On digital PI and PID controller design

Digital PI and PID algorithms are usually obtained through their analog versions by the use of numerical approximation method. . There are, however, other transformation methods which if applied to these controllers may produce better results. This thesis studies the effects of transformation methods on the characteristics of the PI and PID algorithms. A number of algorithms are developed by several transformation methods and their performances are investigated. Some unexpected properties of the algorithms which do not conform to the continuous system theory are shown. The possibility of controller-caused instability is discussed and it is shown that high sampling rate does not necessarily result in improved performance for all the algorithms. Also, several modifications in the standard PID algorithms which improve the performance of the algorithm are presented. The thesis compares the advantages and disadvantages of the algorithms obtained by various transformation methods and concludes that the methods presented here often give better results than the commonly-used numerical approximation method. Finally, a set of guidelines based on problem requirements and parameters are provided for the designer to choose the most appropriate transformation method for his problem. The guidelines are examined by several typical process control problems.