Nonlinear Discontinuous Dynamics Averaging and PWM-Based Sliding Control of Solenoid-Valve Pneumatic Actuators

A pneumatic actuator with solenoid valves is a discontinuous-input system because each valve can be either in on or off state. For such an actuator, this paper proposes a sliding-mode control scheme that is based on an averaged continuous-input model of the discontinuous-input open-loop system. The averaged model is obtained from the nonlinear dynamics of the open-loop system undergoing pulse width modulation (PWM) at the input (i.e., valve open/close action). The PWM duty cycle will be regarded as a continuous input to the proposed averaged model, and thus generated by the proposed sliding-mode controller. For the sliding control design, we note that a pneumatic actuator has two chambers with a total of four on/off valves. Thus, there are sixteen possible combinations for the valves´ switching. Seven of these sixteen operating “modes” are considered both functional and unique. The proposed sliding control utilizes and switches between these seven modes of the open-loop system in order to select the ones with necessary and sufficient amounts of drive energy. In comparing the new seven-mode controller to previous controllers, we will demonstrate reductions in the position tracking error and the number of switches made by the actuator´s on/off valves. The proposed control scheme is used in both position control of a pneumatic cylinder and bilateral control of a one degree of freedom teleoperation system. Experimental results are presented to validate our theoretical findings.