Model predictive control of processes with input multiplicities

Sistu, Phani B.; Bequette, B. Wayne

doi:10.1016/0009-2509(94)00477-9

Cited by 89 publications

(66 citation statements)

References 27 publications

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“…The control objective is to maintain x 2 at a set-point of one. Consequently, the desired steady states for x1 and u are 2.5 and 25, respectively [14], [7]. We linearize (21) We implement the constrained LQR law on this linear system, with an appropriate shift of the origin to account for the nonzero setpoint.…”

Section: A Van De Vusse Reactormentioning

confidence: 99%

Constrained linear quadratic regulation

Scokaert

Rawlings

1998

IEEE Trans. Automat. Contr.

479

276

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Abstract-This paper is a contribution to the theory of the infinitehorizon linear quadratic regulator (LQR) problem subject to inequality constraints on the inputs and states, extending an approach first proposed by Sznaier and Damborg [16]. A solution algorithm is presented, which requires solving a finite number of finite-dimensional positive definite quadratic programs. The constrained LQR outlined does not feature the undesirable mismatch between open-loop and closed-loop nominal system trajectories, which is present in the other popular forms of model predictive control (MPC) that can be implemented with a finite quadratic programming algorithm. The constrained LQR is shown to be both optimal and stabilizing. The solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution. Inherent to the approach is the removal of a tuning parameter, the control horizon, which is present in other MPC approaches and for which no reliable tuning guidelines are available. Two examples are presented that compare constrained LQR and two other popular forms of MPC. The examples demonstrate that constrained LQR achieves significantly better performance than the other forms of MPC on some plants, and the computational cost is not prohibitive for online implementation.Index Terms-Constraints, infinite horizon, linear quadratic regulation, model predictive control.

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Section: A Van De Vusse Reactormentioning

confidence: 99%

Constrained linear quadratic regulation

Scokaert

Rawlings

1998

IEEE Trans. Automat. Contr.

479

276

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“…Such kind of nonlinear behavior creates a situation where the same state value is obtained for two different values of the manipulated variable. From a closed-loop control point this behavior is undesirable since, under certain conditions, it has been related to the presence of right-hand plane zeros [18], which limit the response speed of the closed-loop system. The emergence of right-hand plane zeros makes the use of PID controllers impractical because of slope sign changes [19].…”

Section: Cstr With Simultaneous Reactions and Input Multiplicitiesmentioning

confidence: 99%

Simultaneous Cyclic Scheduling and Control of a Multiproduct CSTR

Flores‐Tlacuahuac

Grossmann

2006

Ind. Eng. Chem. Res.

159

200

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In this work we propose a scheduling and control formulation for simultaneously addressing scheduling and control problems by explicitly incorporating process dynamics in the form of system constraints that ought to be met. The formulation takes into account the interactions between such problems and is able to cope with nonlinearities embedded into the processing system. The simultaneous scheduling and control problems is cast as a Mixed-Integer Dynamic Optimization (MIDO) problem where the simultaneous approach, based on orthogonal collocation on finite elements, is used to transform it into a Mixed-Integer Nonlinear Programming (MINLP) problem. The proposed simultaneous scheduling and control formulation is tested using three multiproduct continuous stirred tank reactors featuring hard nonlinearities.2

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“…No fi xed parameter linear controller with integral action can be designed for closed-loop stable behaviour at operating points on different "sides" of this peak. An additional problem is that systems with input multiplicity often have a non-minimum phase zero (resulting in "inverse response" or "wrong-way" behaviour) region on one side of the peak, as shown by Sistu and Bequette (1995). This results in an additional complication even for a non-linear strategy that accounts for the change in the sign of the gain of a system with input multiplicity.…”

Section: Motivating Non-linear Behaviourmentioning

confidence: 99%

Non‐Linear Model Predictive Control: A Personal Retrospective

Bequette

2007

Can J Chem Eng

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An overview of non-linear model predictive control (NMPC) is presented, with an extreme bias towards the author's experiences and published results. Challenges include multiple solutions (from non-convex optimization problems), and divergence of the model and plant outputs when the constant additive output disturbance (the approach of dynamic matrix control, DMC) is used. Experiences with the use of fundamental models, multiple linear models (MMPC), and neural networks are reviewed. Ongoing work in unmeasured disturbance estimation, prediction and rejection is also discussed.On présente un aperçu général du contrôle prédictif par modèles non linéaires (NMPC), en mettant l'accent en particulier sur les expériences des auteurs et les résultats publiés. Les défi s incluent des solutions multiples (à partir des problèmes d'optimisation non convexes), ainsi que la divergence entre les sorties de modèle et d'installation lorsque la perturbation de sortie additive constante (la méthode du contrôle de matrice dynamique, DMC) est utilisée. Les expériences avec les modèles fondamentaux, les modèles linéaires multiples (MMPC) et les réseaux neuronaux sont examinées. Le travail actuellement mené sur l'estimation, la prédiction et le rejet des perturbations non mesurées est également examiné.

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Model predictive control of processes with input multiplicities

Cited by 89 publications

References 27 publications

Constrained linear quadratic regulation

Constrained linear quadratic regulation

Simultaneous Cyclic Scheduling and Control of a Multiproduct CSTR

Non‐Linear Model Predictive Control: A Personal Retrospective

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