On Directional Change and Anti-Windup Compensation in Multivariable Control Systems

Taking control limits, ubiquitous in the real world, into consideration is crucial for achieving high performance of designed control systems. There are two ways in which one can consider possible constraints during the synthesis of controllers. In the first approach, imposing constraints during the design procedure of the controller usually leads to difficulties with obtaining explicit forms of control laws, apart from computationally very simple cases. The other approach is to assume the system is fully linear and, subsequently, having designed the controller for the unconstrained system (by means of optimisation, using Diophantine equations, etc.), impose constraints, which would require additional changes in the control system due to the presence of constraints. A situation when because of, e.g., constraints (or, in general, nonlinearities) internal controller states do not correspond to the actual signals present in the control systems is referred to in the literature as the windup phenomenon (Horla, 2004; Walgama and Sternby, 1993; Doná et al., 2000). It is obvious that, due to not taking control signal constraints into account during the controller design stage, one can expect degraded performance because of the infeasibility of the computed control signals, as they can only be applied having been constrained first. There are various methods of compensating the windup phenomenon in single-input single-output systems, but few result in satisfactory performance improvement in the case of multivariable systems (Horla, 2004; Öhr, 2003). In such a case, apart from the windup phenomenon itself, one can also observe directional change in the control vector due to different implementations of constraints, which could affect the direction of the unconstrained (i.e., computed) control vector.