Open-Loop Characterisation of Soft Actuator Pressure Regulated by Pulse-Driven Solenoid Valve

Solenoid valves are widely used for pressure regulation in soft pneumatic robots, but their inherent electromechanical nonlinearities—such as dead zones, saturation, and pressure-dependent dynamics—pose significant challenges for accurate control. Conventional pulse modulation techniques, including pulse-width modulation (PWM), often exacerbate these effects by neglecting valve-switching transients. This paper presents a physics-informed dynamic modelling framework that captures transient and pressure-dependent behaviours in solenoid valve-driven soft pneumatic systems operating under pulse modulation. The model is experimentally validated on a soft pneumatic actuator (SPA) platform using four modulation schemes: PWM, integral pulse frequency modulation (IPFM), its inverted variant (IIPFM), and ΔΣ modulation. Results demonstrate that only the IIPFM scheme produces near-linear input–pressure characteristics, in close agreement with model predictions. The proposed framework provides new physical insights into valve-induced nonlinearities and establishes a systematic basis for high-fidelity modelling and control of soft pneumatic robotic systems.