Optimal tuning of linear controllers for power electronics/power systems applications

This paper presents a new method for tuning various linear controllers such as Proportional–Integral (PI), Proportional–Integral–Derivative (PID) and Proportional–Resonant (PR) structures which are frequently used in power electronics and power system applications. The linear controllers maintain a general structure defined by the Internal Model Principle (IMP) of control theory. The proposed method in this paper is twofold. The first perspective uses the well-known concept of the Linear Quadratic Regulator (LQR) to address the problem as a regulation problem. The Q matrix of the LQR design is then finely adjusted in order to assure the desired transient response for the system. The second perspective redefines the LQR in order to add capability to address the optimal tracking problem and is then generalized to systems with more than two states. These methods are then applied to two specific examples, one in an uninterruptible power supply (UPS) inverter system and the other one in a distributed generation (DG) system. In these examples, the tuning of PR and PI controllers is studied in great detail. These proposed design methods provide an easy and algorithmic procedure without jeopardizing stability or robustness. These tuning methods can also be utilized for linear state-space realization of any power converters. Both examples are supported via simulation and the results, which confirm analytical derivations, are presented and discussed.