Relay feedback analysis and auto-tuning for a class of servo control systems

In this paper, a class of second-order servo plants under relay feedback is studied. Complete results on the uniqueness of solutions, existence and stability of the limit cycles are established using the point transformation method. A numerical method is developed for determining the amplitude and period of a stable limit cycle from the plant parameters. On the other hand, closed-form formulas are obtained for directly computing the plant parameters from a limit cycle in time domain, and an analytical technique is developed for tuning lead/lag/PD controllers for minimization of the integral squared error (ISE) instead of normally used gain and phase margins.