This Thesis is concerned with the approximation of high order controllers or the controller reduction problem. We firstly consider approximating high-order controllers by low order controllers based on the closed-loop system approximation. By approximating the closed-loop system transfer function, we derive a new parametrized double-sided frequency weighted model reduction problem. The formulas for the input and output weights are derived using three closed-loop system configurations: (i) by placing a controller in cascade with the plant, (ii) by placing a controller in the feedback path, and (iii) by using the linear fractional transformation (LFT) representation. One of the weights will be a function of a free parameter which can be varied in the resultant frequency weighted model reduction problem. We show that by using standard frequency weighted model reduction techniques, the approximation error can be easily reduced by varying the free parameter to give more accurate low order controllers. A method for choosing the free parameter to get optimal results is being suggested. A number of practical examples are used to show the effectiveness of the proposed controller reduction method. We have then considered the relationships between the closed-loop system con gurations which can be expressed using a classical control block diagram or a modern control block diagram (LFT). Formulas are derived to convert a closed-loop system represented by a classical control block diagram to a closed-loop system represented by a modern control block diagram and vice versa.
|Qualification||Doctor of Philosophy|
|Publication status||Unpublished - 2008|