Indirect closed-loop systems identification of distributed systems

In many cases it is impossible to remove the feedback during systems identification as it will make the system unstable. This paper presents an identification method for spatially interconnected distributed systems with identical subsystems operating in closed-loop feedback control. The proposed method takes into consideration the boundary conditions. The approach provides parameters estimate with minimum bias for unstable plant models when there is additive colored noise in output data. This yields consistent parameters estimate and, compared with other techniques to identify such systems under similar situations, takes far less time. The method is illustrated for two-dimensional systems (one for time and one for space), but is equally applicable for systems having more dimensions in space. The proposed technique is for general two-dimensional systems which may be causal, semi-causal (spatially interconnected systems) or non-causal. The effectiveness of the approach is demonstrated with a simulation example.