Modified Pleated McKibben Actuator: Dynamic Analysis and PID Control Analysis

Abstract

This paper presents the design, fabrication, and Lyapunov-based closed-loop control of a novel Pleated McKibben (PMcKibben) pneumatic artificial muscle for upper-limb rehabilitation robots. The actuator is fabricated from ultra-soft Ecoflex 00-20 (Shore 00-20 hardness), which substantially reduces the threshold and maximum operating pressures compared with conventional McKibben actuators, while enabling larger actuation strokes through the pleated geometry. Although PID-type controllers are widely applied to pneumatic artificial muscles, a formal closed-loop stability analysis for Proportional (P), Proportional-Derivative (PD), and Proportional-Integral-Derivative (PID) controllers applied to the full nonlinear PAM dynamics has not been previously reported. This paper addresses that gap: adopting the state-of-the-art nonlinear PAM model of Slightam and Nagurka (2020)—comprising force generation, Mooney–Rivlin hyperelastic stiffness, Coulomb and viscous friction, and compressed-air dynamics—as the analytical basis, rigorous Lyapunov stability proofs are derived for all three controllers. Each proof explicitly specifies the state variables, formally verifies all Lyapunov candidate function conditions, and establishes Uniform Ultimate Boundedness (UUB) of all closed-loop state variables under bounded disturbances and parameter uncertainties, with explicit UUB bounds derived. The UUB framework guarantees that bounded disturbances—such as modelling errors, friction variability, and measurement noise—produce only bounded deviations, confirming theoretical robustness without requiring disturbance-free conditions. The controllers are experimentally implemented on the fabricated PMcKibben actuator mounted on a human arm replica, with no model inversion required. Quantitative performance metrics—Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Integral of Absolute Error (IAE)—are reported for all nine simulation experiments and four closed-loop hardware tests. Results demonstrate progressive improvement from P to PD to PID control, with the PID controller achieving the best tracking accuracy: RMSE of 1.2 mm in simulation and 2.8° in experiments.