Multiswitching Surface Based Sliding Mode Controller for a Class of Underactuated Nonlinear Systems: With Application to Ball and Plate System

This correspondence focuses on the design of sliding mode control (SMC) schemes for the class of underactuated nonlinear systems represented in the cascaded form. Though SMC strategies have been developed for this class of systems, strict assumptions on the system dynamics make them nonfeasible when the system function is coupled with actuated variables. Moreover, these schemes are not realizable for underactuated systems with control input singularity. This manuscript proposes novel multiswitching surface based SMC schemes for the chosen class of systems with actuated variable coupled system function and control input singularity. The stability and robustness properties of the proposed sliding surface is established analytically. The controller parameters are optimally tuned using particle swarm optimization. The proposed schemes are employed for a ball and plate system and the performance is verified through simulations. The results are experimentally validated on a laboratory scale ball and plate module. Compared to the conventional SMC schemes, the proposed multiswitching surface based SMC scheme exhibits improved transient performance in the presence of parameter variations as well as disturbances. With the proposed method, there is a 30
$\%$
decrease in settling time and more than 40
$\%$
reduction in overshoot and integral absolute error. As the multiswitching surface chosen is integral in nature, the control input chattering inherently present in conventional SMC schemes is also eliminated.