Several studies have been conducted to develop innovative solutions for satisfying industrial requirements. In soft pneumatic actuators (SPAs), which use compressed air for actuation, the air inlet/outlet is typically provided by proportional-pressure-control valves. According to the latest proposals found in the literature, replacing the latter with lighter and cheaper 2/2 or 3/2 digital solenoid valves is challenging. PI, PID, and sliding mode controllers have been proposed to achieve this goal. The performance of these controllers is often influenced by the identification of analytical models under simplifying assumptions. This paper proposes an analytical model to describe the charging and discharging of the SPA by experimentally identifying the lumped parameters of the corresponding pneumatic circuit. Both the chocked mass flow condition and the variations of the time constants were considered in the model. A closed-loop fuzzy controller is developed and simulated in MATLAB Simulink environment. The controller manages a square waveform command signal's duty cycle (DC) for a 3/2 digital solenoid valve by the pulse width modulation (PWM) technique with charge and discharge asymmetry compensation. Numerical results show the proposal's effectiveness for constant reference pressures and reference pressure-time sequences.