Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

scholarly journals H∞ state feedback control of commensurate fractional order systems

2013 ◽  
Vol 46 (1) ◽  
pp. 54-59 ◽  
Author(s):  
Lamine Fadiga ◽  
Jocelyn Sabatier ◽  
Christophe Farges
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback ◽  
State Feedback Control ◽  
Fractional Order Systems

Active Compressor Surge Control Using Piston Actuation

2011 ◽  
Author(s):  
Nur Uddin ◽  
Jan Tommy Gravdahl
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Linear Feedback ◽  
Control Law ◽  
Asymptotically Stable ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Closed Loop System ◽  
Linear Feedback Control ◽  
Surge Control

A novel approach to active surge control in compressors using piston actuation is presented. Two control laws are compared in order to evaluate the feasibility of implementing the concept. The first control law is a nonlinear feedback control derived by using backstepping and the second one is a linear feedback control derived by analyzing the eigenvalues of the linearized system around the operating point. The nonlinear feedback control law makes the closed loop system globally asymptotically stable (GAS) and uses full states feedback. The linear feedback control is only using feedback from plenum pressure and piston velocity and the removal of the mass flow feedback is advantageous for implementation. The closed loop system with the linear feedback control is locally asymptotically stable around the operating point. Simulations show that both controllers are capable of stabilizing surge.

scholarly journals Projective Synchronization ofN-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Baogui Xin ◽  
Tong Chen
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Projective Synchronization ◽  
Control Technique ◽  
Linear Feedback ◽  
Fractional Order Systems ◽  
Financial Systems ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

Based on linear feedback control technique, a projective synchronization scheme ofN-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

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