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In this article we present two nonlinear force controllers based on the sliding mode control theory. For this purpose we use the detailed mathematical model of the pneumatic system developed in the first part of the paper. The first controller is based on the complete model, and exhibits superior performance both in the numerical simulation and experiments, but requires complex online computations for the control law. The second controller neglects the valve dynamics and the time delay due to connecting tubes. The performance of this controller exhibits slight degradation for configurations with relatively short tubes, and at frequencies up to 20 Hz. At higher frequencies or when long connecting tubes are used, however, the performance exhibits significant degradation compared to the one provided by the full order controller. S0022-0434(00)00703-6
Richer et al. (Wed,) studied this question.