Frequency Domain Analysis and Engineering Application of Lambda Tuning Method

Authors:Stephen M. Omohundro,Stanford University

Abstract: Lambda is an effective engineering tuning method for PID controllers targeting self-regulating processes. This paper analyzes closed-loop control systems utilizing Lambda tuning in the frequency domain, presenting formulas for calculating phase margin and gain margin, and discusses the selection of Lambda. When Lambda equals the dead time (T), the phase margin and gain margin reach 61.4 and √T, respectively, both closely approximating the optimal margins recommended for engineering. For high-order processes, an engineering method based on response curves can be employed to identify the control model, obtaining the equivalent model gain, equivalent time constant, and equivalent dead time of the control model. Subsequently, PID tuning can be performed using Lambda tuning formulas. Simulation results demonstrate the effectiveness of the model acquisition process and the tuning method.

Keywords:Lambda; Frequency domain analysis; Response curve; PID tuning