Describing Function Approach with PID Controller to Reduce Nonlinear Action

Abstract

The nonlinear effect in the control system is so important and it may have a hard or soft effect on the electrical, mechanical, biological, and many other systems. This paper analyzes the describing function (DF) which is the transfer function of the nonlinear (NL) control systems of many NL elements found such as saturation, and backlash. The effect of the NL on the third-order delayed system is considered. The PID controller is considered the heart of the control system and continuously finds the error between input and output, and formulates the desired signal for the actuator to control the plant. Experimental tanning of PID controller with the saturation NL as a case study with buffer Operation Amplifier (Op-Amp) to maintain the gain and phase shift. In addition, a low pass filter (LPF) is used in the feedback to minimize and attenuate the effect of the NL in the closed-loop control system. The Fourier series is used to analyze the DF. The results show the effectiveness of the proposed algorithm.