Discrete Time State Estimation with Kalman Filter and Adaptive LQR Control of a Time Varying Linear System

Abstract

In this study, a new adaptive controller design was created that compensates for variable load effects and provides high control performance. In the proposed control method, Discrete Time Kalman Filter method (DKF), which estimates system output states, and Discrete Time Linear Quadratic Regulator (DLQR) method, one of the optimal control methods, were used. Although the DLQR control method produces good results when applied to unvarying systems, it cannot provide the desired response in time varying systems because it has no adaptation mechanism. In order to solve this problem, an adaptation mechanism based lyapunov method which has been developed that adapts to different environmental conditions, constantly updating a new state feedback gain matrix value (newK ) and optimal lyapunov adaptation gain values (1 ,2 ,3 ,4 ,5 and6 ) used for system control block such as position (1x ) control, speed (2x ) control and current (3x ) control. In this mechanism, lyapunov adaptation gain initial values were calculated using the Artificial Neural Network (ANN) method as a new approach. Thus, it was aimed to eliminate the variable load effects and to increase the stability of the system. In order to demonstrate the effectiveness of the proposed method, a variable loaded VsimLabs (Virtual Simulation laboratories) servo system was modelled as a time-varying linear system and used in practical implementation and simulation in Matlab-Simulink environment. Based on the experimental results and performance measurements such as Integral Square Error (ISE), Integral Absolute Error (IAE) and Integral time absolute error (ITAE), it was observed that the proposed method increases the system performance and stability by minimizing variable load effect and steady state error.