Design of variable structure controllers using adaptive bound on uncertainty

Abstract

Variable structure control (VSC) is a viable high speed switching feedback control and provides an effective and robust means of controlling nonlinear/uncertain systems. The silent feature of VSC is the so-called sliding mode on the switching surface within which the system remains insensitive to internal parameter variations and extraneous disturbance. For controlling nonlinear/uncertain systems, control algorithms using the theory of variable structure system (that is, VSC) have been recently developed by many researchers. However, in these control algorithms, the information on the possible size of the uncertainty/nonlinearity is needed. To overcome this difficulty, we firstly propose an adaptive variable structure controller which renders nonlinear/uncertain systems asymptotically stable, under the assumption that all uncertainties are met the matching conditions. In this control design, using a simple gradient adaptation law, the possible size of the uncertainty is estimated. A drawback to this control law is that the control is discontinuous about the switching surface. This characteristic may induce the undesirable chattering problem which involves extremely high control activity and furthermore may excite the neglected high frequency dynamics. To avoid the possibility of control chattering, we introduce the boundary layer in a neighborhood of the switching space and design a continuous feedback control which renders the uncertain dynamical systems uniformly ultimately bounded. Secondly, based on a Lyapunov function we suggest a sufficient condition guaranteeing the robustness on the uncertainty and design a robust linear output feedback controller for a class of uncertain dynamical systems using eigenstructure assignment technique via output feedback. Designing this robust linear output feedback controller, the so-called matching conditions on the uncertainty are relaxed and measurable output vector is only used. In order to improve the transient respon...