Design of Non-Parametric Optimal PID Tuning Rules for a Magnetic Levitation System, Based on Two Relay Controller test

Abstract

Magnetic Levitation (Maglev) has a wide range of applications in both industry and research. The technology provides many advantages to electromechanical systems. Magnetic levitation system (MLS) employs Maglev principal to suspend a ferromagnetic object to the desired position. The system is characterized by open loop instability and highly nonlinear dynamical behavior [1], which requires developing a robust and optimal position controller. Many linear and nonlinear control strategies has been proposed in the past few decades for MLS, due to the high demand for a simple, efficient and widely applicable control solution. Among those, PID control is the most popular. In the current research, we propose a novel non-parametric tuning approach of a PID controller in which the parameters of the MLS are not determined in advance. The tuning includes a self-excited oscillation test based on the two-relay controller (TRC) and a set of designed tuning rules. The TRC approach is used to excite non-vanishing oscillations of the MLS where the oscillation parameters, namely the ultimate amplitude and the ultimate frequency, are measured. The tuning rules are then developed to meet the gain margin specification for the linearized open loop system, the linearization is done with respect to the motion in the vicinity of the operating point. To further enhance the performance of MLS, the coordinated test and tuning is consecutively repeated for different operating points. The tuning results are then integrated through gain scheduling control for varying operating points. In the presented thesis, we design optimal tuning rules for a PID and a PD controller by accurately identifying the MLS physical model dynamics, including the parasitic dynamics, and applying the two-stage optimization. The optimization is aimed to define the combination of tuning rules that will provide the best results in term of the step response in the first stage of optimization. The model parameters are identified with respect to six operating conditions leading to six different models. The optimal tuning rules for each model are formulated as a solution of optimization of an integral performance criterion where two different criterions are selected as follows: the Integral Time Absolute Error (ITAE) for PID controller and the Integral Time Absolute Error under settling (ITAUS) for PD controller. In order to determine the optimal tuning rules that are suitable for the considered class of models, we conduct the second stage of optimization and evaluate the cost function of the integral performance criterion for each combination of model specific optimal tuning rules with each model. We then measure the deterioration when non-optimal tuning rules are applied to a specific model by taking the ratio between the cost function to the optimal cost function of a particular model. The worst performance for each model specific tuning rules is then assessed by defining the maximum value of deterioration. The optimal tuning rules that provide the best performance for all class of models is the one that provides the smallest value of deviation compared to the other tuning rules. The theory presented in the thesis, involving the TRC approach, the non-parametric PID tuning and the design of optimal tuning rules for PID and PD controller, was carefully investigated through analytical interpretation, comprehensive simulation, and practical demonstration.

Date of Award	Apr 2019
Original language	American English
Supervisor	IGOR Boiko (Supervisor)