Modelling, System Identification and Position Control Based on LQR Formulation for an Electro-Hydraulic Servo System

Abstract

Abstract This study presents the mathematical modelling, system identification using grey-box model estimation and position-tracking control for an electro-hydraulic servo system (EHSS) using four control strategies based on LQR formulation: Linear quadratic regulator (LQR) approach for servo systems, linear quadratic integral (LQI), linear quadratic tracking (LQT) and a variation of LQT named here LQTβ. First, the nonlinear model of the electro-hydraulic servo system was obtained using differential equations based on hydraulic theory and physical laws. The model was then linearized and its parameters were estimated using grey-box method when the open-loop system was excited with a chirp signal from 0 to 30 [Hz]. The estimated model was verified with experimental data of the open-loop system response for square wave and continuous step inputs of different amplitudes and frequencies. For the position-tracking four control strategies based on LQR formulation were proposed. The main difference among them is the conception of the cost function that is minimized: the LQR includes all the system’s states and the control signal, the LQI includes all system’s states, the tracking error and the control signal, the LQT includes only the tracking error and the LQTβ the tracking error and its derivative. The four control strategies were simulated in MATLAB Simulink and initially tuned using Bryson’s rule, then were implemented in the real system and finely tuned by trial and error until the best performance is achieved. They all were tested using step, square wave and sine wave inputs, and were analyzed in terms of settling time, rising time, peak time, overshoot margin, steady-state error, energy consumption and repeatability against a conventional PID controller. The experimental results showed better tracking, better repeatability and less energy consumption using the LQR based techniques than using the PID control, specifically the LQR and the LQTβ showed the fastest response and smallest steady-state error among the LQR based strategies. This study was carried out with the electro-hydraulic servo system (EHSS) of the seismic shaker table of the Dynamics and Structural Control Lab at Universidad Industrial de Santander. The seismic shaker table is composed of a Parker double rod dynamic hydraulic cylinder commanded by an MTS 252.24G-04 servo valve and powered by an MTS 505.11 hydraulic power unit. Cylinder’s position was measured using an integrated Trans-Teck LVDT. The control system was build and implemented in MATLAB Simulink using Quanser Q8-USB card.