Performance assessment of MIMO systems based on I/O delay information

The minimum variance (MV) control is one of the most popular benchmarks in control performance assessment. For a SISO process, the minimum variance can easily be estimated given the information of the process time delay. However, it is more difficult to obtain the MV benchmark for a multivariable system since the solution relies on the process interactor matrix. The computation of the interactor matrix requires knowledge of Markov parameter matrices of the plant, which is tantamount to complete knowledge of the process model. This requirement is usually unrealistic, since the model is either not available or not accurate enough for a meaningful calculation. However, the time delays between the inputs and outputs are relatively easy to obtain and can be used to construct an I/O delay matrix. This paper shows how to estimate upper and lower bounds of the MIMO MV performance from routine operating data with the I/O delay matrix known. In order to estimate the upper bound, the introduction of additional time delays into the controller is normally needed. However, should this be considered restrictive, then another upper bound which has recently been proposed can be used instead. On the other hand, the lower bound can readily be estimated from routine data. The results are illustrated by a simulation example.