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Nonlinear parametric identification using flat differential model: Application to an intensity/pressure converter

In this paper we consider systems which are nonlinear with respect to its variables and to its parameters. A particular case is considered here: an intensity/pressure converter which able us to command an artificial muscle. One of the main problems in control of such system is to have an accurate model and so to know with sufficiently accuracy the different parameter's values. When the system is nonlinear, nonlinear algorithms must be used to determine the values of different parameters. In this paper a classical Gauss Newton is used to determine these values. An important modification of this algorithm, based on the flatness of the system is proposed. Indeed, when the nonlinear system is flat (i.e. if flat outputs can be found, any variable in the system is a differential function of the flat outputs) we can reverse the Gauss Newton principle. In this case the parameter's optimization parameter is not made by minimizing a quadratic error between the real output and a simulated output but by minimizing a error between the applied input and a input reconstructed from the measured output. With this modification the new algorithm doesn't need any integration that permits an important saving of time. This algorithm can also be used in the case of online identification. Experimental results are given for the considered process.