scholarly journals Robust Takagi-Sugeno Fuzzy Dynamic Regulator for Trajectory Tracking of a Pendulum-Cart System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Miguel A. Llama ◽  
Wilfredo De La Torre ◽  
Francisco Jurado ◽  
Ramon Garcia-Hernandez
Keyword(s):  
Trajectory Tracking ◽  
Fuzzy Controller ◽  
Reference Signal ◽  
Fuzzy Model ◽  
Viscous Friction ◽  
Upright Position ◽  
Linear Matrix ◽  
Fuzzy Controllers ◽  
Fuzzy Partition ◽  
Takagi Sugeno

Starting from a nonlinear model for a pendulum-cart system, on which viscous friction is considered, a Takagi-Sugeno (T-S) fuzzy augmented model (TSFAM) as well as a TSFAM with uncertainty (TSFAMwU) is proposed. Since the design of a T-S fuzzy controller is based on the T-S fuzzy model of the nonlinear system, then, to address the trajectory tracking problem of the pendulum-cart system, three T-S fuzzy controllers are proposed via parallel distributed compensation: (1) a T-S fuzzy servo controller (TSFSC) designed from the TSFAM; (2) a robust TSFSC (RTSFSC) designed from the TSFAMwU; and (3) a robust T-S fuzzy dynamic regulator (RTSFDR) designed from the RTSFSC with the addition of a T-S fuzzy observer, which estimates cart and pendulum velocities. Both TSFAM and TSFAMwU are comprised of two fuzzy rules and designed via local approximation in fuzzy partition spaces technique. Feedback gains for the three fuzzy controllers are obtained via linear matrix inequalities approach. A swing-up controller is developed to swing the pendulum up from its pendant position to its upright position. Real-time experiments validate the effectiveness of the proposed schemes, keeping the pendulum in its upright position while the cart follows a reference signal, standing out the RTSFDR.

scholarly journals Electronic Throttle Valve Takagi-Sugeno Fuzzy Control Based on Nonlinear Unknown Input Observers

2018 ◽  
Vol 13 (5) ◽  
pp. 808-823
Author(s):  
Wafa Gritli ◽  
Hajer Gharsallaoui ◽  
Mohamed Benrejeb ◽  
Pierre Borne
Keyword(s):  
Control Strategy ◽  
Fuzzy Controller ◽  
Reference Signal ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Unknown Input ◽  
Electronic Throttle ◽  
Throttle Valve ◽  
Unknown Input Observers ◽  
Takagi Sugeno

This paper deals with the synthesis of a new fuzzy controller applied to Electronic Throttle Valve (ETV) affected by an unknown input in order to enhance the rapidity and accuracy of trajectory tracking performance. Firstly, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate this nonlinear system. Secondly, a novel Nonlinear Unknown Input Observer (NUIO)-based controller is designed by the use of the concept of Parallel Distributed Compensation (PDC). Then, based on Lyapunov method, asymptotic stability conditions of the error dynamics are given by solving Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed control strategy in terms of tracking trajectory and in the presence of perturbations is verified in comparison with a control strategy based on Unknown Input Observers (UIO) of the ETV described by a switched system for Pulse-Width-Modulated (PWM) reference signal.

scholarly journals Further results on robust fuzzy dynamic systems with LMI D-stability constraints

2014 ◽  
Vol 24 (4) ◽  
pp. 785-794 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Local System ◽  
Linear Matrix ◽  
Fuzzy Modelling ◽  
Ts Fuzzy Model ◽  
Input Noise ◽  
Takagi Sugeno

Abstract This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

scholarly journals Q-learning trajectory planning based on Takagi–Sugeno fuzzy parallel distributed compensation structure of humanoid manipulator

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141983020 ◽  
Author(s):  
Shuhuan Wen ◽  
Xueheng Hu ◽  
Xiaohan Lv ◽  
Zongtao Wang ◽  
Yong Peng
Keyword(s):  
Reinforcement Learning ◽  
Trajectory Planning ◽  
Trajectory Tracking ◽  
Fuzzy Controller ◽  
Learning Algorithm ◽  
Fuzzy Model ◽  
Large Error ◽  
Learning Trajectory ◽  
Tracking Accuracy ◽  
Takagi Sugeno

NAO is the first robot created by SoftBank Robotics. Famous around the world, NAO is a tremendous programming tool and he has especially become a standard in education and research. Aiming at the large error and poor stability of the humanoid robot NAO manipulator during trajectory tracking, a novel framework based on fuzzy controller reinforcement learning trajectory planning strategy is proposed. Firstly, the Takagi–Sugeno fuzzy model based on the dynamic equation of the NAO right arm is established. Secondly, the design and the gain solution of the state feedback controller based on the parallel feedback compensation strategy are studied. Finally, the ideal trajectory of the motion is planned by reinforcement learning algorithm so that the end of the manipulator can track the desired trajectory and realize the valid obstacle avoidance. Simulation and experiment shows that the end of the manipulator based on this scheme has good controllability and stability and can meet the accuracy requirements of trajectory tracking accuracy, which verifies the effectiveness of the proposed framework.

DELAYED FUZZY CONTROLLER DESIGN FOR HYPERCHAOS WITH APPLICATION TO HYPERCHAOTIC CHEN'S SYSTEM

2007 ◽  
Vol 18 (07) ◽  
pp. 1095-1105 ◽  
Author(s):  
XINGWEN LIU ◽  
XIN GAO
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed State Feedback ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Compensation Design ◽  
Hyperchaotic Systems ◽  
Control Criterion

Studied in this paper is the control problem of hyperchaotic systems. By combining Takagi–Sugeno (T–S) fuzzy model with parallel distributed compensation design technique, we propose a delay-dependent control criterion via pure delayed state feedback. Because the result is expressed in terms of linear matrix inequalities (LMIs), it is quite convenient to check in practice. Based on this criterion, a procedure is provided for designing fuzzy controller for such systems. This method is a universal one for controlling continuous hyperchaotic systems. As illustrated by its application to hyperchaotic Chen's system, the controller design is quite effective.

Takagi-Sugeno Fuzzy Load-Following Control of Nuclear Reactors Based on Reactor Point Kinetics Equations

2014 ◽  
Author(s):  
Xiuchun Luan ◽  
Jie Zhou ◽  
Yu Zhai
Keyword(s):  
Control System ◽  
Linear Models ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Neutron Density ◽  
Load Following ◽  
Wide Range ◽  
Takagi Sugeno ◽  
Operating Points

A state differential feedback control system based Takagi-Sugeno (T-S) fuzzy model is designed for load-following operation of nonlinear nuclear reactor whose operating points vary within a wide range. Linear models are first derived from the original nonlinear model on several operating points. Next the fuzzy controller is designed via using the parallel distributed compensation (PDC) scheme with the relative neutron density at the equilibrium point as the premise variable. Last the stability analysis is given by means of linear matrix inequality (LMI) approach, thus the control system is guaranteed to be stable within a large range. The simulation results demonstrate that the control system works well over a wide region of operation.

scholarly journals Nonlinear modelling and optimal control via Takagi-Sugeno fuzzy techniques: A quadrotor stabilization

2020 ◽  
Vol 71 (1) ◽  
pp. 1-10
Author(s):  
Miroslav Pokorný ◽  
Tomáš Dočekal ◽  
Danica Rosinová
Keyword(s):  
Closed Loop ◽  
Fuzzy Controller ◽  
Fitness Function ◽  
Fuzzy Model ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Fuzzy Aggregation ◽  
Takagi Sugeno

AbstractUsing the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.

Further Results on T-S Fuzzy Controller Design Subject to Input Constraint

2008 ◽  
Vol 12 (2) ◽  
pp. 190-197 ◽  
Author(s):  
Hugang Han ◽  
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Input Constraint ◽  
Initial State ◽  
Control Gain ◽  
Matrix Variable ◽  
Takagi Sugeno

In general, when using the Takagi-Sugeno (T-S) fuzzy model to develop a control system, the state feedback control gain can be obtained by solving some linear matrix inequalities (LMIs). In this paper, we consider a class of nonlinear systems with input constraint (saturation). To obtain the control gain, we require to employ certain extra LMIs besides the general ones. As a result, all the LMIs are more conservative. At the same time, one of the extra LMIs confines the initial state to a region, which is referred to as an ellipsoid, and is relevant to a matrix variable in the LMIs. Therefore, the goals of this paper are: 1) making the ellipsoid as large as possible so that the initial state can be confined to the region easily and; 2) making all the LMIs more feasible to obtain the control gain.

scholarly journals Improved T-S Fuzzy Control for Uncertain Time-Delay Coronary Artery System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Zhenyu Zhu ◽  
Zhanshan Zhao ◽  
Haoliang Cui ◽  
Fengdong Shi
Keyword(s):  
Coronary Artery ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Practical Significance ◽  
Linear Matrix ◽  
System State ◽  
Fuzzy Models ◽  
The Stability ◽  
Uncertain Time ◽  
Takagi Sugeno

This paper is based on the Takagi-Sugeno (T-S) fuzzy models to construct a coronary artery system (CAS) T-S fuzzy controller and considers the uncertainties of system state parameters in CAS. We propose the fuzzy model of CAS with uncertainties. By using T-S fuzzy model of CAS and the use of parallel distributed compensation (PDC) concept, the same fuzzy set is assigned to T-S fuzzy controller. Based on this, a PDC controller whose fuzzy rules correspond to the fuzzy model is designed. By constructing a suitable Lyapunov-Krasovskii function (LKF), the stability conditions of the linear matrix inequality (LMI) are exported. Simulation results show that the method proposed in this paper is correct and effective and has certain practical significance.

scholarly journals Control of a Variable Blade Pitch Wind Turbine Subject to Gust Wind and Actuators Saturation

2021 ◽  
Vol 11 (17) ◽  
pp. 7865
Author(s):  
Chokri Sendi
Keyword(s):  
Wind Turbine ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
External Disturbances ◽  
Control Gain ◽  
Dynamics And Control ◽  
Takagi Sugeno ◽  
And Control ◽  
The Mathematical Model

This paper examines the dynamics and control of a variable blade pitch wind turbine during extreme gust wind and subject to actuators saturation. The mathematical model of the wind turbine is derived using the Lagrange dynamics. The controller is formulated using the Takagi–Sugeno fuzzy model and utilizes the parallel distributor compensator to obtain the feedback control gain. The controller’s objective is to obtain the generator electromagnetic torque and the blade pitch angle to attenuate the external disturbances. The (T–S) fuzzy controller with disturbances rejection properties is developed using the linear matrix inequalities technic and solved as an optimization problem. The efficacy of the proposed (T–S) fuzzy controller is illustrated via numerical simulations.

Robust Stability and Stabilization of Fractional Order Systems Based on Uncertain Takagi-Sugeno Fuzzy Model With the Fractional Order 1≤v < 2

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Li Junmin ◽  
Li Yuting
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Stability And Stabilization ◽  
Takagi Sugeno ◽  
Robust Stability And Stabilization

This paper addresses the problems of the robust stability and stabilization for fractional order systems based on the uncertain Takagi-Sugeno fuzzy model. A sufficient and necessary condition of asymptotical stability for fractional order uncertain T-S fuzzy model is given, and a parallel distributed compensate fuzzy controller is designed to asymptotically stabilize the model. The results are obtained in terms of linear matrix inequalities. Finally, a numerical example and fractional order Van der Pol system are given to show the effectiveness of our results.

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