Robust identification of pneumatic servo actuators in the real situations

Intensive research in the field of mathematical modelling of the pneumatic cylinder has shown that its mathematical model is nonlinear and that a lot of important details cannot be included in the model. Selection of the model and the identification method have been conditioned by the following facts: (a) The nonlinear model of the system can be approximated by a linear model with time-variant parameters. (b) There is the influence of the combination of heat coefficient, unknown discharge coefficient and change of temperature on the pneumatic cylinder model. Therefore it is assumed that the parameters of the pneumatic cylinder are random (stochastic parameters). (c) In practical conditions, observations have a non-Gaussian distribution. Due to the abovementioned reasons, it is assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. The Masreliez-Martin filter (robust Kalman filter) was used for identification of parameters of the model. For the purpose of increasing the practical value of the filter, the following two heuristic modifications were performed: (1) It was adopted that T(k) = 1 holds for the scalar transformation of residuals. (2) Fisher information was approximated by a derivative of the Huber's function. The proposed modifications were confirmed through intensive simulations. In order to provide persistent excitation, the autocovariance function 1/f of the signal was used. The behaviour of the new approach to identification of the pneumatic cylinder is illustrated by simulations.