Backstepping Control Design for a Continuous-stirred Tank

This paper deals with the nonlinear control of a three-state continuous-stirred tank system (CSTR) using the backstepping technique. A nonlinear state transformation is introduced so that the backstepping technique could be utilized on the transformed system. The backstepping controller is first designed for the nominal CSTR system. Then an augmented backstepping control law is designed for the uncertain CSTR model where a high gain switching term, based on sliding mode control theory, is utilized to add robustness to the proposed controller. The proposed controllers are shown to drive the output trajectories to their respective desired values, hence, ensuring the stability of the closed-loop system. Finally, several simulation studies are presented to illustrate the effectiveness of the proposed control laws.