Effect of feedback controllers in state estimation schemes

It is common practice in state estimation of chemical systems to include au gmented states modeled as random-constant or random-walk processes. When pr ocess controllers with integral terms are present, undesirable interaction effects may occur between the augmented states and the controllers. If no a ttention is paid to this interaction, the resulting estimator may diverge. In this work the interaction between controller and augmented states is ana lyzed. Using the linear systems theory, it is shown that the unwanted inter action and final divergence are caused by lack of detectability of the augm ented system. A specific test, based on the Popov-Belevitch-Hautus rank tes t, to check the detectability in the system under study is derived. In many cases the test can be performed by simple inspection. A series of examples are given where the concept of detectability is applied to help in discove ring and preventing the negative interaction between controllers and augmen ted states. Finally, a discussion is presented comparing the results of the standard observability test, applied to a real problem, with those obtaine d with the test derived here and with the behavior of a real estimator for the same problem. It is concluded that the standard observability test is n ot able to discriminate between different estimator designs and consequentl y to produce practical results as those obtained with the alternative test, i.e., the disclosure of unfeasible estimator designs.