Robust Backstepping Sliding Mode Control Design for a Class of Underactuated Electro–Mechanical Nonlinear Systems

This paper presents a backstepping sliding mode control (BSMC) scheme for uncertain underactuated nonlinear systems. Since, underactuated electro-mechanical nonlinear systems (UEMNS) operate under the fewer number of inputs than the degree of freedom, therefore, the control of such systems remains a complex task. In this work, a class of UEMNS is considered which can be transformed into the so-called regular form. In the design process, these UEMNS are first transformed into regular form. In this form, the systems are properly subdivided into series cascaded blocks in which the one of the blocks is indirectly driven by the applied control input whereas the second block is directly controlled by the control input. This structure is apparently suitable for backstepping design. Hence, all the controller steps are designed via the proposed backstepping sliding mode technique. The step by step stability is proved rigorously by considering the Lyapunov approach. In term of benefits, this designed control law provides low-frequency vibration as compared to conventional SMC along with robust performance in the presence of matched uncertainties. This claim is verified via the numerical simulation results of the cart-pendulum system. For further confirmation, these results are also compared with the standard literature results to demonstrate the benefits and effectiveness of the aforesaid control scheme for such class.