Comparison of a switching controller to 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 plants. Our goal is to motivate the use of a particular switching architecture that has been the subject of our prior work. We show 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). We then compare the response of the switching controller to two other forms of LTI control in a servo configuration, one in which the order of the controller is unconstrained, and 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). We shall 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 shall be discussed which yields controllers of very high order. We shall also show that the switching architecture can outperform first order LTI control and shall illustrate this via a particular design example.