Adaptive backstepping sliding mode control for hydraulic system without overparametrisation

The paper proposes an adaptive backstepping sliding mode control method for a hydraulic system with non-linear unknown parameters, which enter the system equations in a non-linear way. Backstepping sliding-mode method always assume that the parameters are certain and known. But in practical hydraulic system, the parameters are unknown or time varying. However, the upper bound of the lumped uncertainty is difficult to obtain in advance practical applications. Therefore, an adaptive law is proposed to adapt the value of the lumped uncertainty in real time. The main novelty of the developed adaptive control laws is that the number of parameter estimates is exactly equal to the number of unknown parameters throughout the entire coupled tanks system. Consequently, the phenomenon of overparametrisation, a significant drawback of backstepping technique to treat the control of coupled tanks in the previous literature, is eliminated in this study. Finally, experimental results are given to illustrate the tracking performance of interconnected system with the developed adaptive control schemes.