Performance assessment and robustness analysis using an ARMarkov approach

Abstract

Application of the ARMarkov model-based formulation offers significant advantages for assessment/monitoring and robustness analysis of process systems. The ARMarkov method does not require a priori specification of the system time delay/interactor matrix, needs only an approximate estimate of model order and can be done using open or closed-loop process data. By appropriate use of standard, linear model estimation techniques, it directly produces statistically consistent estimates of the first few, user-specified number of Markov parameters even in the presence of colored noise. It is shown in this paper that the Markov parameters and the ARMarkov model can be used to calculate the interactor matrix and several process performance metrics including sensitivity/complementary-sensitivity functions and time-domain criteria such as speed of response, minimum variance values etc. In addition it is shown that model-based predictive control (MPC) systems formulated using ARMarkov models have a special state space structure that leads to less conservative robustness bounds for specific types of uncertainties (such as gain mismatch, uncertainty in the fast or slow dynamics, etc.) than applying the Small Gain Theorem directly to the conventional state space model structure.