Aim. The research aims to develop a method of optimal PI-controller tuning, which allows to take into account the constraints and to minimize the undesirable indicators of the automatic control quality. Method. In order to carry out the investigation, the problem of optimal PI-controller tuning was stated in a general form. The analysis of the elements of the problem has been conducted. It allowed substituting the elements to the requirements of individual minimization criteria. Development of the general (complex) criterion, which includes these criteria, was conducted with taking into account weight coefficients. They considerably differ from each other. It allowed created the desired topology of the general criterion. Results. Based on the problem of optimal PI-controller tuning with constraints, a method has been developed that ensures the stability of the automatic control, met the constraints and minimizes the complex optimization criterion. The implementation of the method is connected with the MISO-function, which should be minimized during the calculation process and which is based on the mathematical model of the plant. The method does not impose hard constraints on the mathematical properties of the problem (for example, the continuity of optimization criteria). Scientific novelty. For the first time, the method of optimal PI-controller tuning with constraints has been developed, which may be used for plants of arbitrary order. In addition, the method allows minimization of several optimization criteria, provided that the importance of each must be estimated by some numerical indicator. The developed method allows taking into account the conditions of stability. It can also be generalized for PID-controllers and controllers of arbitrary structure (including nonlinear ones). Practical significance. Significant reduction of the mean integral error is stated. It relates to the cases of the developed method application (in comparison with other engineering methods of PI-controllers tuning). The comparison has been made between those methods, which allow obtaining zero overshoot during setpoint reaching. For example, for a plant described by the transfer function G(s)=1/(s+1)2, the mean integral error decreased by 1.87… 3.14 times, for a plant with the transfer function G(s)=1/(s+1)3 this criterion decreased by 1.32… 2.10 times. The method may also be applied to the problems of minimization of other undesirable indicators of integral or positional type.
1. Åströn K.J., Hägglund T., Advanced PID control, ISA: The Instrumentation, Systems, and Automation Society, 2006, 460 p.
2. Denysenko V.V. "PYD-rehuliatory: pryntsypy postroenyia y modyfykatsyy. Chast 1" ["PID-conrollers: the principles of design and modifications. Part 1"], Sovremennye tekhnolohyy avtomatyzatsyy [Modern automation technologies], № 4, P. 66-74, 2006, [in Russian].
3. Ziegler J.G., Nichols N.B., Optimum settings for automatic controllers, Transactions of the ASME, 1942, Vol. 64, pp. 759-768.
4. O'Dwyer. Handbook of PI and PID controller tuning rules, Ireland: Imperial College Press, 3rd edition, 2009, 623 p.
https://doi.org/10.1142/p575
5. Beginner's search https://depatisnet.dpma.de/DepatisNet/depatisnet?action=einsteiger (access 09.03.2019)
6. Romasevych Yu., Loveikin V. A Novel Multi-Epoch Particle Swarm Optimization Technique, Cybernetics and Information Technologies, 2018, 18(3), pp. 62-74.
https://doi.org/10.2478/cait-2018-0039
7. Romasevych Yu., Loveikin V., Usenko S. PI-controller tuning optimization via PSO-based technique, PRZEGLĄD ELEKTROTECHNICZNY, R. 95 NR 7/2019, pp. 33-37.
https://doi.org/10.15199/48.2019.07.08
8. Åströn K.J., Hägglund T. Benchmark Systems for PID Control, International Federation of Automatic Control, 2000, pp. 165-166.
https://doi.org/10.1016/S1474-6670(17)38238-1
9. Åström K.J., Hägglund T. PID Controllers: Theory, Design and Tuning, Instrument Society of America NC.: Research Triangle Park, 2 edition, 1995, 344 p.
10. Chien K.L., Hrones J.A., Reswick J.B. On the automatic control of generalized passive systems, Transaction of the ASME, 1952, Vol. 74, No.2, pp. 175- 185.
11. Eriksson L. Control Design and Implementation of Networked Control Systems, Licentiate thesis' Department of Automation and Systems Technology, Helsinki University of Technology, 2008, 118 p.