There are many different methods for combined estimation and control of a chemical process. Presented below is a partial listing of some relevant work.
Moving horizon control has been effectively used in the process industries for many years, particularly the petroleum industries. Model Predictive Control solves an optimization problem at discrete time steps to minimize the error between the process measurements and a reference. A method for basic MPC using linear models with Kalman Filter based state estimation is presented in [17]. Methods for MPC have also been proposed using nonlinear models of a system to solve a nonlinear optimization problem at each time step [2] as well as extensions for use of nonlinear estimation techniques [13].
Parameter estimation and disturbance estimation can both be treated as a general state estimation problem. Kalman filtering has been used extensively to solve linear estimation problems. Nonlinear estimation techniques have also been applied. The Extended Kalman Filter (EKF) has met with much success [18,22]. Other types of Principal Component Analysis (PCA) can also be used for determination of the state of a process [6,5]. Moving horizon methods can produce results similar to those of Kalman Filtering. An overview of nonlinear estimation is found in [12]. Work with linear moving horizon methods [18,19] as well as nonlinear moving horizon methods [1,15,16] have show the effectiveness and usefulness of moving horizon approaches.
In some cases, disturbances affect a system in deterministic, stepwise manners. This type of effect can be considered similar to a fault detection and diagnosis problem. Fault diagnosis infers the use of qualitative rules. Parameter estimation can be treated as a moving horizon optimization problem. The combination of estimation and diagnosis results in a problem that can be formulated and solved using Mixed Integer (MI) optimization methods. Mixed Integer Quadratic Programming (MIQP) formulations have been proposed in [20,21]. A Mixed Integer Linear Programming (MILP) formulation and efficient solution methods have been discussed by [7]. Both MIQP and MILP of formulations expresses qualitative rules about a system as constraints involving integer variables.
Other fault detection and isolation methods are available for chemical engineers attempting to minimize process down time and industrial accidents. Rule-based diagnosis and root cause analysis has been presented in numerous sources [3]. A method for diagnosis based on digraph representations has also had some success [10,14]. Many fault detection and isolation methods are adequate for dealing with faults on a purely qualitative level. In many cases one desires a more useful estimate of the current system state, so a combined moving horizon estimation technique with propositional logic constraints is desired.