Input designs to obtain uncorrelated outputs in MIMO system identification

A problem in open-loop identification of multiple-input multiple-output (MIMO) systems is that standard designs using uncorrelated inputs tend to produce correlated outputs. If the system is ill-conditioned, this correlation may be very strong. Such a correlation reduces identifiability and may result in a model with different controllability properties than the true system. If the model is used for control system design, the result may be poor closed-loop performance and even instability.The author has recently presented an experiment design method for MIMO system identification that solves the main problem by producing uncorrelated outputs for the model used in the design. The solution to the design problem is not unique, however. For a given type of input, the same output covariance can be obtained by different input designs. In this paper, various design options are studied. One of them is to minimize the input amplitudes. The considered signal types are pseudo random binary sequences (PRBS) and multi-sinusoidal signals with optimized phase shifts. Two systems having different directionality properties and number of inputs/outputs are used for illustration.