Type-I Control Loops

Abstract

In this chapter, the tuning of the PID controller via the Magnitude Optimum criterion for type-I control loops is presented. Initially, the revision of the conventional Magnitude Optimum design criterion for tuning the PID type controller’s parameters is presented in Sect. 3.2, which serves as a basis for the reader to understand the current state of the art, see Sects. 3.2.1–3.2.4. This revision reveals three fundamental drawbacks, which are summarized in Sect. 3.2.5 and prove to restrict the PID controller’s optimal tuning in terms of robustness and disturbance rejection at the output of the plant. Sorting out these drawbacks in the beginning, one can argue that: (1) with the conventional PID tuning and for determining the PID controller’s zeros, exact pole-zero cancellation has to be achieved between the processes’ poles and the controller’s zeros. (2) To this end, the conventional PID tuning via the Magnitude Optimum criterion restricts the controller’s zeros to be tuned only with real zeros. (3) Last but not the least, the conventional design procedure via the Magnitude Optimum criterion has been tested only to a limited class of simple process models. To overcome the aforementioned drawbacks, a revised PID type control law is then proposed in Sect. 3.3. For the development of the control law a general transfer function process model is employed in the frequency domain. The final control law consists of analytical expressions that involve all modeled process parameters. The resulting control law can be applied directly to any linear single input single output stable process regardless of its complexity. A summary of the explicit solution is presented in Sect. 3.3 and the analytical proof of the control law is presented in Appendix B.1. For evaluating the proposed theory, an extensive simulation test batch between the conventional and the revised PID tuning is performed in Sect. 3.4 for various benchmark processes. Throughout this evaluation, the validity of several literature comments related to the Magnitude Optimum criterion is discussed in Sects. 3.4.6 and 3.4.7. Finally, it is shown that the performance of the proposed control law compared to the conventional PID design procedure achieves satisfactory results both in the time and the frequency domain, in terms of robustness and disturbance rejection.