Anti-windup compensators for multivariable control systems

Model-based anti-windup compensation is here considered for multiple-input multiple-output (MIMO) systems. The aim will be to modify the dynamics of a control loop when actuators saturate, so that a good transient behaviour is attained after desaturation, while avoiding limit cycle oscillations and repeated saturations. It is of advantage if such effects can be controlled separately, while leaving the nominal dynamics unchanged when no actuators saturate. A controller structure with three degrees of freedom, with feedback from saturated control signals, is therefore proposed. The transfer function of this controller corresponds to that of a nominal controller, with two degree of freedom, as long as none of the actuators saturate. The structure of the controller is selected such that the loop gain around the bank of saturations is made diagonal. The properties of the loop around each saturation can then be tuned separately. We propose one way of doing this, by-means of solving a set of separate scalar H₂ problems. The proposed approach is applicable to continuous-time as well as discrete-time systems. Although it is here presented for systems in input-output form, it can be used in state-space designs just as well.