Linear control of systems with actuator constraints

Sammanfattning: This thesis deals with the problem of how to design a linear and time invariant controller (continuous- or discrete-time) for a SISO- or SIMO-system with amplitude constraints in the actuator. One of the basic ideas is to model the constraints by means of a 'disturbance' δ acting at the input of the process. That is, whenever the actuator saturates, the difference between its output and input is interpreted as being caused by this 'disturbance'. Since the non-linearity thus becomes hidden in a non-linear relationship between the controller output and δ , the system appears to be linear. It is discussed how this makes it possible to utilize conventional linear theory to gain insight about how the closed-loop system is affected by actuator saturation. This effect is interpreted as a windup phenomenon, and its dynamic properties are characterized by the transfer operator Hδ from δ to the output of the system. By investigating some of the anti-windup methods which are most frequently encountered in the literature, it is revealed that none of them provides a sufficient parameterization with respect to the needs for manipulation of Hδ It is shown how this problem can be overcome by extending the controller with some additional 'anti-windup dynamics', in such a way that the corresponding modes are excitable only by δ This is done for both a polynomial and a state-space parameterization, where in the latter case a general form and an 'explicit-observer' form are considered. Since the additional modes appear as poles in Hδ it becomes possible to interpret the anti-windup design as a pole-placement problem. This makes the method well-suited for incorporation as a natural step in conventional text-book methods for design of linear controllers. This possibility is emphasized through the development of a design algorithm for polynomial-controllers (with antiwindup) intended for SISOsystems. It is demonstrated how suitable locations for the poles of Hδ can be found by means of either a time- or a frequency-domain approach. In the latter, describing function analysis is utilized as a tool for prediction of whether a certain location is likely to cause problems with 'repeated saturation' (non-linear oscillations).