A novel LQR based optimal tuning method for IMP-based linear controllers of power electronics/power systems

This paper presents a new method for tuning linear controllers such as Proportional-Integrating (PI) and Proportional-Resonant (PR) structures which are frequently used in different power electronic and power system applications. Those controllers are placed within a general structure offered by the Internal Model Principle (IMP) of control theory. In this paper, the first perspective uses the well-known concept of Linear Quadratic Regulator (LQR) to address the problem as a regulation problem. Matrix Q of the LQR design is then finely adjusted in order to assure desired transient response for the system. The second perspective is based on redefining the LQR problem in order to make it capable of addressing the optimal tracking problem. Two specific examples of the method applications, one in a UPS inverter system and the other one in a DG system, as applied to tuning of a PR and a PI controller are studied in detail. Both examples are simulated in PSCAD and the results confirm analytical derivations.