Application of Floquet Theory to On-Off Valve Controlled Pneumatic Actuators

A periodic linear time varying (LTV) model for on-off valve controlled pneumatic actuation systems, was described in an earlier paper by the authors. Based on this LTV model formulation, Floquet’s Theorem is invoked to characterize dynamic response of the system. A new computational technique called the expanded state space method is developed to calculate the frequency response of the LTV system with staircase coefficient variations. This technique is computationally superior to the straightforward solution scheme. Floquet Theory is also used to assess the nature of transient response. A single acting cylinder system controlled by an on-off valve is considered to illustrate the stability and transient response issues. Computer simulation based on the nonlinear model is used to obtain detailed results. It is shown that application of the Floquet Theory provides valuable insight into the dynamic response of the class of actuators considered.