Development of PID tuning rules for low-order dynamic models using multi-criteria optimization

Abstract

This report is a Research Thesis report for tuning PID controllers for optimum performance under non-standard-assumption circumstances, using the integral performance criteria. The thesis also involves development and use of new integrals' performance indicators for assessment and comparison, and a new method for creating Pareto plots for multiple objective optimization. Considering the impractical results provided by analytical methods, this problem was investigated and approached from the basics in order to arrive to better controllers in applied industry's point of view. The target set for the research dictated consideration of practical needs of the industry; Bode's sensitivity integral and development of a performance evaluation criterion, accordingly. After review of available literature and previous work, the report describes the project stages and the work done. Problems and difficulties encountered in use of MATLAB are also pointed out. Describing study's stages is vital for understanding the output; because the study methodology and goals were reviewed recursively along the study; based on the findings. Results of this project are more robust and comprehensive mathematical formulae that use a system's model parameters to calculate optimal PID parameters; as well as investigation of system's behaviour in optimization in frequency domain. The first stage of the work was verification of existing tuning models of PID controllers based on the ITAE criterion for step input only. Work proceeded into investigation of two objectives optimization. Some of the aspects were Pareto efficiency principle, and development of a new performance index for the new objective. The following stage involved investigation of optimization in the frequency domain alone. This is because this aspect is sophisticated enough on its own to be considered alone, before integrated with other objectives. Investigation to choose a good performance index is discussed in the report. Candidates discussed include functions evaluated analytically, and one function for optimization in SIMULINK. The discussion involves the advantages and disadvantages of each concept. Moreover, complexity also lies in choosing the boundaries for the period of frequencies to simulate the system at. Interesting and new results are obtained on the behaviour of PID gains with respect to that. It was observed that even for the same system under consideration, choice of the upper limit of the frequency range for consideration affects the controller's gains. Behaviour of the like of bifurcation is noticed for the gain of the integral part of the PID controller, abruptly and steeply falling from a finite value to zero at a certain frequency value. A factor predicting the borderline value is found to be applicable for all systems. Study also considered using plant's bandwidth as the upper limit frequency of evaluation. All of this work was done for FOPDT systems then, repeated for SOPDT system, keeping in mind findings and lessons learned from FOPDT systems. Furthermore, SOPDT plants have one more parameter compared to FOPDT, which calls for more sophisticated regression and modelling tools. This lead to increase in simulation time to an extent where an orthodox programming approach and a general-purpose computer are not sufficient. The program code was re-developed from scratch, in order to utilize parallel computing, where simulations are run in parallel rather in series. Later on, the Institution's High Performance Computer Cluster dedicated for research was used. The HPCC allowed running the simulation on up to 31 cores, compared to 2 or 4 cores as in a personal computer. Job execution time went down from a prelimenary estimate of 2-3 months, to less than 5 days. Finally, an application study is carried out to test and confirm our hypothesis. The application study involved a single-bus power system with a fourth order linearization of its nonlinear dynamics. The study aimed to find optimum tuning parameters for different types of controllers, using the same concepts.

Date of Award	2015
Original language	American English
Supervisor	Youssef Abdel-Magid (Supervisor)