notice that 1( )V k∆ is negative definite in the variables ( )oe k , ( )kΘ . Since ( )V k in a
decreasing and non-negative function, it converges to a constant value 1 0V ∞
≥ , as k → ∞ ,
hence, 1( ) 0V k∆ → . This implies that both ( )oe k and ( )kθ% remain bounded for all k , and
lim ( ) 0o
k
e k
→∞
= .
3.2. Controller Design
Based on the observer (11), the data-driven inverse control law can be described as
( )*
2
ˆˆ ˆ( ) ( 1) ( ) ( ) ( )
( ) ( 1) ,
ˆ ( )
ok y k y k Ke k d k
u k u k
k
ϑ
ϑ α
+ − − − ∆
= − +
+
| ( ) |for u k δ∆ ≤ (16)
( ) ( 1) sign( ( )), for | ( ) |u k u k u k u kδ δ= − + ∆ ∆ >
where *
( )y k is reference trajectory. α and δ as given finite positive numbers. Notice that, in
many practical systems, because their actuators cannot change too fast, the number δ can be
obtained.
Define observer tracking error *
ˆ( ) ( ) ( )e k y k y k= − , thus
* * ˆˆ ˆ( 1) ( 1) ( 1) ( 1) ( ) ( ) ( ) ( )T
oe k y k y k y k y k k k Ke kθ+ = + − + = + − − Φ − (17)
The robustness of the stability and the performance for data-driven control law (16) are given in
Theorem 2.
7. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
19
Theorem 2: For given * * *
| ( ) ( 1) |y k y k y− − ≤ ∆ , using the data-driven control law (16), the
solution of close-loop observer error system (17) is uniformly ultimately bounded (UUB) [19]
for all k with ultimate bound 2
1
lim | ( ) |
1
o
k
a
e k
a→∞
≤
−
, where *
y∆ is a given positive constant,
00 ( ) 1s k< ≤ ,
0
1 0 2
( )
1 ( ) ,
ˆ ( )
s k
a s k
k
α
ϑ α
= − +
+
*0
2 0 2
( ) ˆ1 ( ) ( ) ( )
ˆ ( )
o
s k
a s k y Ke k d k
k
α
ϑ α
= − + ∆ − − ∆
+
.
Proof: Define a variable 0 ( )s k where 00 ( ) 1s k< ≤ for all k . The control law (16) is
equivalently expressed as
( )*
02
ˆˆ ˆ( ) ( 1) ( ) ( ) ( )
( ) ( )
ˆ ( )
ok y k y k Ke k d k
u k s k
k
ϑ
ϑ α
+ − − − ∆
∆ =
+
(18)
where
0 ( ) 1, for | ( ) |s k u k δ= ∆ ≤
00 ( ) 1, for | ( ) |s k u k δ< < ∆ >
Using (18), (17) becomes
( )
( )
*0
0 2
* *0
0 2
*0 0
0 02 2
( ) ˆˆ| ( 1) | 1 ( ) ( 1) ( ) ( ) ( )
ˆ ( )
( ) ˆ1 ( ) ( 1) ( ) ( ) ( ) ( )
ˆ ( )
( ) ( )
1 ( ) ( ) 1 ( ) ( )
ˆ ˆ( ) ( )
o
o
o
s k
e k s k y k y k Ke k d k
k
s k
s k y k y k e k Ke k d k
k
s k s k
s k e k s k y Ke k
k k
α
ϑ α
α
ϑ α
α α
ϑ α ϑ α
+ = − + × + − − − ∆
+
= − + × + − + − − ∆
+
≤ − + + − + ∆ − −
+ +
1 2
ˆ( )
| ( ) |o
d k
a e k a
∆
= +
(19)
Choosing a Lyapunov function as ( ) | ( ) |oV k e k= , from (19), one has
1 2( 1) | ( 1) | | ( ) | (1 ) ( )o oV k e k e k a V k a∆ + = + − = − + . Since 10 1a≤ < and 2a is bounded,
according to the lemma in [19], using the control law (16), the results of close-loop observer
system (17) are UUB for all k with ultimate bound 2
1
lim | ( ) |
1
o
k
a
e k
a→∞
≤
−
.
Corollary 1: Under the controller (16), together with the observer (11), adaptive laws (13), we
can guarantee that the system (9) tracking error *
( ) ( ) ( )ce k y k y k= − is UUB with ultimate
bound 2
1
lim | ( ) |
1k
a
e k
a→∞
≤
−
.
8. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
20
Proof: Since
( ) ( ) ( )c oe k e k e k= − (20)
Taking the absolute value and limiting on both sides of (20), we obtain
2
1
lim | ( ) | lim | ( ) | lim | ( ) |
1
o c
k k k
a
e k e k e k
a→∞ →∞ →∞
≤ + ≤
−
(21)
So the tracking error ( )e k is UUB for all k with ultimate bound 2
1
lim | ( ) |
1k
a
e k
a→∞
≤
−
.
3.3. Enhanced Controller Design
In this paper, the internal model structure is adopted to improve the robustness of close-loop
system. Where observer (11) is seem as internal model. Although adaptive internal model can
ensure the close-loop is stable. The modeling errors still exists, and it will reduce the robustness
and stability. The traditional method is to introduce a feedback low-pass filter. In order to further
improve the robustness, the low-pass filter can be designed in the proposed controller. The block
diagram of the enhanced MFACl method is shown in Fig. 2, where the low-pass filter is
described as
1
1
( )
1
F z
z
ς
ς −
−
=
−
(22)
Figure 2: Block diagram of enhanced model free adaptive
Under the control architecture as shown in Fig. 2, the equivalent control law can be represented
as follows:
( )*
2
ˆˆ ˆ( ) ( 1) ( ) ( ) ( ) ( ) ( )
( ) ( 1) ,
ˆ ( )
o ok y k y k Ke k d k F z e k
u k u k
k
ϑ
ϑ α
+ − − − ∆ −
= − +
+
| ( ) |for u k δ∆ ≤ (23)
( ) ( 1) sign( ( )), for | ( ) |u k u k u k u kδ δ= − + ∆ ∆ >
Corollary 2: For given * * *
| ( ) ( 1) |y k y k y− − ≤ ∆ , using the enhanced model free control law
(23), the solution of tracking error ( )ce k is UUB where *
y∆ is a given positive constant.
Proof: The proof is similar as Theorem 2 with Corollary 1.
9. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
21
4. EXPERIMENTAL SETUP
In this section, the control algorithm is validated by the simulation model which is obtained
from the helicopter-on-arm platform [10]. First, the parameters of the non-affine nonlinear yaw
dynamic model are identified as follows
2
1 2 3 4 5 ( )tr tr tr
r
r k r k k k k d t
ϕ
ϕ θ θ θ
=
= + + + + Ω +
&
&
(24)
with 1 1.38k = − , 2 3.33k = − , 3 63.09k = , 4 11.65k = , 5 0.14k = − and 1200Ω = . It is
obviously that 2
3 4 5tr tr trk k kθ θ θ+ + Ω is a non-affine nonlinear function with respect to the control
input trθ .
For the proposed control law, we choose the sampling time 1sT = . The parameters of proposed
control law in Section III are 0.9ck = , 0.1µ = , 0.01α = , 0.2δ = , 10
10−
=ò and ˆ(1) 10φ = .
The parameter of filter (22) is 0.75ς = .
In the following simulations, the initial conditions are (0) 5ϕ = , (0) 0r = . The tracking command
of cϕ is
25,
10, 20
15, 20 40
t>40
c
t
tϕ
≤
= < ≤
Pass cϕ through a filter, such as
0.8
0.8
d
c
c
F
s
ϕ
ϕ
= =
+
. So desired trajectory
0.8
0.8
d d cy
s
ϕ ϕ= =
+
. In order to verify the robustness of our proposed method for the unknown
uncertainties/disturbances, in the simulation, the disturbance is designed to change according to the
time-varying changing, i.e.
2
2
0 deg/
( )
5sin( ) 4cos(2 ) 3co
10 t
1s(3 )sin(2 ) deg t/ 0<
s
d t
t t t t sπ π π π
=
+
≥
+
(25)
We compare two control methods, they are proposed in [17] and in this paper. System responses
are shown by the control method of [17] in Fig. 3, which are included output signals and input
signals. From Fig. 3, because of the fast time-varying disturbance (25), the close-loop control
system cannot achieve asymptotic tracking under the [17]. However, it can be seen from Fig. 4, the
tracking error significantly decreases using the proposed control method in this paper. The
proposed model free controller can achieve a better performance in the presence of same fast time-
varying disturbance (25).
10. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
22
0 10 20 30 40 50 60
0
5
10
15
20
25
30
x
1
(deg)
Time(s)
y*
y
0 10 20 30 40 50 60
-6
-4
-2
0
2
4
6
8
10
12
x
2
(deg/s)
Time(s)
0 10 20 30 40 50 60
-2
-1.5
-1
-0.5
0
0.5
Time(s)
u(deg)
Figure 3: System responses using the control approach of [17]
11. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
23
0 10 20 30 40 50 60
0
5
10
15
20
25
30
x
1
(deg)
Time(s)
y*
y
0 10 20 30 40 50 60
-6
-4
-2
0
2
4
6
8
10
12
x
2
(deg/s)
Time(s)
0 10 20 30 40 50 60
-2
-1.5
-1
-0.5
0
0.5
Time(s)
u(deg)
Figure 4: System responses using the proposed control approach in this paper.
12. International Journal of Instrumentation and Control Systems (IJICS) Vol.5, No.4, October 2015
24
5. CONCLUSIONS
We have studied a systematic study on the yaw channel of a UAV helicopter in this paper. The
yaw channel of an unmanned-aerial-vehicle helicopter is non-affine in the control input. In order
to improve operational performance, we have developed a new MFAC algorithm via CFDL. The
proposed MFAC scheme can guarantee the asymptotic output tracking of the closed-loop control
systems in spite of unknown uncertainties and disturbances. Finally, simulation results are
provided on yaw dynamics of a small-scale UAV helicopter to show the effective and advantages
of the new proposed control strategy.
ACKNOWLEDGEMENTS
This work is supported by National Natural Science Foundation of China (61503156), the
Fundamental Research Funds for the Central Universities (JUSRP11562).
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