Boundary Logic-Based Hybrid PID-SMC Scheme for a Class of Underactuated Nonlinear Systems-Design and Real-Time Testing

This article presents the design of a boundary logic-based hybrid scheme of sliding mode (SM) and proportional integral derivative (PID) controllers for the class of underactuated nonlinear systems modeled in the cascaded structure. Though the PID control schemes developed for this class of underactuated systems perform well if the controller parameters are tuned using systematic approaches, it lacks robustness when employed for a wide operating region. The robustness characteristic of sliding mode control (SMC) renders it suitable for this class of systems. However, the solid assumptions considered to simplify the system dynamics and control input singularity make it unworkable for practical implementation. Moreover, SMC schemes ensure robust stabilization with a trade-off between convergence speed and chattering. In this article, a boundary-based adaptive exponential reaching law is developed to enhance the efficacy of SMC. This SMC scheme is used together with a double loop PID controller in hybrid mode to utilize the advantages of both schemes. The SM and PID controllers are operated according to a boundary logic and the stability of the system is proven by Lyapunov method. The controller parameters are optimized using a modified particle swarm optimization (PSO) algorithm. The proposed scheme is implemented on a ball balancer system, and the performance is analyzed via simulations. Real-time testing and validation of the developed control schemes are performed on a laboratory setup of a ball balancer module. In comparison to PID and SMC schemes, the proposed boundary logic-based hybrid scheme demonstrates enhanced transient performance, even under the influence of disturbances and parametric uncertainties. By employing the proposed hybrid control scheme, the settling time is decreased by 40%, the maximum deviation in ball position is reduced by 50%, and the integral absolute error (IAE) and the root mean square error (RMSE) are lessened by more than 30%.