Nonlinear Disturbance Observer-Based Dynamic Surface Control for Trajectory Tracking of Pneumatic Muscle System

In this paper, a phenomenological model of pneumatic muscle is established consisting of a contractile element, spring element, and damping element in parallel. To verify the practicability of pneumatic muscle (PM) modeling, dynamic surface control (DSC) characterized by convenient design and good transient performance is employed for realizing PM tracking control. However, parametric uncertainty is inevitable in PM modeling as friction and unknown external disturbances exist in a PM system. These PM modeling errors and unknown variables can undermine and deteriorate the control performance of PM systems. To solve this problem and improve control accuracy, a novel nonlinear disturbance observer-based dynamic surface control (NDOBDSC) is proposed for trajectory tracking of PM system. Through employing the nonlinear disturbance observer, the stated uncertainties can be estimated online and compensated. The proposed novel control scheme therefore integrates the advantages of DSC, while estimating time-varying uncertainties to achieve compensation of inherent uncertainties. The established control law guarantees that the closed-loop system is semiglobally uniformly and ultimately bounded. Both the simulation studies and practical experiments demonstrate the effectiveness of NDOBDSC, showing that the control performance of NDOBDSC is satisfactory in the presence of modeling errors, friction, changing load, and other uncertainties in the PM system.