An Eclectic Approach to the State Feedback Control of Nonlinear Dynamical Systems

1989 ◽  
Vol 111 (4) ◽  
pp. 631-640 ◽  
Author(s):  
S. H. Z˙ak
Keyword(s):  
Dynamical Systems ◽  
Feedback Linearization ◽  
State Feedback ◽  
Nonlinear Dynamical Systems ◽  
Sliding Mode ◽  
Design Method ◽  
Variable Structure ◽  
High Gain ◽  
Feedback Stabilization ◽  
State Feedback Control

This paper examines the problem of robust state-feedback stabilization of a class of nonlinear multi-input dynamical systems. Four approaches to the problem are investigated: the variable structure control (VSC) method, the high-gain feedback technique, the feedback linearization algorithm, and finally the deterministic approach to the control of uncertain systems. It is shown that each design method can lead to a controller such that the closed-loop system exhibits a sliding mode property. The sliding mode is a desirable property since it results in a robust control. The analysis is illustrated by means of a simple numerical example.

scholarly journals Non-smooth Modeling and Variable Structure Control of a Class of Hybrid Dynamical Systems

2021 ◽  
Vol 2090 (1) ◽  
pp. 012108
Author(s):  
Yasser A. Bin Salamah
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Feedback Linearization ◽  
Controller Design ◽  
Sliding Mode ◽  
Variable Structure ◽  
Hybrid Dynamical Systems ◽  
Structure Control ◽  
Output Tracking ◽  
Output Tracking Control

Abstract In this work, we propose a modeling formulation and controller design for a class of hybrid dynamical systems. In this formulation, a switching dynamical system is modeled as a dynamical system with discontinuous right hand side. More specifically, the system is transformed to a nonlinear system with discontinuous nonlinearities. Then, a synthesis of feedback linearization and sliding mode control is employed for output tracking control problem. Application and implementation of this approach is illustrated via a chemical process example.

Sampled-Data State Feedback Stabilization of Boolean Control Networks

2016 ◽  
Vol 28 (4) ◽  
pp. 778-799 ◽  
Author(s):  
Yang Liu ◽  
Jinde Cao ◽  
Liangjie Sun ◽  
Jianquan Lu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Global Stabilization ◽  
Sampled Data ◽  
Control Networks ◽  
Piecewise Constant Control ◽  
Necessary And Sufficient

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

scholarly journals Variable structure observer design for a class of uncertain systems with a time-varying delay

2012 ◽  
Vol 22 (3) ◽  
pp. 575-583 ◽  
Author(s):  
Wen-Jeng Liu
Keyword(s):  
Uncertain Systems ◽  
Sliding Mode ◽  
Variable Structure ◽  
Observer Design ◽  
State Feedback Control ◽  
Invariance Property ◽  
Time Varying ◽  
Time Varying Delay ◽  
Error System ◽  
Varying Delay

Abstract Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.

State Feedback Linearization of a Non-linear Permanent Magnet Synchronous Motor Drive

2016 ◽  
Vol 1 (3) ◽  
pp. 534 ◽  
Author(s):  
Pilla Ramana ◽  
Karlapudy Alice Mary ◽  
Munagala Surya Kalavathi
Keyword(s):  
Control System ◽  
Feedback Linearization ◽  
State Feedback ◽  
Permanent Magnet Synchronous Motor ◽  
Pi Controller ◽  
State Feedback Control ◽  
Pole Placement ◽  
Motor Speed ◽  
Control Loops ◽  
Non Linear

Control system design for inverter fed drives previously used the classical transfer function approach for single-input singleoutput (SISO) systems. Proportional plus Integral (PI) controllers were designed for individual control loops.It is found that the transient response of a PI controller is slow and is improved by pole placement through state feedback. However, the effective gains of the PI controller are substantially decreased as a function of the increase of motor speed. A control system is generally characterized by the hierarchy of the control loops, where the outer loop controls the inner loops. The inner loops are designed to execute progressively faster. The speed controller (PI controller) processes the speed error and generates the reference torque. In the inner loop, firstly a non-linear controller is designed for the system by which the system nonlinearity is canceled using state or exact feedback linearization. In addition, a linear state feedback control law based on pole placement technique including the integral of output error (IOE) is used in order to achieve zero steady state error with respect to reference current specification, while at the same time improving the dynamic response.The proposed scheme has been validated through extensive simulation using MATLAB.

Design of Spacecraft Controller Based on Adaptive Fuzzy Sliding Mode Variable Structure

2013 ◽  
Vol 380-384 ◽  
pp. 278-281
Author(s):  
Ju Huo ◽  
Jia Shan Cui
Keyword(s):  
Sliding Mode Control ◽  
Feedback Linearization ◽  
Sliding Mode ◽  
Variable Structure ◽  
External Interference ◽  
Adaptive Fuzzy ◽  
Mode Control ◽  
Adaptive Fuzzy Sliding Mode ◽  
Fuzzy Sliding Mode ◽  
Sliding Mode Variable Structure

Using of feedback linearization technique to solve the problem of traditional sliding mode control chattering. The fuzzy adaptive control and sliding mode variable structure was designed by combining a novel adaptive fuzzy sliding mode variable structure controller. Through fuzzy inference and the stability analysis based on Lyapunov function to obtain fuzzy control rules adaptive law and effective solution to the traditional sliding mode control of the need to determine the parameter perturbation and external interference supremum uncertainty. Simulation results show that this method has better stability and robustness.

Single state feedback stabilization of unified chaotic systems and circuit implementation

Open Physics ◽  
2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Chun-Guo Jing ◽  
Ping He ◽  
Tao Fan ◽  
Yangmin Li ◽  
Changzhong Chen ◽  
...  
Keyword(s):  
Chaotic System ◽  
State Feedback ◽  
Chaotic Systems ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Uncertain Parameter ◽  
Circuit Implementation ◽  
Unified Chaotic System ◽  
Unified Chaotic Systems ◽  
Single State

AbstractThis paper focuses on the single state feedback stabilization problem of unified chaotic system and circuit implementation. Some stabilization conditions will be derived via the single state feedback control scheme. The robust performance of controlled unified chaotic systems with uncertain parameter will be investigated based on maximum and minimum analysis of uncertain parameter, the robust controller which only requires information of a state of the system is proposed and the controller is linear. Both the unified chaotic system and the designed controller are synthesized and implemented by an analog electronic circuit which is simpler because only three variable resistors are required to be adjusted. The numerical simulation and control in MATLAB/Simulink is then provided to show the effectiveness and feasibility of the proposed method which is robust against some uncertainties. The results presented in this paper improve and generalize the corresponding results of recent works.

scholarly journals Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Radiša Ž. Jovanović ◽  
Zoran M. Bučevac
Keyword(s):  
Discrete Time ◽  
Control Algorithm ◽  
Fuzzy Controller ◽  
Sliding Mode ◽  
Linear Time ◽  
Variable Structure ◽  
State Feedback Control ◽  
Initial State ◽  
Variable Structure System ◽  
Lyapunov’S Second Method

The exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the control law is obtained by using a simple fuzzy controller. The analytical structure of the proposed controller is derived and used to prove exponential stability of sliding subspace. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspaceS, in finite time and with prescribed velocity estimate. Inside the sliding subspaceS, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, DC servo motor, and simulation and experimental results are given.

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