This study presents the modelling, design and analysis of three controllers applied to the non-linear model of a hydraulic uniaxial seismic shake table. Firstly, the system’s non-linear model is constructed based on the dynamic and mathematical analysis of the hydraulic actuator and the servo valve. Then, three control systems based on the LQR formulation are designed for the acceleration tracking: Linear quadratic integral (LQI), linear quadratic tracking (LQT) and a variation of LQT. Lastly, simulations are carried out using the non-linear model as the plant and the results showed that the variation of the LQT control exhibited the best acceleration tracking performance.