Describing function of the pneumatic flapper-nozzle valve

This paper addresses the mass flow rate characteristic of a pneumatic valve set in the frequency domain. The valve set consists of a flapper-nozzle type valve and a constant isothermal volume chamber. It represents a part of the control system of the pneumatic parallel robot platform. Different flow regimes are analyzed because of air compressibility. The nonlinearity originating from the mass flow rate characteristic is approximated by the sinusoidal input describing function. Analytical determination of the describing function in a general case is not possible. However, the equivalent nonlinearity and the corresponding Hammerstein model can be introduced for a certain flow regime. In that case, the describing function of nonlinearity can be determined analytically. Amplitude and frequency responses show that the nonlinearity becomes more prominent at smaller frequencies and higher amplitudes of the exogenous signal. Analytical results show good agreement with the experimental results.