Input/output fractional transfer function in path tracking design using multivariable crone controller

An approach to path tracking using fractional differentiation has been proposed with its application by simulation on a multivaribale system. This approach has been based on direct optimization of the closed loop output. The global transfer function is assimilated to a Davidson-Cole prefilter for which important property doesn't present overshoot on the plant output. This approach allows synthesis from only two parameters. The I/O transfer function optimum settling time is obtained. An extension to multivariable systems is the purpose of this work. Using MIMO-QFT (Multi Input Multi output-Quantitative Feedback Theory) robust synthesis methodology combined with CRONE control and taking into account the plant uncertainties, a fractional prefilter has been deduced. The optimization of two parameters of the prefilter is founded on the plant output error integral minimization, considering the actuators physical constraints and the tracking performance specifications.