Synthesis and experimental demonstration of a hybrid adaptive PID-SMC algorithm for a class of underactuated nonlinear systems

• Published in: Nonlinear dynamics Vol. 113; no. 12; pp. 15037 - 15056
• Main Authors: Dil Kumar, T. R., Mija, S. J.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.06.2025
• Subjects: Adaptive algorithms; Algorithms; Controllers; Design; Error reduction; Hybrid control; Nonlinear systems; Optimization techniques; Parameters; Proportional integral derivative; Robust stabilization; Sliding mode control; Stability analysis; Synthesis; System dynamics; Systems stability; Transient performance
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-025-10903-z

This paper presents the synthesis of a hybrid control scheme of proportional integral derivative (PID) and sliding mode (SM) controllers for stabilizing the class of underactuated nonlinear systems described in the cascaded form. The PID controller performs well when the controller parameters are optimally tuned using standard methods, but its performance degrades in a broad operating region and in the presence of disturbances. Even though the inherent robustness property of sliding mode control (SMC) makes it an apt choice for this class of systems, strict assumptions on system dynamics make them impractical when the system function is coupled with actuated variables. Moreover, the SMC scheme is not feasible for underactuated systems having control input singularity. In addition, SMC ensures robust stabilization with a trade-off between convergence rate and chattering. This article proposes a novel adaptive double loop PID-SM control scheme to address these control challenges associated with the class of underactuated systems. The parameters of the PID controllers are adapted with respect to the sliding surface of the SM controller. The stability of the system is established using the Lyapunov stability analysis. The proposed scheme is experimentally demonstrated for stabilization of the ball on a plate module. The adaptive PID-SM hybrid controller exhibits improved transient performance and good robustness characteristics compared to conventional PID and SMC schemes. With the proposed method, the settling time decreases by 20%, maximum deviation in ball position reduces by 30%, and there is a more than 20% reduction in error in ball position in terms of the integral absolute error.