Sliding Mode Control of Vibration in Uncertain Time-delay Systems

Abstract

This paper presents a proportional-integral sliding mode control (PISMC) methodology for the robust control of vibration in a linear uncertain system with state and input delays. The systems are assumed to have structured, unmatched and time-varying parameter uncertainties. Based on Lyapunov stability theorem and linear matrix inequality (LMI) H∞ technique, a sufficient condition is derived to guarantee the global stability of the dynamics and achieve a prescribed H∞ norm bound of disturbance attenuation for all admissible uncertainties without the state predictor. Furthermore, this scheme assures robustness against state delays, input delays, parameter uncertainties and disturbances simultaneously. Simulation results demonstrate the efficacy of the proposed control methodology.

RETRACTED: Neural network-based fuzzy logic parallel distributed compensation controller for structural system

“…The simulation results prove that the proposed method is able to stabilize delayed nonlinear structural systems, while at the same time having strong robustness in terms of preventing modeling errors and external excitations. Pai (2010) presented a proportional-integral sliding mode control (PISMC) methodology for the robust control of vibration in a linear uncertain system with state and input delays. The systems are hypothesized to have structured, unmatched and time-varying parameter uncertainties.…”

New discrete-time robust H2/H∞ algorithm for vibration control of smart structures using linear matrix inequalities

“…Over the past few decades many active control algorithms have been developed such as the linear quadratic regulator (LQR) (Stavroulakis et al, 2006), linear quadratic Gaussian (LQG) (Wu and Yang, 2000), sliding mode control (SMC) (Alli and Yakut, 2005;Pai, 2010;Wang and Adeli, 2012, 2015a, 2015b, H 1 control (Yang et al, 1996), proportional-integral-derivative (PID) control (Kang et al, 2009), model predictive control (Wang et al, 2015), parallel control , and optimal control algorithm Saleh and Adeli, 1997, 1998a, 1998b. Saleh (1998, 1999) present an integrated control and optimization strategy for design of both civil structures and control system.…”

Design of an adaptive chattering avoidance global sliding mode tracker for uncertain non-linear time-varying systems

“…(Majd and Mobayen, 2015; Mobayen and Javadi, 2015; Nechadi et al, 2012; Norton et al, 2015; Temel and Ashrafiuon, 2015). The main features of SMC are robustness in the contradiction of perturbations, fast response, satisfactory transient performance and computational ease towards other robust techniques (Pai, 2010; Mobayen, 2015f). The SMC design process is separated into two phases: (a) constructing an appropriate switching surface so that the system indicates desired dynamics, and (b) designing the corresponding controller so that the states of the system arrive at the switching surface (Majd and Mobayen, 2015; Mobayen et al, 2016; Temel and Ashrafiuon, 2015).…”