An Experimental Study on Friction Identification of a Pneumatic Actuator and Dynamic Modeling of a Proportional Valve

In this paper, the dynamic model of a pneumatic system which comprises a pneumatic actuator and a proportional directional electrical valve is derived. Accordingly, an experimental method is proposed to the end of modeling unknown parameters which are unmeasurable directly from the available pneumatic system. Friction force and viscous coefficient in dynamic equation of the actuator and mass flow rate in dynamic equations of electrical proportional valve are unknown parameters which are subject to be identified. The dynamic behavior of the unknown parameters are modeled by using exponential, polynomial and fourier series transform functions. Pressure of the pneumatic actuator and supply pressure are measured by the means of pressure sensors. Displacement encoder and IMU-GY80 sensor are employed to obtain the value of position and acceleration of the cylinder, respectively. Viscous coefficient is calculated in such a way that pneumatic force is not exerted which is based on the so-called Free-Fall test. By solving a second order differential equation of cylinder dynamics, viscous coefficient and Coulomb friction are obtained. Finally, the identified model is validated by comparing the state space variables of the pneumatic system measured by experimental tests and the identified model. From the experimental results, it has been revealed that the mean absolute percentage error for estimating the state variables are 19.94 (position), 26.78 (velocity), 0.78 (pressure 1) and 0.21 (pressure 2). The latter certifies the exactitude and performance of the identified dynamic model.