Development of Block Oriented Recursive and Constrained Parameter Estimation Schemes for ARMAX Models

In the process industry, black box linear perturbation models are often used for the development of model predictive controllers. Maintaining a high-quality model so as to achieve good control performance in the face of changing operating conditions is a difcult task. In adaptive control schemes, the model parameters are updated online using recursive least square schemes. These recursive schemes typically update the model parameters at every sampling instant. Since in many chemical/biological processes, the model parameters change at a relatively slow rate compared to state variables, it is beneficial to update the model parameters using blocks of data points instead of updating at each sampling instant. In this work, a constrained update scheme based on blocks of data is proposed for updating ARMAX model parameters online. The inclusion of constraints ensures that the noise model is stable and inversely stable. The constrained formulation is further simplifed to arrive at two unconstrained recursive parameter update schemes. The efficacy of the proposed schemes is demonstrated using a simulation study on an artificial system and experimental data obtained from a temperature control system and benchmark quadruple tank system.