This paper describes comparative study of various controllers on Rotary Inverted Pendulum (RIP). PID,
LQR, FUZZY LOGIC and H∞ controllers are tried on RIP in MatLab Simulink. The same four controllers
have been tested on test bed of RIP system the controllers are compared from various aspects. The
controllers in simulink are compared with the controllers in real time.
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
This project was developed for an Embedded systems class: we implemented a PID controller for a mechanical inverted pendulum. It was very interesting to experiment in practice with a simple control plant.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
This project was developed for an Embedded systems class: we implemented a PID controller for a mechanical inverted pendulum. It was very interesting to experiment in practice with a simple control plant.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
STABILIZATION AT UPRIGHT EQUILIBRIUM POSITION OF A DOUBLE INVERTED PENDULUM W...ijcsa
A double inverted pendulum plant has been in the domain of control researchers as an established model for studies on stability. The stability of such as a system taking the linearized plant dynamics has yielded satisfactory results by many researchers using classical control techniques. The established model that is analyzed as part of this work was tested under the influence of time delay, where the controller was fine tuned using a BAT algorithm taking into considering the fitness function of square of error. This proposed
method gave results which were better when compared without time delay wherein the calculated values
indicated the issues when incorporating time delay
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Analysis & Control of Inverted Pendulum System Using PID ControllerIJERA Editor
This Analysis designs a two-loop proportional–integral–derivative (PID) controller for an inverted cart– pendulum system via pole placement technique, where the (dominant) closed-loop poles to be placed at the desired locations are obtained from an Linear quadratic regulator (LQR) design. It is seen that in addition to yielding better responses (because of additional integral action) than this LQR (equivalent to two-loop PD controller) design, the proposed PID controller is robust enough. The performance and of the PID compensation are verified through simulations as well as experiments.
Mathematical model analysis and control algorithms design based on state feed...hunypink
XZ-Ⅱtype rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ-Ⅱrotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Mat lab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.
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
The Polysolenoid Linear Motor (PLM) have been playing a crucial role in many industrial aspects because it provides a straight motion directly without mediate mechanical actuators. Some control methods for PLM based on Rotational Motor are applied to obtain several good performances, but position and velocity constraints which are important in real systems are ignored. In this paper, we analysis control problem of tracking position in PLM under state-independent disturbances via min-max model predictive control. The proposed controller brings tracking position error converge to zero and satisfies state including position and velocity and input constraints. The simulation results validity a good efficiency of the proposed controller.
PID Controller Design for a Real Time Ball and Beam System – A Double Integra...idescitation
In this paper, the authors have discussed and shown
how to tune the PID controller in closed loop with time-delay
for the double integrator systems for a particular stability
margins. In math model it is assumed that time delay (ô) of
the plant is known. As a case study the authors have consid-
ered the mathematical model of the real-time beam and ball
system and analyzed the simulation and real time response.
Quadrotor is one of rotary wing UAV types which is able to perform a hover position. In order to take off, landing, and hover, it needs controllers. Conventional controllers have been widely applied in quadrotor, yet they have drawbacks namely overshoot. This paper presents attitude and altitude control algorithm in order to obtain a response as quadrotor hovered optimally within minimum overshoot, rise time, and settling time. The algorithm used is Fuzzy Logic Controller (FLC) algorithm with Mamdani method. By using the algorithm, the quadrotor is able to hover with minimum overshoot and maximum rise time. The advantage of the algorithm is that it does not require linearization model of the quadrotor.
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.
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.
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.
This paper describes comparative study of various controllers on Rotary Inverted Pendulum (RIP). PID,
LQR, FUZZY LOGIC and H∞ controllers are tried on RIP in MatLab Simulink. The same four controllers
have been tested on test bed of RIP system the controllers are compared from various aspects. The
controllers in simulink are compared with the controllers in real time.
Abstract - This paper addresses some of the potential benefits of
using fuzzy logic controllers to control an inverted pendulum
system. The stages of the development of a fuzzy logic controller
using a four input Takagi-Sugeno fuzzy model were presented.
The main idea of this paper is to implement and optimize fuzzy
logic control algorithms in order to balance the inverted
pendulum and at the same time reducing the computational time
of the controller. In this work, the inverted pendulum system was
modeled and constructed using Simulink and the performance of
the proposed fuzzy logic controller is compared to the more
commonly used PID controller through simulations using Matlab.
Simulation results show that the Fuzzy Logic Controllers are far
more superior compared to PID controllers in terms of overshoot,
settling time and response to parameter changes.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
STABILIZATION AT UPRIGHT EQUILIBRIUM POSITION OF A DOUBLE INVERTED PENDULUM W...ijcsa
A double inverted pendulum plant has been in the domain of control researchers as an established model for studies on stability. The stability of such as a system taking the linearized plant dynamics has yielded satisfactory results by many researchers using classical control techniques. The established model that is analyzed as part of this work was tested under the influence of time delay, where the controller was fine tuned using a BAT algorithm taking into considering the fitness function of square of error. This proposed
method gave results which were better when compared without time delay wherein the calculated values
indicated the issues when incorporating time delay
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Analysis & Control of Inverted Pendulum System Using PID ControllerIJERA Editor
This Analysis designs a two-loop proportional–integral–derivative (PID) controller for an inverted cart– pendulum system via pole placement technique, where the (dominant) closed-loop poles to be placed at the desired locations are obtained from an Linear quadratic regulator (LQR) design. It is seen that in addition to yielding better responses (because of additional integral action) than this LQR (equivalent to two-loop PD controller) design, the proposed PID controller is robust enough. The performance and of the PID compensation are verified through simulations as well as experiments.
Mathematical model analysis and control algorithms design based on state feed...hunypink
XZ-Ⅱtype rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ-Ⅱrotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Mat lab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.
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
The Polysolenoid Linear Motor (PLM) have been playing a crucial role in many industrial aspects because it provides a straight motion directly without mediate mechanical actuators. Some control methods for PLM based on Rotational Motor are applied to obtain several good performances, but position and velocity constraints which are important in real systems are ignored. In this paper, we analysis control problem of tracking position in PLM under state-independent disturbances via min-max model predictive control. The proposed controller brings tracking position error converge to zero and satisfies state including position and velocity and input constraints. The simulation results validity a good efficiency of the proposed controller.
PID Controller Design for a Real Time Ball and Beam System – A Double Integra...idescitation
In this paper, the authors have discussed and shown
how to tune the PID controller in closed loop with time-delay
for the double integrator systems for a particular stability
margins. In math model it is assumed that time delay (ô) of
the plant is known. As a case study the authors have consid-
ered the mathematical model of the real-time beam and ball
system and analyzed the simulation and real time response.
Quadrotor is one of rotary wing UAV types which is able to perform a hover position. In order to take off, landing, and hover, it needs controllers. Conventional controllers have been widely applied in quadrotor, yet they have drawbacks namely overshoot. This paper presents attitude and altitude control algorithm in order to obtain a response as quadrotor hovered optimally within minimum overshoot, rise time, and settling time. The algorithm used is Fuzzy Logic Controller (FLC) algorithm with Mamdani method. By using the algorithm, the quadrotor is able to hover with minimum overshoot and maximum rise time. The advantage of the algorithm is that it does not require linearization model of the quadrotor.
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.
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.
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.
This paper describes comparative study of various controllers on Rotary Inverted Pendulum (RIP). PID,
LQR, FUZZY LOGIC and H∞ controllers are tried on RIP in MatLab Simulink. The same four controllers
have been tested on test bed of RIP system the controllers are compared from various aspects. The
controllers in simulink are compared with the controllers in real time.
Abstract - This paper addresses some of the potential benefits of
using fuzzy logic controllers to control an inverted pendulum
system. The stages of the development of a fuzzy logic controller
using a four input Takagi-Sugeno fuzzy model were presented.
The main idea of this paper is to implement and optimize fuzzy
logic control algorithms in order to balance the inverted
pendulum and at the same time reducing the computational time
of the controller. In this work, the inverted pendulum system was
modeled and constructed using Simulink and the performance of
the proposed fuzzy logic controller is compared to the more
commonly used PID controller through simulations using Matlab.
Simulation results show that the Fuzzy Logic Controllers are far
more superior compared to PID controllers in terms of overshoot,
settling time and response to parameter changes.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
Vibration and tip deflection control of a single link flexible manipulatorijics
In this paper, a hybrid control scheme for vibration and tip deflection control of a single link flexible
manipulator system is presented. The purpose of this control is for input tracking, vibration control of hub
angle and tip deflection control. The control scheme consists of a resonant controller and a fuzzy logic
controller (FLC).The resonant controller is used as the inner loop feedback controller for vibration control
using the resonant frequencies at different resonant modes of the system which were determined from
experiment. The fuzzy logic controller is designed as the outer loop feedback controller for the tracking
control and to achieve zero steady state error. The performance of the proposed control scheme is
investigated via simulations and the results show the effectiveness of the control scheme, in addition the
controller is tested to show it robustness using different values of payload.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Feedback linearization and Backstepping controllers for Coupled Tanksieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms inorder
to control a nonlinear Coupled Tanks System. The first control procedure is called the
Feedbacklinearisation control (FLC), this type of control has been found a successful in achieving a global
exponentialasymptotic stability, with very short time response, no significant overshooting is recordedand with a negligible norm of the error. The second control procedure is the approaches of Backsteppingcontrol (BC) which is a recursive procedure that interlaces the choice of a Lyapunov functionwith the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may beencountered in other methods. Finally both of the proposed control schemes guarantee theasymptoticstability of the closed loop system meeting trajectory tracking objectives
FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKSieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms inorder to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedbacklinearisation control (FLC), this type of control has been found a successful in achieving a global exponentialasymptotic stability, with very short time response, no significant overshooting is recordedand with a negligible norm of the error. The second control procedure is the approaches of Backsteppingcontrol (BC) which is a recursive procedure that interlaces the choice of a Lyapunov functionwith the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may beencountered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKSieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms in order to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedback linearisation control (FLC), this type of control has been found a successful in achieving a global exponential asymptotic stability, with very short time response, no significant overshooting is recorded and with a negligible norm of the error. The second control procedure is the approaches of Back stepping control (BC) which is a recursive procedure that interlaces the choice of a Lyapunov function with the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may been countered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
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.
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.
A COMPARATIVE ANALYSIS OF FUZZY BASED HYBRID ANFIS CONTROLLER FOR STABILIZATI...ijscmcjournal
This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted
Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller
was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy
controller shows better results in comparison to triangular fuzzy controller. Secondly, an Adaptive neuro
fuzzy inference system (ANFIS) controller was used to optimize the results obtained from trapezoidal fuzzy
controller. Finally, the study illustrates the effect of variation in shape of MF's on Performance parameters
of the IP system. The results shows that ANFIS controller provides better results in comparison to both
fuzzy controller.
A Comparative Analysis of Fuzzy Based Hybrid Anfis Controller for Stabilizati...ijscmcj
This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy controller shows better results in comparison to triangular fuzzy controller. Secondly, an Adaptive neuro fuzzy inference system (ANFIS) controller was used to optimize the results obtained from trapezoidal fuzzy controller. Finally, the study illustrates the effect of variation in shape of MF's on Performance parameters of the IP system. The results shows that ANFIS controller provides better results in comparison to both fuzzy controller.
Comparative analysis of observer-based LQR and LMI controllers of an inverted...journalBEEI
An inverted pendulum is a multivariable, unstable, nonlinear system that is used as a yardstick in control engineering laboratories to study, verify and confirm innovative control techniques. To implement a simple control algorithm, achieve upright stabilization and precise tracking control under external disturbances constitutes a serious challenge. Observer-based linear quadratic regulator (LQR) controller and linear matrix inequality (LMI) are proposed for the upright stabilization of the system. Simulation studies are performed using step input magnitude, and the results are analyzed. Time response specifications, integral square error (ISE), integral absolute error (IAE) and mean absolute error (MAE) were employed to investigate the performances of the proposed controllers. Based on the comparative analysis, the upright stabilization of the pendulum was achieved within the shortest possible time with both controllers however, the LMI controller exhibits better performances in both stabilization and robustness. Moreover, the LMI control scheme is effective and simple.
Adaptive Neuro-Fuzzy Control Approach for a Single Inverted Pendulum System IJECEIAES
The inverted pendulum is an under-actuated and nonlinear system, which is also unstable. It is a single-input double-output system, where only one output is directly actuated. This paper investigates a single intelligent control system using an adaptive neuro-fuzzy inference system (ANFIS) to stabilize the inverted pendulum system while tracking the desired position. The nonlinear inverted pendulum system was modelled and built using MATLAB Simulink. An adaptive neuro-fuzzy logic controller was implemented and its performance was compared with a Sugeno-fuzzy inference system in both simulation and real experiment. The ANFIS controller could reach its desired new destination in 1.5 s and could stabilize the entire system in 2.2 s in the simulation, while in the experiment it took 1.7 s to reach stability. Results from the simulation and experiment showed that ANFIS had better performance compared to the Sugeno-fuzzy controller as it provided faster and smoother response and much less steady-state error.
Comparison of a triple inverted pendulum stabilization using optimal control ...Mustefa Jibril
In this paper, modelling design and analysis of a triple inverted pendulum have been done using
Matlab/Script toolbox. Since a triple inverted pendulum is highly nonlinear, strongly unstable
without using feedback control system. In this paper an optimal control method means a linear
quadratic regulator and pole placement controllers are used to stabilize the triple inverted
pendulum upside. The impulse response simulation of the open loop system shows us that the
pendulum is unstable. The comparison of the closed loop impulse response simulation of the
pendulum with LQR and pole placement controllers results that both controllers have stabilized
the system but the pendulum with LQR controllers have a high overshoot with long settling time
than the pendulum with pole placement controller. Finally the comparison results prove that the
pendulum with pole placement controller improve the stability of the system.
This work treats the modeling and simulation of non-linear system behavior of an induction motor using backstepping sliding mode control (BACK- SMC). First, the direct field oriented control IM is derived. Then, a sliding for direct field oriented control is proposed to compensate the uncertainties, which occur in the control. Finally, the study of Backstepping sliding controls strategy of the induction motor drive. Our non linear system is simulated in MATLAB SIMULINK environment, the results obtained illustrate the efficiency of the proposed control with no overshoot, and the rising time is improved with good disturbances rejections comparing with the classical control law.
Navigation of Mobile Inverted Pendulum via Wireless control using LQR TechniqueIJMTST Journal
Mobile Inverted Pendulum (MIP) is a non-linear robotic system. Basically it is a Self-balancing robot
working on the principle of Inverted pendulum, which is a two wheel vehicle, balances itself up in the vertical
position with reference to the ground. It has four configuration variables (Cart position, Cart Velocity,
Pendulum angle, Pendulum angular velocity) to be controlled using only two control inputs. Hence it is an
Under-actuated system. This paper focuses on control of translational acceleration and deceleration of the
MIP in a dynamically reasonable manner using LQR technique. The body angle and MIP displacement are
controlled to maintain reference states where the MIP is statically unstable but dynamically stable which
leads to a constant translational acceleration due to instability of the vehicle. In this proposal, the
implementation of self balancing robot with LQR control strategy and the implementation of navigation
control of the bot using a wireless module is done. The simulation results were compared between PID control
and LQR control strategies.
Sliding mode control-based system for the two-link robot armIJECEIAES
In this research, the author presents the model of the two-link robot arm and its dynamic equations. Based on these dynamic equations, the author builds the sliding mode controller for each joint of the robot. The tasks of the controllers are controlling the Torque in each Joint of the robot in order that the angle coordinates of each link coincide with the desired values. The proposed algorithm and robot model are built on Matlab-Simulink to investigate the system quality. The results show that the quality of the control system is very high: the response angles of each link quickly reach the desired values, and the static error equal to zero.
Similar to A Comparative study of controllers for stabilizing a Rotary Inverted Pendulum (20)
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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
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• Remote control system for accessing CCR and allied system over serial or TCP.
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Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
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A Comparative study of controllers for stabilizing a Rotary Inverted Pendulum
1. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
DOI : 10.5121/ijccms.2014.3201 1
A Comparative study of controllers for stabilizing a
Rotary Inverted Pendulum
Velchuri Sirisha and Dr. Anjali. S. Junghare
Electrical Engineering Department, Visvesvaraya National Institute of Technology,
Nagpur, India
Abstract
This paper describes comparative study of various controllers on Rotary Inverted Pendulum (RIP). PID,
LQR, FUZZY LOGIC and H∞ controllers are tried on RIP in MatLab Simulink. The same four controllers
have been tested on test bed of RIP system the controllers are compared from various aspects. The
controllers in simulink are compared with the controllers in real time.
Keywords
Fuzzy Logic, H∞, LQR, PID, RIP
1.Introduction
A typical unstable non-linear Inverted Pendulum system is often used as a benchmark to study
various control techniques in control engineering. Analysis of controllers on RIP illustrates the
analysis in cases such as control of a space booster rocket and a satellite, an automatic aircraft
landing system, aircraft stabilization in the turbulent air-flow, stabilization of a cabin in a ship etc.
RIP is a test bed for the study of various controllers like PID controller, LQR controller, and
fuzzy controller. A normal pendulum is stable when hanging downwards, an inverted pendulum
is inherently unstable, and must be actively balanced in order to remain upright, this can be done
either by applying a torque at the pivot point, by moving the pivot point horizontally as part of
a feedback system.
In this paper controllers are developed that keep the pendulum upright without any oscillations.
The model is simulated using the MATLAB application. The paper is organized as follows.
Section 2 deals with the modeling of the system, Section 3 discusses the control techniques PID,
LQR, Fuzzy Logic and H infinity controllers, Section 4 gives the test bed results, Section 5
discusses the conclusion drawn from the analysis of these controllers in simulink and on test bed.
1.Modelling of Rotary Inverted Pendulum
The system, as shown in Fig. 1, consists of a vertical pendulum, a horizontal arm, a gear chain,
and a servomotor which drives the pendulum through the gear transmission system. The rotating
arm is mounted on the output gear of the gear chain. An encoder is attached to the arm shaft to
measure the rotating angle of the arm. At the end of the rotating arm there is a hinge instrumented
with an encoder. The pendulum is attached to the hinge.
2. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
2
Fig.1. Rotary Inverted Pendulum system
The inverted pendulum is shown in Fig. 2, with its physical parameters α and θ are employed as
the generalized coordinates to describe the inverted pendulum system. The pendulum is displaced
with a given α while the arm rotates with an angle of θ.
.
Fig.2. Figure showing physical parameters to be measured
Using the Lagrangian method [1], the equation of Rotary Inverted Pendulum is as follows:
ሺܬ + ݉ݎଶሻߠሷ + ݉ݎܮ sinሺߙሻ ߙሶଶ
− ݉ݎܮ cosሺߙሻߙሷ
= ܶ − ߠܤሶ ሺ1ሻ
4
3
݉ܮଶ
ߙሷ − ݉ݎܮ cosሺߙሻߠሷ − ݉݃ܮ sin ߙ = 0 ሺ2ሻ
Where Torque T is given as, ܶ = ߟߟܭ௧ܭ
ି ఏሶ
ோ
Table I
PHYSICAL PARAMETERS OF THE SYSTEM
Parameter
Description Value(SI)
J Moment of inertia at the
load 0.0033
m Mass of pendulum arm 0.1250
r Rotating arm length 0.2150
3. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
3
L Length to pendulum’s
center of mass 0.1675
g Gravitational constant 9.81
B Viscous damping
coefficient 0.0040
ܭ௧ Motor torque constant 0.0077
ܭ SRV02 system gear ratio 70
ܭ Back-EMF constant 0.0077
ܴ Armature resistance 2.6
ߟ Motor efficiency 0.69
ߟ Gear efficiency 0.90
Solving the equations (1), (2) and (3) and values from the Table I, state space model is formed
which is written as,
൦
ߠሶ
ߙሶ
ߠሷ
ߙሷ
൪ = ൦
0 0 1 0
0 0 0 1
0 39.32 −14.52 0
0 81.78 −13.98 0
൪ ൦
ߠ
ߙ
ߠሶ
ߙሶ
൪ + ൦
0
0
25.54
24.59
൪ ܸ
The state space parameters [2] are written as,
ܣ = ൦
0 0 1 0
0 0 0 1
0 39.32 −14.52 0
0 81.78 −13.98 0
൪ ; ܤ = ൦
0
0
25.54
24.59
൪
C= ቂ
1 0 0 0
0 1 0 0
ቃ; D=0;
1.Controller Design
3.1 PID Controller
Proportional, integral derivative are the controllers whose output, a control variable (CV), is
generally based on the error (e) between some user-defined set point (SP) and some measured
process variable (PV).
4. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
4
Fig.3. Schematic diagram for the closed loop system with force as a disturbance
The transfer function of PID is written as [3]
ܭሺݏሻ = ܭ +
ܭ
ݏ
+ ܭௗݏ
Manual tuning method is used to determine the gains [4].
Ki and Kd are set to zero. Then, Kp is increased until the output of the loop oscillates, after
obtaining optimum Kp value, it is set to approximately half of that value for a "quarter amplitude
decay" type response. Then, Ki is increased until any offset is corrected in sufficient time for the
process. However, too much Ki will cause instability. Finally, Kd is increased, until the loop is
acceptably quick to reach its reference after a load disturbance [5].
Fig.4. Simulink diagram of system using PID controller
Tuning the gain values Kp, Ki, Kd with 4, 2, 0.5 respectively along with a negative feedback as
shown in the simulink model of Fig.4, the position of pendulum gets stabilized as shown in Fig 5.
5. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
5
Fig.5 Variation of pendulum angle alpha (deg) with time (sec)
From Fig 5, it is observed that using PID control pendulum angle becomes zero within 1 second.
3.2 LQR Controller
LQR is a method in modern control theory that uses state-space approach to analyze a system like
inverted pendulum. The theory of optimal control is concerned with operating a dynamic
system at minimum cost. The case where system dynamics are described by a set of linear
differential equations and the cost is described by quadratic functions which are called LQ
problem [6]. The goal of such problem is to find an optimal control that minimizes a quadratic
cost functional associated with a linear system.
A system is expressed in state variable form as,
ݔሶ = ݔܣ + ݑܤሺ3ሻ
The initial condition is x (0). Assuming here all the states measurable and seek to find a state-
variable feedback (SVFB) control
ݑ = −ݔܭ + ݒ (4)
To design a SVFB that is optimal, an Index called performance index (PI) is used and is given by,
ܬ =
1
2
න ሺݔ்
ஶ
ܳݔ + ݑ்
ܴ ݑሻ݀ ݐሺ5ሻ
Substituting the SVFB control equation in equation (1) yields
ܬ =
1
2
න ݔ்
ஶ
ሺܳ + ܭ்
ܴ ܭሻ ݐ݀ ݔሺ6 ሻ
The objective in optimal design is to select the SVFB K that minimizes the performance index J.
Solving equations(3) to (6), equation (7) is obtained,
ܣ்
ܲ + ܲܣ + ܳ + ܭ்
ܴܭ − ܭ்
ܤ்
ܲ − ܲܭܤ = 0 (7)
taking, ܭ = ܴିଵ
ܤ்
ܲ
it gives, ܣ்
ܲ + ܲܣ + ܳ − ܴܲܤିଵ
ܤ்
ܲ = 0
It is a matrix quadratic equation that is solved to get the value of auxiliary matrix P. After getting
the value of matrix P, SVFB gain K is determined.
6. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
6
Gain value is found as,
K = [-1.13 14.5 -1.44 2.46]
Fig.6 Simulink diagram of system using LQR control
By substituting the SVFB gain into the system and implemented in Simulink model of Fig.6,
system gets stabilized. Fig 7 is the response of the pendulum position of the system.
Fig. 7 Variation of pendulum position α (in deg) w.r.t time (in sec)
From Fig 7, it is observed that using LQR control, pendulum angle becomes zero within 1.5
seconds. Rotary Inverted Pendulum is stabilized at 34 degrees, and arm velocity becomes zero
within 2 seconds.
Hence, Rotary Inverted Pendulum is stable within 1.5 seconds.
3.3 Fuzzy Logic Controller (FLC)
FLC provides a simple way to arrive at a definite conclusion based upon vague, ambiguous,
imprecise, noisy, or missing input information [7]. FLC's approach to control problems mimics
how a person makes decisions. Fuzzy control describes the algorithm for process control as a
fuzzy relation between information about the condition of the process to be controlled, x and y
and the input for the process. The control algorithm is given in the IF - THEN expression such as
if x is small and y is big then z is medium.
if x is big and y is medium, then z is big.
7. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
7
The input and output variables as shown in FIS editor in Fig.8 are quantized into several modules
or fuzzy subsets and the appropriate labels are assigned in this controller [8].
Fig. 8 FIS editor with two input and one output
There is FLC to control pendulum angle. Five fuzzy subsets have been taken to quantize each
fuzzy variable for FLC as shown in Table II.
Table II
STANDARD LABELS OF QUANTIZATION
Linguistic Term Label
Negative big NB
Negative small NS
Zero ZE
Positive small PS
Positive big PB
Depending upon the range of alpha and alpha_dot, controlled voltage is decided. If alpha is NB
and alpha_dot is PB then according to the rule base shown in Table III, the voltage applied to the
system is zero.
Table III
FUZZY RULE BASE
8. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
8
Fig. 9 and Fig.10 shows the simulink model and simulation result of the system using fuzzy logic
controller:
Fig. 9. Simulink diagram of system for fuzzy logic controller
Fig. 10. Variation of pendulum angle with time (sec)
From results it is concluded that using fuzzy logic controller Rotary Inverted pendulum is
stabilized within 0.5 sec.
3.4 H infinity controller
In order to achieve robust performance or stabilization, the H-Infinity control method is used.
The H∞ name derives from the fact that mathematically the problem may be set in the space H∞,
9. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
9
which consists of all bounded functions that are analytic in the right-half complex plane [9]. H∞
method is also used to minimize the closed loop impact of a perturbation depending on the
problem formulation the impact will be measured in terms of either stabilization or performance.
This problem is defined by the configuration of Fig 11.
Fig.11 Generalized plant
The “plant” is a given system with two inputs and two outputs. It is often referred to as the
generalized plant [9]. The signal w is an external input and represents driving signals that
generate disturbances, measurement noise, and reference inputs. The signal u is the control input.
The output z has the meaning of control error and ideally should be zero. The output y, finally, is
the observed output and is available for feedback.
The augmented plant is formed by accounting for the weighting functions W1, W2, and W3 as
shown in the Fig 12.
Fig.12. Plant with weighting functions for H∞ design
Choosing weights W1, W2 and W3 as,
W1=0.99*(s+50)/(s+.001);
W2=1;
W3=10*(s+50)/(s+500);
Using weights, controller in the form of state space form is obtained,
10. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
10
A =
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
−0.001 0 0 0 0
8.356e − 025 −500 82.33 0 0
6.685e − 024 −3.829e − 007 −15.08 0 1
−110.9 0.6872 −425.9 48.48 −84.08
−106.7 0.6616 −454 46.67 −80.95ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
;
B =
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
11.11
−3.961
−23.69
−42.23
−178.7ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
;
C =[−2.763 0.01 −10.92 1.57 −2];
D = [0];
The new state space model which is obtained is implemented in simulink diagram (Fig.13) as a
feedback and pendulum angle alpha is observed in Fig.14.
Fig.13. Simulink diagram of system using H infinity control
Fig.14 Variation of pendulum angle with time (sec)
11. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
11
1.Test Bed Results
4.1 PID Controller
Real time results of alpha i.e. pendulum angle using PID control is shown in Fig.15. Here,
controller is activated as soon as pendulum reaches to the reference position and pendulum is
stabilized.
Fig.15 Real time result of system using PID control
4.2 LQR Controller
Fig.16 Real time result of system using LQR control
Fig.16 shows the real time results of alpha i.e. pendulum angle and controlled voltage using
Linear Quadratic Control. Here, pendulum is oscillating between 1 and -3 degrees which is
approximately negligible.
Time (sec)
Alpha(deg)
Time (sec)
Alpha(deg)
12. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
12
4.3 Fuzzy Logic Controller
Fig.17 Real time result of system using FUZZY LOGIC control
Fig.17 shows the real time results of alpha i.e. pendulum angle and controlled voltage using fuzzy
logic controller. Here, controller is activated as soon as pendulum reaches to the reference
position and pendulum is slightly oscillating.
1.Conclusion
5.1 COMPARISON OF SIMULATION RESULTS
In this section comparison of all the four controllers based on Simulation Results are discussed.
Parameters compared are percentage peak overshoot and rise time as shown in Table IV.
Table IV
Comparison of controllers based on simulation results
Controller
Peak overshoot
(%Mp)
Rise time (tr)
PID 0.3 0.1
LQR 4.8 0.1
Fuzzy Logic 0.09 0.05
H∞ 7.8 0.25
Comparing simulation results of all the four controllers, from the Table IV, it is concluded that,
percentage peak overshoot is less in case of Fuzzy Logic controller as compared to other three
controllers. Rise time is also less for this controller.
5.2 COMPARISON OF TEST BED RESULTS
Time (sec)
Alpha(deg)
13. International Journal of Chaos, Control, Modelling and Simulation (IJCCMS) Vol.3, No.1/2, June 2014
13
In this section comparison of all the four controllers based on Test bed Results are discussed.
Parameters compared are percentage peak overshoot and rise time as shown in Table V.
Table V : Comparison of controllers based on Test Bed results
Controller
Peak overshoot
(%Mp)
Rise time (tr)
PID 2 0.3
LQR 2.5 0.5
Fuzzy Logic 10 0.1
H∞ -- --
Comparing test bed results of PID, LQR and FUZZY LOGIC, from the Table V it is concluded
that, percentage peak overshoot as well as rise time of response is less for LQR controller as
compared to PID and Fuzzy Logic controller
1.REFERENCES
[1] Quanser Inc.SRV02 Exp7 Inverted Pendulum.pdf.2003
[2] Quanser Inc.SRV02 Exp1 position control.pdf.2003
[3] T.Sugie and K. Fujimoto, “Controller design for an inverted pendulum based on approximate
linearization,” Int. J. of Robust and Nonlinear control, vol. 8, no 7, pp. 585-597, 1998.
[4] Katebi M R and M.H. Moradi (2001):“Predictive PID Controllers”. IEE Proc. Control Theory
Application, Vol. 148, No. 6; November 2001, pp. 478-487.
[5] K. Ang, G. Chong, and Y. Li, “PID control system analysis, design and technology,” IEEE
Trans.Control System Technology, vol. 13, pp. 559-576, July 2005.
[6] Md. Akhtaruzzaman and A. A. Shafie, “Modeling and Control of a Rotary Inverted Pendulum Using
Various Methods, Comparative Assessment and Result Analysis”, Proceedings of the 2010 IEEE,
International Conference on Mechatronics and Automation, August 4-7, 2010, Xi'an, China
[7] Chen Wei Ji, Fang Lei, Lei Kam Kin, I997 IEEE International Conference on Intelligent Processing
System October 28 - 31.“Fuzzy Logic Controller for an Inverted Pendulum System”
[8] Muskinja, N. and B. Tovornik, 2006. “Swinging up and stabilization of a real Inverted pendulum”.
IEEE Trans. Ind. Elect., 53. DOI: 10.1109/TIE.2006.870667
[9] Ximena CeliaM´endez Cubillos and Luiz Carlos Gadelha de Souza, 2009.“Using of H-Infinity Control
Method in Attitude Control System of Rigid-Flexible Satellite”, Hindawi Publishing Corporation
Mathematical Problems in Engineering Volume 2009, Article ID 173145, 9 pages
doi:10.1155/2009/173145