State Estimation with Reduced-Order Observer and Adaptive-LQR Control of Time Varying Linear System

Abstract

In this study, a new controller design was created to increase the control performance of a variable loaded time varying linear system. For this purpose, a state estimation with reduced order observer and adaptive-LQR (Linear–Quadratic Regulator) control structure was offered. Initially, to estimate the states of the system, a reduced-order observer was designed and used with LQR control method that is one of the optimal control techniques in the servo system with initial load. Subsequently, a Lyapunov-based adaptation mechanism was added to the LQR control to provide optimal control for varying loads as a new approach in design. 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 rotary servo system was modelled as a time-varying linear system and used in simulations in Matlab-Simulink environment. Based on the simulation results and performance measurements, it was observed that the proposed method increases the system performance and stability by minimizing variable load effect.

Kalman Filtresi ile Ayrık Zamanlı Durum Tahmini ve Zamanla Değişen Doğrusal Bir Sistemin Adaptif LQR Kontrolü

“…Our main goal in this study is to ensure that the system adapts to different environmental conditions by constantly updating the state feedback gain matrix value u outputs [21]. As is understood from study in [22], the Lyapunov function needs to be higher than zero for the system to be stable. Additionally, the derivative of the same function needs to be smaller than zero.…”

“…If the gain matrix value at discrete LQR output and also the adaptively produced feedback gain value are respectively defined as   u outputs [21]. As is understood from study in [22], the Lyapunov function needs to be higher than zero for the system to be stable. Additionally, the derivative of the same function needs to be smaller than zero.…”