Path tracking design based on I/O Davidson-Cole transfer function for square MIMO systems

The aim of this paper concerns motion control and robust path tracking design for square MIMO systems. A path tracking approach using fractional differentiation is proposed, based on direct optimization of an I/O Davidson-Cole type transfer function. The main important property of this transfer function is that it does not present overshoot on its output and allows synthesis with only two parameters to obtain an optimal settling time. The SISO approach was presented in previous works. This paper presents an extension for square multivariable systems. Using MIMO-QFT robust synthesis methodology and taking into account the plant uncertainties, the fractional prefilters are deduced. This method specifically deals with the appropriate transformation of the MIMO system to the equivalent MISO system. The optimization of the two prefilter parameters is founded on the plant output error integral minimization, considering the actuators physical constraints and the tracking performance specifications. A numerical example is considered to indicate performances of the used procedure.