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In this paper, we developed a detailed mathematical model of dual action pneumatic actuators controlled with proportional spool valves. Effects of nonlinear flow through the valve, air compressibility in cylinder chambers, leakage between chambers, end of stroke inactive volume, and time delay and attenuation in the pneumatic lines were carefully considered. We performed system identification, numerical simulation, and model validation experiments for two types of air cylinders and different connecting tubes length. The mathematical model of the present article is used in a sequel article to develop high performance nonlinear pneumatic force controllers. S0022-0434(00)00503-7
Richer et al. (1999) studied this question.