Adaptive fuzzy sliding mode controller for linear systems with mismatched time-varying uncertainties

Abstract

A new design approach for an adaptive fuzzy sliding mode controller (AFSMC) for linear systems with mismatched time-varying uncertainties is presented. The coefficient matrix of the sliding function can be designed to satisfy a sliding coefficient matching condition provided time-varying uncertainties are bounded. With the sliding coefficient matching condition satisfied, an AFSMC is proposed to stabilize the uncertain system. The parameters of output fuzzy sets in the fuzzy mechanism are on-line adapted to improve the performance of the fuzzy sliding mode control system. The bounds of uncertainties are not required to be known in advance for the AFSMC. Stability of the fuzzy control system is guaranteed and the system is shown to be invariant on the sliding surface. Moreover, chattering around the sliding surface in sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed AFSMC.

New methodologies for adaptive sliding mode control

“…As recalled previously, this problem is an exciting challenge for applications given that, in many cases, gains are also over-estimated, which gives larger control magnitude and larger chattering. In order to adapt the gain, many controllers based on fuzzy tools [18,24] have been published ; however, these papers do not guarantee the tracking performances. In [10], gain dynamics directly depends on the tracking error (sliding variable): the control gain is increasing since sliding mode is not established.…”

Disturbance attenuation–based sliding mode control with disturbance observer for mismatched uncertain system

“…The first category mainly uses different control strategies to reduce the impact of mismatched uncertainties on the stability of the system, such as linear matrix inequality (LMI)-based approach, 9 the Riccati approach, 10 fuzzy and neural network based control, [11][12][13] adaptive approach, [14][15][16][17] invariant ellipsoid method, 18 and integral SMC approach. [19][20][21][22] The uncertainty of the mismatch uncertainties requires the bounds or vanity of the H2 norm in above methods.…”

Adaptive enhanced sliding mode control for permanent magnet synchronous motor drives

“…In [13] and [14], the fuzzy basis function is used to approximate the ideal control law, and a hitting controller is designed to compensate for the approximation error between the fuzzy controller and the ideal controller. In [15], the fuzzy logic control is used to mimic the hitting control, and the parameters of the output fuzzy sets are online adapted to simplify the controller design. However, these control schemes are relatively complex, and the computational burden is heavy, which would deteriorate the control performance in real-time applications.…”