Multivariable identification using centralized fixed modes

A procedure to determine a state space model of a multivariable system (lambda inputs, m outputs) is presented. The model is suitable for control studies and uses single input, single output (SISO) system data in the identification procedure. The procedure can be defined in three distinct steps. First, the system's lambda x m SISO transfer functions are identified by using any standard or known identification technique for SISO systems. One objective of this step is to identify SISO transfer functions with as few distinct modes as possible between any two functions. Second, the time domain realization of each SISO transfer function is obtained in a straightforward manner and combined into a total multivariable realization. This total realization, in all probability, has more state variables than are required to define system response. In the third step, these excess or redundant states are removed by using minimal realization theory. The remaining states are related to system centralized fixed modes. Eigenvalue-eigenvector techniques were recently reported that yield a computationally feasible solution to the problem posed in step three. The procedure is applied to QCSEE data to demonstrate its feasibility.