Adaptive state feedback control of a time-varying system

This study conducted adaptive state feedback control of a linear system that was purified from noise and disruptive effects. For this purpose, first of all, state variables of the system were estimated by using a discrete-time kalman filter and reduced-order state observer. Optimal control of the system was performed by Linear Quadratic Regulator (LQR) method. Since the state feedback gain matrix is stable in LQR control method, it cannot display the desired performance in time-varying systems even though actualizing the optimal control performance in time-invariant systems. For this purpose, the adaptive state feedback controller structure was designed by supporting the Lyapunovbased adaptive mechanism to provide the optimal control of time-variant systems. Thus, stability has increased by minimizing the effects of noise and variable load. Recursive least squares (RLS)-based adaptive state feedback control method was revealed in the second stage of the study. A system identification block that gives the mathematical model of a time-variant system by utilizing input/output data packages of the controller was established at first. Parameters of the time-variant system are updated by observing the system thanks to this block. LQR is renewed based on these updated parameters; thus, it is provided for the system to adjust itself based on changing system parameters. So, the effects of the time-variant load have been minimized via the RLSbased adaptive state feedback control approach. Matlab/Simulink state-space model belongs to Variable Loaded Servo (VLS) system module was obtained for simulation experiments; system control was performed by the new methods offered. The offered method and Kalman filter in literature were compared with reduced-order observer and results of the method using LQR together. It is seen when the results are evaluated by considering performance indexes that the offered method increases the system performance and stability by minimizing noise and variable load better compared to other studies in the literature. Moreover, there were performed trials on Virtual Simulation Laboratories (VSIMLABS) servo control testing equipment to obtain the practical application results of the proposed methods. The effectiveness of the method was observed by basing the indexes of performance. It is seen from the obtained results that the simulation and application results are compatible. Furthermore, simulation and practical application results reveal that the offered approach minimizes the load effect and noise and also the system operates at high efficiency.