On Experiment Design for Identification of Ill-Conditioned Systems

In this paper experiment design for identification of ill-conditioned systems is studied. A short overview of recently proposed techniques is presented. These are mainly based on a singular value decomposition (SVD) of an estimated gain matrix. A summary of this approach with some extensions is given. Another approach is to find a D-optimal solution; the result is essentially the same as found by SVD methods. A result is that it is very important properly to excite the so-called low-gain direction of the system. The methods are motivated by the desire to guarantee integral controllability in model based control designs such as model predictive control (MPC). The dynamics of the process have not been a consideration in these works. However, it is well known from practical studies and simple models that high gains tend to be associated with slow dynamics and low gains with fast dynamics. For experiment design, it is useful to know how general this behaviour is. In this paper it is shown analytically that this indeed is a general property. Simple examples from the literature are used to support the result. Some possible modifications to existing design methods are given for situations, where the dynamics are not aligned with the gain directions.