Robust non‐fragile H_∞ ∕ L₂ − L_∞control of uncertain linear system with time‐delay and application to vehicle active suspension

Abstract

SummaryThis paper presents an approach to design robust non‐fragile H ∞ ∕ L2 − L ∞ static output feedback controller, considering actuator time‐delay and the controller gain variations, and it is applied to design vehicle active suspension. According to suspension design requirements, the H ∞ and L2 − L ∞ norms are used, respectively, to reflect ride comfort and time‐domain hard constraints. By employing a delay‐dependent Lyapunov function, existence conditions of delay‐dependent robust non‐fragile static output feedback H ∞ controller and L2 − L ∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities. Then, a new procedure based on LMI optimization and a hybrid algorithm of the particle swarm optimization and differential evolution is used to solve an optimization problem with bilinear matrix inequality constraints. Simulation results show that the designed active suspension system still can guarantee their own performance in spite of the existence of the model uncertainties, the actuator time‐delay and the controller gain variations. Copyright © 2014 John Wiley & Sons, Ltd.

Adaptive backstepping‐based control design for uncertain nonlinear active suspension system with input delay

“…The projection operator-based adaptive control law proĵ(r e 2 (t) Δ 1 (x, t)) has the following three main features: 1 The parameter estimation̂(t) can be always ensured within a known range, ie, min <̂(t) < max . 2 The hold of̃(t) (r −1 proĵ(r e 2 (t) Δ 1 (x, t)) − e 2 (t) 1 (x, t)) ≤ 0 can be always guaranteed. 3 A constrained function of tanh (e i ) is used to replace the linear feedback term e i with the purpose of avoiding the safety constraints going beyond its limits that are caused by the overlarge tracking error e i .…”

“…It is well known that active suspension systems have been widely studied and implemented in vehicle application scenarios due to its advantages including the isolation, absorption, and dissipation of the vibration energies caused by road roughness. 1,2 Generally, the key issue of developing controller in active suspensions involves a trade-off between ride quality and road handling stability, which has been a subject of many research literatures. [3][4][5] Therefore, to deal with this issue, a number of control schemes such as adaptive fuzzy control, 6,7 robust H ∞ control, 8 slide mode control, 9,10 and adaptive backstepping control 11,12 have been proposed to improve the vehicle performance in the presence of system uncertainties and to minimize the negative effect of road disturbance on the control system.…”

A Novel SHLNN Based Robust Control and Tracking Method for Hypersonic Vehicle under Parameter Uncertainty

“…It has also been concerned with a problem of nonfragile robust optimal guaranteed cost control for a class of uncertain two-dimensional discrete state-delayed systems and the state feedback controllers are designed [29]. Robust nonfragile control of uncertain linear system and application to vehicle active suspension were described in [30]. In [31,32], nonfragile guaranteed cost control of parametric uncertain systems was studied and the guaranteed cost nonfragile tracking control on the omnidirectional rehabilitative training walker was examined.…”

Robust adaptive backstepping sliding mode control for motion mode decoupling of two‐axle vehicles with active kinetic dynamic suspension systems

“…However, the traditional state feedback H∞ control highly depends on the accurately measurement or estimation of state information, which limits its application to a certain extent. Thus, output‐feedback based H∞ control has drawn the attention of researchers . Josep et al proposed a two‐step computation approach of static output‐feedback controller for vehicle suspensions, the results indicate that proposed controller exhibit a good performance with restricting feedback information.…”