A Nonlinear Integral Sliding Surface to Improve the Transient Response of a Force-Controlled Pneumatic Actuator With Long Transmission Lines

A force-controlled pneumatic actuator with long connecting tubes is a well-accepted solution to develop magnetic resonance imaging (MRI)-compatible force control applications. Such an actuator represents an uncertain, second-order, nonlinear system with input delay. The integral sliding mode control, because of guaranteed robustness against matched uncertainties throughout the system response, provides a favorable option to design a robust controller for the actuator. However, if the controller is based on a linear integral sliding surface (LISS), the response of the actuator overshoots, especially when there are large initial errors. Minimizing overshoot results in a smaller controller bandwidth and a slower system response. This paper presents a novel nonlinear integral sliding surface (NLISS) for a sliding mode controller to improve the transient response of the actuator. The proposed surface is a LISS augmented by a nonlinear function of tracking error and does not have a reaching phase when there are initial errors and even multiple steps in the desired trajectory. The surface enables the integral sliding mode controller to offer variable damping, which changes from low to high as the transient error approaches small values and vice versa. Simulation studies and experimental results show that the controller based on the proposed sliding surface successfully eliminates the overshoot without compromising the controller bandwidth, rise, and settling times. For performance evaluation, the controller parameters are tuned using the globalized and bounded Nelder–Mead (GBNM) algorithm with deterministic restarts. The study also establishes the asymptotic stability of the controller based on the proposed sliding surface using Lyapunov's stability criterion.