A comparative study of optimal control techniques

Two least-integral-square based optimal control techniques are presented and compared here for single-input-single-output processes. The foundation of both techniques is the selection of a performance index based upon sound engineering principles. It is the selection of this performance index that, in fact, will guarantee the evolution of an optimal controller for the process at hand.

This study first develops the least-square based mathematical model proposed by Youla-Bongiorno-Jabr, 1976. The study then continues by examining the method developed by S.S.L Chang, 1961, and derives results for both single, and multiple controller system configurations. The method proposed by Youla, et. al., starts by selecting a specific control system configuration. Then, using a performance based index, the derivation of a single optimal compensator which may account for external noise and disturbance is made possible. Chang's method, also least-square based, begins with no specific preassigned control configuration. This is an important difference that sets Chang's and the Youla, et. al method apart. Chang's method may be used to obtain one, or more, optimal closed-loop transfer functions for the system. After a specific control configuration is chosen, one or more optimal controllers may be found using the results from Chang's general control configuration. These controllers also may account for noise and disturbance effects which may be present external to the system.

These results are then applied to a DC motor and load control situation, with an external disturbance. Single optimal controllers, which account for this disturbance in their derivation are found using both methods mentioned above, and are compared by simulation to compensators which account for disturbance in their evolution. These results are compared to a dual controller configuration, in which the two optimal compensators were derived by Chang's method. Results show that the two controller configuration has superior disturbance suppression characteristics than the single compensator configuration using both Youla, et al and Chang's single controllers. These results, therefore, support the use of Chang's method due to its ability to achieve multiple optimal controllers and its ease of use.