Directional Change Issues in Multivariable State-Feedback Control

Abstract

Control limits are ubiquitous in real world, in any application, thus taking them into consideration is of prime importance if one aims to achieve high performance of the control system. One can abide constraints by means of two approaches – the first case is to impose constraints directly at the design of the controllerwhat usually leads to problemswith obtaining explicit forms (or closed-form expressions) of control laws, apart from very simple cases, e.g. quadratic performance indexes. The other approach is based on assuming the system is linear and having imposed constraints on the controller output (designed for unconstrained case – bymeans of optimisation, using Diophantine equations, etc) one has to introduce necessary amendments to the control system because of, possibly, active constraints (Horla, 2004a; Horla, 2007d; Ohr, 2003; Peng et al., 1998). When internal controller states do not correspond to the actual signals present in the control systems because of constraints, or in general – nonlinearity at controller output, then such a situation is referred in the literature as windup phenomenon (Dona et al., 2000; Horla, 2004a; Ohr, 2003). It is obvious that due to not taking control signal constraints into account during the controller design stage, one can expect inferior performance because of infeasibility of computed control signals. Many methods of anti-windup compensation are known from the single-input single-output framework, but a few work well enough in the case of multivariable systems (Horla, 2004a; Horla, 2004b; Horla, 2006a; Horla, 2006b; Horla, 2006c; Horla, 2007a; Horla, 2007b; Horla, 2007c; Horla, 2007d; Ohr, 2003; Peng et al., 1998; Walgama & Sternby, 1993). For multivariable systems have additional feature – windup phenomenon is tightly connected with directional change phenomenon in the control vector due to different implementations of constraints, affecting in this way the direction of the computed control vector. Even for a simple amplitude-constrained case, the constrained control vector