Johannes Philippus Maree

Performance and Stability for Combined Economic and Regulatory Control in MPC

Abstract We propose a dual-objective MPC formulation in which the dual objective is the convex combination of an economic- and regulatory stage cost, using a specially formulated state-and input-dependent dynamic weight function. The purpose of the dynamic weight function is to promote increased economic performance while ensuring asymptotic stability for the economically optimal steady-state setpoint. First, sufficient conditions are derived for which the dual-objective MPC value function is a Lyapunov candidate function. Next, we propose a weight function which satisfies these conditions. We implement the combined economic and regulatory MPC, with proposed weight function, in an isothermal CSTR numerical case study, which illustrates how economics are emphasized during process transients, while retaining stability by emphasizing the regulatory cost close to the setpoint.

Combined economic and regulatory predictive control

A combined economic and regulatory Model Predictive Control (MPC) framework, referred to as dual-objective MPC, is presented. Economic and regulatory cost objectives are combined using an explicitly defined dynamic weight function. The features embedded in the weight function allow for increased economic online performance during process transients, while simultaneously steering the process to an optimal economic steady-state. The proposed strategy gives an online optimization problem of same type as typical nonlinear MPC formulations, with the same number of variables. Increased economic transient performance is illustrated for an acetylene hydrogenation case, when compared to regulatory MPC. A link to dissipativity theory for the presented dual-objective MPC strategy concludes the work.

On combining economical performance with control performance in NMPC

Abstract An overview is presented on existing multi-objective, one-layer and two-layer architectures that incorporate dynamic real-time optimisation for optimal process performance. A one-layer architecture, that entails a Non-linear Model Predictive Control formulation, is consequently proposed that attempts to address shortcomings identified with one-layer approaches. The proposed architecture is applied to a simplified non-linear, multi-well oil production case study, which illustrates the benefits of such an approach.

On convergence of the unscented Kalman–Bucy filter using contraction theory

Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilising stochastic contraction theory to conclude on exponential convergence of the unscented Kalman–Bucy filter. The underlying process and measurement models of interest are Itô-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual–actual systems framework to establish deterministic contraction of the estimated expected mean of process values. Under mild conditions of bounded process noise, we extend the results on deterministic contraction to stochastic contraction of the estimated expected mean of the process state. It follows that for the regions of contraction, a result on convergence, and thereby incremental stability, is concluded for the unscented Kalman–Bucy filter. The theoretical concepts are illustrated in two case studies.

Optimal control strategies for oil production under gas coning conditions

Gas coning, which can lead to gas breakthrough in thin oil-rim reservoir fields, may deteriorate economics in oil production. This work reports on optimal control policies to be considered for short-term oil production optimization under gas coning conditions. These policies, incorporating an oil-rate dependent Gas-Oil ratio model, are formulated as an optimal control problem which optimize the oil production rate, subject to gas processing capacity constraints. The result thereof is implemented in a closed-loop receding horizon control policy. Control philosophies investigated for increased oil production optimization include cyclic oil production shut-in at the vicinity of gas breakthrough (limiting the economic-deteriorating effects of excessive gas production, given gas processing constraints), and, steady oil production at-or after- the point of gas breakthrough. Near-well gas coning analysis reveals that gas coning dynamics may indicate which control philosophy (cyclic or steady oil production after process transients) may be optimal during closed-loop process operation.

On asymptotic closed-loop performance for linear MPC with terminal constraints

Employing Lyapunov theorems, under mild conditions, to establish asymptotic stability of the origin, is now common practice in the field of regulatory Model Predictive Control (MPC). However, feasibility and stability does not necessarily constitute towards optimality. By optimality we imply the closed-loop optimality of a receding-horizon control law with respect to the infinite-horizon cost function. Recent results in literature has quantified the sub-optimal closed-loop performance of stabilizing, receding-horizon control laws for MPC formulations with stabilizing terminal state regions. In this work we extend on the aforementioned results on performance, by stipulating necessary conditions under which one can compare asymptotic closed-loop performance of different MPC formulations with terminal regions of varying size. In particular, we present results for linear MPC where one can apply inverse optimality to some degree; hence, conclude results for asymptotic closed-loop performance. The developed concepts are illustrated on two numerical linear case studies.

On set-theoretic methods in tracking MPC

The construction of an enlarged terminal constraint set, which consequently implies a larger domain of attraction, is presented for the dual-mode control paradigm for tracking problems. Subsequently, a receding horizon optimal control problem is formulated as a Quadratic Programming problem, which can be efficiently solved on-line. The resulting formulation allows tracking to a set of admissible steady-state/input pairs, thereby, promoting on-line change of economic objectives, by the selection of different operational set-points, whilst, guaranteeing stability and feasibility of the underlying problem. Proof of asymptotic convergence and stability, using Lyapunov arguments, is given for this enlarged set of admissible steady-states.

Fault detection for the Benfield process using a parametric identification approach

A closed-loop process monitoring framework that entails subspace identification, and parametric fault detection are discussed, and subsequently applied to the Benfield process for fault detection. An extension to the derivation of the observability matrix of the subspace identification method guarantees stable identified system matrices. For fault detection, Extended Kalman filtering is utilized to recursively update a joint-set of initial system states and parameters, using current sampled process data and initial estimated parameters, obtained via the subspace method. Framework validation and verification is established via simulation, as well as using delayed, real-time measured process data from the Benfield process.