NSGA-II BASED MULTI-OBJECTIVE OPTIMIZATION OF WEIGHT MATRICES FOR LQR CONTROLLER APPLIED TO DC MOTOR

Abstract

In addition to ensuring the stability of a Linear Time Invariant system with the LQR control approach, the fact that the feedback gain to be applied to the system is achieved by minimizing a quadratic performance criterion makes this control approach capable of shaping the performance expected from a closed-loop system. At this point, it is important in terms of controller performance to create the quadratic performance criterion or cost function to be minimized, over the weight matrices it contains, in accordance with the purpose. Therefore, the optimization of the weight matrices used in the design of the LQR controller should be carried out in line with the multiple performance objectives expected from the controller. This situation creates a multi-objective optimization problem. Although the weight matrices of the quadratic cost function can be adjusted with the help of classical methods such as trial and error, pole assignment, without optimization, this can be tiring and time consuming. In order to overcome this difficulty, it is possible to benefit from various multi-objective optimization techniques. Within the scope of this study, LQR-based optimal DC motor control is aimed. For the LQR controller, the Q and R weight matrix parameters of the square cost function need to be adjusted. Relevant parameters are adjusted with the help of the optimization algorithm known as Non-Dominated Sorted Genetic Algorithm (NSGA-II), which is one of the multi-purpose optimization techniques. By using the optimum parameters obtained, the performance findings of the synthesized LQR controller on the system are presented with simulation results.