Two-Relay Controller Test Approach to Non-parametric PID Tuning of a Magnetic Levitation System

A non-parametric PID tuning approach for a Magnetic Levitation System (MLS) is proposed in this paper. The proposed tuning method is non-iterative and is based on a test involving the two-relay controller (modified twisting algorithm), that provides identification at frequencies higher than the phase cross over frequency of the process. The tuning procedure has two consecutive stages. First, generating self-excited oscillations in the closed loop of the MLS using the two-relay controller test, and measuring the ultimate frequency and ultimate amplitude of the generated oscillations. Second, using the results obtained from the test and certain non-parametric tuning rules, the parameters of the PID controller are determined. The tuning rules that are produced and used guarantee the specified gain margin for the corresponding linearized system and the motion in the vicinity of the specific set point. To ensure optimal performance of the MLS, the test and tuning are repeated at other set points, and the results are incorporated through gain scheduling. We illustrate the tuning procedure of the MLS controller through simulations using Matlab/Simulink and validate the approach using the MLS experimental setup. The effectiveness of the proposed approach is demonstrated.