Experiment designs for identification of multivariable dynamic systems

Systems with multiple inputs and multiple (MIMO) outputs are more difficult to identify than systems with a single input and a single output (SISO) due to interactions between the variables. Surprisingly little is said about the experiment design for MIMO system identification in major textbooks on system identification. The most advanced advice is that the inputs should be perturbed simultaneously in an uncorrelated way. It has been noted that this kind of excitation tends to produce poor data for system identification if the model is to be used for control system design. In this paper, an overview is given of proposed methods to overcome this problem by excitation of the (estimated) gain directions of the system. A new method, where the dynamics are explicitly taken into account, is also presented. This method is significantly simpler than some other methods proposed for inclusion of dynamics in the design. Thus, it is suitable for practical application. The methods are illustrated and compared by an instructive example of a 2x2 system. A dynamic experiment design for a 3x3 system is also presented.