Sliding mode control experiments of uncertain dynamical systems with time delay

• A nonlinear system with parameter uncertainty under a delayed control is studied.
• Robust sliding mode control is optimally designed to deal with the vibration problem of the system.
• A high-order control design methodology is developed for the sliding mode control.
• Effect of model uncertainty on the control effort is quantitatively studied.
• The control system is experimentally studied and compared with extensive numerical simulations with excellent agreement.

This article presents the simulation and experimental studies for the nonlinear time-delayed dynamical systems with uncertainties. A rotary flexible joint made by Quanser is chosen as the model system to investigate the method for sliding mode control design. We considered the geometric nonlinearity of the flexible joint consisting of two linear springs. The system is assumed to have constant delay time and uncertain parameters with known upper and lower bounds. We also design an optimal sliding surface for the sliding mode control. Simulations and experiments are carried out to demonstrate the utility of the control method. Finally, the results from the simulations and experiments are in excellent agreement.