Process Control Design for Time Delay Systems from Similarity Point of View

Abstract

The habilitation thesis presents author’s research results in the areas of process control design for time delay systems and in the similarity theory application in this design. The motivation and objectives of the habilitation thesis are presented in Chapter 1. The thesis is motivated by open problem - applicability of dominant pole placement method to the PID controller tuning for higher-order plants with delay. In Chapter 2 the time delay systems in control and estimation are surveyed and at the beginning of Chapter 3 the dimensional analysis application to control design is surveyed, too. In Chapter 4 the generalized dominant threepole placement as the design method is presented together with resulting PID controller setting common for a set of dynamically similar plants with delay. The same design method is applied in Chapter 4 to the PID controller tuning for a set of integrating plants with delay. At the end of Chapter 3 the third- and fourth-order plants are investigated as samples of higher-order plants with delay. This thesis as the study on applicability of the dominant three-pole placement method to the PID controller tuning for higher-order plants with delay reveals that the PID controller is still tunable for the admissible third- and fourth-order plants while in case of the inadmissible third- and fourth-order plants the PID controller is not already tunable by this method as concluded in Chapter 4. This revelation is mainly enabled by the dimensional analysis application thoroughly in Chapter 3 which gives the control engineering design the capability of its versatility in the area of reasonably constrained (i.e. admissible) similarity numbers. The reasonable constraints are due to dynamic relevance and practical controllability of the considered higher-order systems with delay. Conclusions to Chapter 3 summarize that the constrained similarity numbers are oscillability, retardedness, dampeningness and stiffness, in particular. Conclusions to Chapter 4 sum up that once the retardedness number is not negligible the PID controller provides admissible control solution to the plants of maximum order – four, including the integrating plants up to the fourth-order. Moreover the admissible third and fourth-order plants with delay allow assigning the natural frequency number greater than the ultimate frequency number without the loss of three-pole dominance while the inadmissible third and fourth-order plants do not. In fact the inadmissible fifth-order PID control loops with delay show that one is already behind the capability of the PID controller, independently of tuning method applied, to cope with higher-order dynamics because the control loop responses are with extreme overshoot and take overlong. In Chapter 5 the thesis as a whole is concluded that the generalized dominant three-pole placement technique provides the delayed fourth- and fifth-order PID control loop response with low overshoot in contrast to well-known PID tuning method based on idealrelay feedback test.