Development of kalman filter state estimation and LQRcontrol algorithms in simulation environment and servosystem application

DC motor is an important drive element in servo systems. They are frequently used in systems requiring speed or position control because they are easy to control and perform well. In this study, a servosystem is modeled, state variables are obtained by using Kalman Filters in noisy and noiseless environments and optimal control with Linear Quadratic Regulator (LQR) is performed. In the study, mathematical model of the servo system was obtained and simulation model was created. The LQR control of the system was then performed with state feedback. With this method, the design required for system control can be calculated optimally without the need for manipulation of the closed-loop poles. In addition, considering that it is not possible to measure all of the state variables in physical systems, the most accurate way to obtain the state variables of the system is an important factor for the control performance. Therefore, in the study, the state variables were obtained by Luenberger observer and Kalman state observer. By applying process and measurement noise to the servo system, the performance of the controller in noisy and noiseless environments was compared with the classical methods. In this way, an algorithm with high stability has been developed which produces predictions of the actual unknown values with uncertainty by predicting the conditions and working with low error in noisy environments.