Delay Equivalences in Tuning PID Control for the Double Integrator Plus Dead-Time

• Published in: Mathematics (Basel) Vol. 9; no. 4; p. 328
• Main Authors: Huba, Mikulas, Vrancic, Damir
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-02-2021
• Subjects: Attenuation; Control systems design; Controllers; derivative action; Design parameters; Double integrators; Equivalence; filtration; Low pass filters; Mathematics; multiple real dominant pole method; Noise; Noise levels; PID control; Proportional integral derivative; Tuning
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math9040328

The paper investigates and explains a new simple analytical tuning of proportional-integrative-derivative (PID) controllers. In combination with nth order series binomial low-pass filters, they are to be applied to the double-integrator-plus-dead-time (DIPDT) plant models. With respect to the use of derivatives, it should be understood that the design of appropriate filters is not only an implementation problem. Rather, it is also critical for the resulting performance, robustness and noise attenuation. To simplify controller commissioning, integrated tuning procedures (ITPs) based on three different concepts of filter delay equivalences are presented. For simultaneous determination of controller + filter parameters, the design uses the multiple real dominant poles method. The excellent control loop performance in a noisy environment and the specific advantages and disadvantages of the resulting equivalences are discussed. The results show that none of them is globally optimal. Each of them is advantageous only for certain noise levels and the desired degree of their filtering.