Design of Robust Modified Repetitive-Control System for Linear Periodic Plants

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Lan Zhou ◽  
Jinhua She ◽  
Min Wu ◽  
Jie Zhang
Keyword(s):  
Control System ◽  
Repetitive Control ◽  
Robust Stabilization ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Stabilization Problem ◽  
Tuning Parameters ◽  
2D System ◽  
Asymptotic Stability Condition

This paper concerns a linear-matrix-inequality (LMI)-based method of designing a robust modified repetitive-control system (MRCS) for a class of strictly proper plants with periodic uncertainties. It exploits the nature of control and learning and the periodicity and continuity of repetitive control to convert the design problem into a robust stabilization problem for a continuous-discrete 2D system. The LMI technique and Lyapunov stability theory are used to derive an LMI-based asymptotic stability condition that can be used directly in the design of the gains of the repetitive controller. Two tuning parameters in the condition enable preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.

Mathematical Modeling and Robust Control for Beam Reheating Furnace

2013 ◽  
Vol 380-384 ◽  
pp. 209-214
Author(s):  
Ling Yan Hu ◽  
Ling Yan Hu
Keyword(s):  
Robust Stabilization ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Stabilization Problem ◽  
Robust Controller ◽  
Nonlinear Characteristics ◽  
Reheating Furnace ◽  
Simulation Results ◽  
The Mathematical Model

According to the large beam reheating furnace widely used in metallurgy area, the mathematical model was built basing on the heat transfer. Considering the uncertain and nonlinear characteristics existing in the system, the robust stabilization problem of the system is investigated basing on Lyapunov stability theory and linear matrix inequality (LMI) method. The robust controller is designed. A numerical example and its simulation results are given.

Design of Repetitive-Control System With Input Dead Zone Based on Generalized Extended-State Observer

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Min Wu ◽  
Pan Yu ◽  
Xin Chen ◽  
Jinhua She
Keyword(s):  
Control System ◽  
Dead Zone ◽  
Repetitive Control ◽  
State Observer ◽  
Control Technique ◽  
Linear Matrix ◽  
Tuning Parameters ◽  
Assignment Method ◽  
Exogenous Disturbance ◽  
The Stability

This paper concerns a repetitive-control system with an input-dead-zone (IDZ) nonlinearity. First, the expression for the IDZ is decomposed into a linear term and a disturbance-like one that depends on the parameters of the dead zone. A function of the system-state error is used to approximate the combination of the disturbancelike term and an exogenous disturbance. The estimate is used to compensate for the overall effect of the IDZ and the exogenous disturbance. Next, the state-feedback gains are obtained from a linear matrix inequality that contains two tuning parameters for adjusting control performance; and the pole assignment method is employed to design the gain of a state observer. Then, two stability criteria are used to test the stability of the closed-loop system. The method is simple, employing neither an inverse model of the plant nor an adaptive control technique. It is also robust with regard to the different parameters of the IDZ, uncertainties in the plant, and the exogenous disturbance. Finally, two numerical examples demonstrate the effectiveness of this method and its advantages over others.

scholarly journals A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Ting-Ting Gang ◽  
Jun Yang ◽  
Qing Gao ◽  
Yu Zhao ◽  
Jianbin Qiu
Keyword(s):  
Nonlinear Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Dynamic Feedback ◽  
Stabilization Problem ◽  
Fuzzy Models ◽  
Quadratic Lyapunov Functions ◽  
Affine Nonlinear Systems ◽  
Semiglobal Stabilization ◽  
Approximation Capability

This paper investigates the stabilization problem for a class of discrete-time stochastic non-affine nonlinear systems based on T-S fuzzy models. Based on the function approximation capability of a class of stochastic T-S fuzzy models, it is shown that the stabilization problem of a stochastic non-affine nonlinear system can be solved as a robust stabilization problem of the stochastic T-S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non-affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.

Stabilization of Fuzzy Markovian Jumping Systems with Distributed Delay

2014 ◽  
Vol 556-562 ◽  
pp. 4386-4390
Author(s):  
Zhao Ping Yuan
Keyword(s):  
Time Delay ◽  
Robust Stabilization ◽  
Distributed Delay ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
Markovian Jumping Systems ◽  
Distributed Time Delay ◽  
Delay Dependent

This paper is concerned with the stabilization problem for fuzzy Markovian jumping systems with distributed time delay. First, fuzzy Markovian jumping systems with distributed time delay are peoposed. Second, a novel criterion of delay-dependent robust stabilization for fuzzy Markovian jumping systems is established in terms of linear matrix inequalities (LMIs) by using Lyapunov stability theory and free-weighting matrix method. When these LMIS are feasible, an explicit expression of a desired adjustable state feedback controller is given. Based on the obtained criterion, the introduced controller ensures the overall closed-loop system asymptotically stable in mean square sense for all admissible uncertainties and time delay.

Nonlinear Position Control of Digital Hydraulic Cylinder Despite Disturbance

2014 ◽  
Vol 998-999 ◽  
pp. 638-641
Author(s):  
Shi Jie Xu ◽  
J.F. Xing ◽  
Li Kun Peng
Keyword(s):  
Control System ◽  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Nonlinear Model ◽  
Position Control ◽  
Hydraulic Cylinder ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Nonlinear Controller ◽  
Position Control System

A nonlinear controller is presented for a digital hydraulic cylinder against disturbance. We first establish the nonlinear model of digital hydraulic cylinder position control system. Then a Lyapunov function and a nonlinear controller are presented. The controller designing problem is translated into the problem of solving a linear matrix inequality. The experiment results show that the controller proposed by this paper has much better performance than traditional one.

scholarly journals Robust Stabilization andH∞Control for Uncertain Neural Networks with Mixed Time Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Bin Wen ◽  
Hui Li ◽  
Li Liang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Time Delays ◽  
Convex Combination ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
Uncertain Neural Networks

This paper is concerned with the problem of robust stabilization andH∞control for a class of uncertain neural networks. For the robust stabilization problem, sufficient conditions are derived based on the quadratic convex combination property together with Lyapunov stability theory. The feedback controller we design ensures the robust stability of uncertain neural networks with mixed time delays. We further design a robustH∞controller which guarantees the robust stability of the uncertain neural networks with a givenH∞performance level. The delay-dependent criteria are derived in terms of LMI (linear matrix inequality). Finally, numerical examples are provided to show the effectiveness of the obtained results.

scholarly journals A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

2014 ◽  
Vol 24 (2) ◽  
pp. 325-334 ◽  
Author(s):  
Lan Zhou ◽  
Jinhua She ◽  
Shaowu Zhou
Keyword(s):  
Control System ◽  
Output Feedback ◽  
Repetitive Control ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Control Input ◽  
Dynamic Output Feedback ◽  
Output Feedback Controller ◽  
Dynamic Output ◽  
Dynamic Output Feedback Controller

Abstract This paper is concerned with the problem of designing a robust modified repetitive-control system with a dynamic output feedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value decomposition of the output matrix and Lyapunov stability theory are used to derive an asymptotic stability condition based on a Linear Matrix Inequality (LMI). Two tuning parameters in the LMI manipulate the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.

LMI-BASED ANALYSIS FOR CONTINUOUS-DISCRETE LINEAR SHIFT-INVARIANT nD SYSTEMS

2005 ◽  
Vol 14 (02) ◽  
pp. 307-332 ◽  
Author(s):  
JACEK BOCHNIAK ◽  
KRZYSZTOF GALKOWSKI
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Robust Stabilization ◽  
Multidimensional Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lmi Approach ◽  
Stability Margins ◽  
Nd Systems

In this paper, we describe the Linear Matrix Inequality (LMI) approach to the analysis and the synthesis of continuous-discrete linear shift-invariant multidimensional systems presented in the Roesser form. We consider stability, stability margins, robust stability, stabilization and stabilization to the prescribed stability margins and robust stabilization. An example is included as illustrations of the obtained results.

Sign in / Sign up

Export Citation Format

Share Document