Comparison between a switching controller and two LTI controllers for a class of LTI plants

We consider the design of three different control architectures for a step response tracking problem within a class of linear time-invariant (LTI) plants. Our goal is to motivate the use of a particular switching architecture that has been the subject of our prior work. We present the design of the particular switching architecture that we use and characterize its step response performance (measured in terms of the percentage overshoot and 1% settling time of the step response). We then compare the response of the switching controller with two other forms of LTI control in a servo configuration, one in which the order of the controller is constrained to be first order (which matches the order of the dynamics of the switching controller) and one in which the order of the controller is unconstrained. We will show that the switching architecture can outperform first-order LTI control, first in the context of a particular example. We shall then provide a weak generalization to extend this result to a more general class of plants. We shall also show that, while the LTI control of unconstrained order can outperform the switching architecture, the performance improvement is bounded (in a sense to be defined). Moreover, one method of designing close-to-optimal controllers will be discussed, which yields controllers of very high order. Copyright q 2008 John Wiley & Sons, Ltd.