Experimental PID Controller Design: A New Frequency Domain Approach Based on Desired Performance

This paper presents an alternative approach to design PID controllers based on frequency response measurements. The proposed method does not require any mathematical model of the system and can handle the design process directly from a small set of frequency domain data. It is shown that for the class of Linear Time-Invariant (LTI) control systems, there exists a rational multilinear function for the frequency response between any two arbitrary breaking points in terms of the design controller. This function can be determined by conducting a small set of frequency response measurements and then will be used to synthesize a controller that guarantee a set of desired frequency-domain specifications. In this paper, we use this result to design a PID controller for a servomechanism control system. In particular, we show that such desirable PID controller can be calculated by solving an optimization problem.