PID – loopshaping controller design for reference tracking of a second – order, open – loop system

This paper introduces a Proportional, Integral, Derivative (PID) controller architecture for reference tracking of a linear system whose dynamics are described by a second – order, transfer function. The proposed controller architecture facilitates the design and the analysis of the control algorithm by utilizing concepts from three popular controller design methods, namely PID controller design, Loop – shaping controller design and Feedback Linearization. The equivalence of the three controller design methods, when using the proposed controller architecture, provides useful insights to the control designer in choosing the parameters of the PID controller in a systematic way. An application of the controller design method is presented in order to explain the rationale in choosing the controller parameters.