H∞ control of multiple model subject to actuator saturation: application to quarter-car suspension system

Abstract

This paper deals with the H ? control of nonlinear systems in multiple model representation subject to actuator saturation. An application to Quarter-Car suspension system under actuator saturation is then given using the multiple model approach. The concept of so-called parallel distributed compensation (PDC) is employed for designing control system. The idea of this controller consists in designing a linear feedback control for each local linear model. To address the input saturation problem in this paper, both constrained and saturated controls input cases are proposed. In the two cases, H ? stabilization conditions in the sense of Lyapunov method are derived. Moreover, a controller design with larger attraction domain is formulated and solved as a linear matrix inequality (LMI) optimization problem. Our simulation results show that both the saturated and constrained controls can stabilize the resulting closed-loop suspension system and eliminate the effect of external disturbances. Indeed, the main roles of car suspension systems, which consist on improving ride comfort of passengers and the road holding capacity of the vehicle, are achieved.

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

“…In the so‐called constrained control, the control input cannot be saturated. In other words, the control input is designed in such away to avoid saturation limits.…”

“…Motivated by the aforementioned observations, this paper intends to derive a robust H ∞ static output‐feedback control for discrete‐time fuzzy systems with cactuator saturation via FWDLF. The contributions of the proposed work are summarized as: (i)Unlike the fuzzy control design methods using a PDC controller for T‐S systems with actuator saturation, thus considering the state variables available; the presented SOF control work does not consider this strong assumption. (ii)Quadratic approaches' results , will be encapsulated into a FWDLF extended approach. (iii)The modeling errors and external perturbations are also taken into consideration via classical H ∞ attenuation using LMI constraints both for constrained and saturated control input. …”

“…Therefore, the control system design must take into account these input constraints in order not to degrade the performance of the closed-loop system that can even lead to instability issues [8,10,25,26,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Many results are reported in the literature regarding stability analysis of linear (more recently, see [35][36][37][38]) and nonlinear systems [8,10,16,25,26,[31][32][33][34][40][41][42]45] subject to input constraints. Several approaches were experienced with T-S systems: bound on the initial conditions to avoid the input saturation in low gain control laws [16,26,40]; estimation of the attraction domain in the presence of actuator saturation [8,10,16,38,40,41,…”

“…Many results are reported in the literature regarding stability analysis of linear (more recently, see [35][36][37][38]) and nonlinear systems [8,10,16,25,26,[31][32][33][34][40][41][42]45] subject to input constraints. Several approaches were experienced with T-S systems: bound on the initial conditions to avoid the input saturation in low gain control laws [16,26,40]; estimation of the attraction domain in the presence of actuator saturation [8,10,16,38,40,41,45]; transformation of the saturation into a dead-zone nonlinearity [8], use of a polytopic model to express the saturation constraints in [10,16,[20][21][22]25,26,[35][36][37][38][39][40][41]45].…”

Adaptive Fuzzy Control for Aircraft Tractor’s Magneto Rheological Semi-active Suspension

“…[3] used optimal control algorithm for quarter body model. The results showed that control is better than passive suspension, but the choice of weighting coefficients mainly depends on the designer's experience, lacking theoretical basis; [4] used robust control, however not only computing increase but controller is conservative and real-time is bad; Fuzzy control does not depend on the precise mathematical model and has advantages in dealing with non-linear problems. With characteristic of self-tuning adaptive control, it can get very good control effect [5].…”