A Control Design Method for Switching Systems with Application to Pneumatic Servo Systems

The motivation for this work is to formulate a control design method for a pneumatic system with discrete input values (resulting from the use of binary or three-position solenoid valves) that addresses the time-delay that is often associated with the flow state of solenoid on/off valves. This method is shown to be applicable to a general class of nonlinear, nonautonomous systems subject to possibly discontinuous governing dynamics. This method is then extended for timedelayed systems and applied to the case of LTI models with a finite number of allowed input values possessing a pure time delay. A pneumatic inertial positioning system employing binary solenoid valves exhibiting a time delay is modeled, and the control design method proposed is applied. An experimental implementation of the resulting control law for accurate position tracking utilizing only position feedback demonstrates the effectiveness of the method.