Composite sliding-mode control of singular perturbation systems

Abstract

A two-stage sliding-mode controller design for a singutar perturbation system is investigated in this paper. At first, we design the slow and fast sliding-mode controllers for the subsystems individually. Then we obtain the composite sliding-mode control (SMC). The upper bound problem of the singular perturbation parameter in such control system is also determined. An efficient way of eliminating the chattering is developed. A numerical example [4] is given to demonstrate the proposed schemes. time--sec time-sec Response of z2,hill order(solid line) Response of z1,full order(so1id line) 0.5 y --, time-sec time-sec Fig1 : Simulation results of the closed-loop control system with S = c, 11 and E 4. I Response of x1,full order(solid line) Response of x2,full order(solid line) -0.5 time-sec llme--sec Response of zl,full order(solid line) Response of t2,fulI order(solid line) I 4 , . -0.5, -' ' 5 0 u 0 . '

Sliding mode control for three time scale system with matched disturbances

“…If all the eigenvalues of (29) are located in the left half plane (except zero poles of sliding surface) [15], then sliding condition is satisfied.…”

“…where Δ can be designed by designed by sigmoid function [15] to eliminate the chattering and is implemented as…”

“…A similar kind of approach was studied by Li . [15], in which the upper bound problem of singular perturbation parameter is also determined. In [18], global stability of closed loop system; reduced in their fast and slow subsystem using singular perturbation with sufficiently small perturbation parameter is addressed.…”

Quasi‐Steady‐State Models of Three Timescale Systems: A Bond Graph Approach

“…e observer problem by the need to obtain the states for a system with singular perturbations is solved in [9]. e composite control of singular perturbation systems using sidling modes is proposed in [10]. e feedback control design for systems with three timescales is introduced in [11].…”

Sliding mode control for singularly perturbed systems

“…Slotine [50] introduced a two-time scale sliding mode controller where he used singular perturbation theory to design two sliding mode controllers, one for the slow subsystem and one for the fast subsystem based on his tracking control approach [49].Heck[22] similarly addressed the use of two sliding mode controllers to control singularly perturbed systems; however she uses a different control strategy to build the control law. Li[37] investigated the results from Heck's article[22] and proposed a condition to ensure that the controller satisfies the sliding condition for the full order system.Other papers [11][20][60] discuss Heck's approach and define another method forstability and robustness analysis. In this chapter we investigate the use of sliding mode control for singularly perturbed systems.4.1 Model Reduction Using Singular PerturbationConsider the linear time-invariant system represented by x E Rn, ZE Rm and UE Rr.…”