Comparative Study of LQR, LQG and PI Controller Based on Genetic Algorithm Optimization for Buck Converters

This paper describes the design procedure of LQR, LQG and PI controller for a buck power converter circuit. Initially, Genetic algorithm (GA) is implemented to determine an optimal value for the feedback gain matrix and Kalman filter estimator gain of the LQR and LQG controllers respectively. LQR control approach is usually implemented when all the state variables of the system are readily available and the system measurements are noise- free. However, sometimes, it is not possible to estimate all the states of the system besides neither the measurement nor the process are free of noises. Therefore, Linear Quadratic Gaussian (LQG) control technique is introduced that is basically an LQR, which is the groundwork of the LQG, with a Kalman filter estimator. The estimation analysis confirms the performance of the designed LQG controller. Simulation results showed that the Kalman filter has succeeded in producing an appropriate estimation in spite of noises presence. Finally, a comparison was made between LQG and PI controllers. It has shown that LQG controller is capable of obtaining the best transient response in term of settling time and peak overshot values as it combines the advantages of both LQR and PI controllers.