Identification in Closed Loop

Abstract

If the design of self-optimizing adaptive control systems is based on identified process models, process identification has to be performed in closed loop. There are also other applications in dynamic processes which must be identified in closed loop. It must first be established whether methods developed for open loop identification can also be applied to the closed loop, taking into account the various convergence conditions. The problem is quite obvious if correlation analysis is considered. For convergence of the cross correlation function between the input u(k) and the output y(k), the input u(k) must be uncorrelated with the noise n(k) contaminating the output y(k). As feedback generates such a correlation, correlation techniques cannot be applied directly to closed loop identification. In the case of parameter estimation the situation changes, as the error signal e(k) only must be un-correlated with the elements of the data vector ψ^T(k). This opens possibilities for closed-loop parameter estimation, as will be shown in this chapter.