A Multistage Stochastic Programming Approach in Real-Time Process Control

Garrido, Izaskun; Steinbach, Marc C.

doi:10.1007/978-3-662-04331-8_25

Cited by 3 publications

(4 citation statements)

References 11 publications

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“…Now, we are going to consider the previous mechanical equation (26) with uncertainties as follows:ẇ (28) where the terms a, b, and f represent the uncertainties of the terms a, b, and f , respectively.…”

Section: Variable Structure Robust Speed Controlmentioning

confidence: 99%

“…Consider the induction motor given by Equation (28). Then, if Assumptions (A1) and (A2) are verified, the control law (35) leads the rotor mechanical speed w m (t) so that the speed tracking error e(t) = w m (t) − w * m (t) tends to zero as the time tends to infinity.…”

Section: Theoremmentioning

confidence: 99%

“…In the special case of normal distribution some alternative approaches are reported in the literature. For example, Garrido [28] proposed a Monte Carlo method based on direct integration of the second-order Taylor series expansion.…”

Section: Second Examplementioning

confidence: 99%

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Robust speed estimation and control of an induction motor drive based on artificial neural networks

Barambones

Garrido

2007

Adaptive Control & Signal

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In this paper, a speed estimation and control scheme of an induction motor drive based on an indirect field-oriented control is presented. On one hand, a rotor speed estimator based on an artificial neural network is proposed, and on the other hand, a control strategy based on the sliding-mode controller type is proposed. The stability analysis of the presented control scheme under parameter uncertainties and load disturbances is provided using the Lyapunov stability theory. Finally, simulated results show that the presented controller with the proposed observer provides high-performance dynamic characteristics and that this scheme is robust with respect to plant parameter variations and external load disturbances.

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Section: Variable Structure Robust Speed Controlmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

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Robust speed estimation and control of an induction motor drive based on artificial neural networks

Barambones

Garrido

2007

Adaptive Control & Signal

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“…Outgoing control formulations are rarely used in stochastic optimization. Two exceptions are the financial model in [12] and the process engineering problem in [18].…”

Section: (A14 Out )mentioning

confidence: 99%

Tree-sparse convex programs

Steinbach

2003

Mathematical Methods of Operations Research (ZOR)

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Dynamic stochastic programs are prototypical for optimization problems with an inherent tree structure inducing characteristic sparsity patterns in the KKT systems of interior methods. We propose an integrated modeling and solution approach for such tree-sparse programs. Three closely related natural formulations are theoretically analyzed from a control-theoretic perspective and compared to each other. Associated KKT system solution algorithms with linear complexity are developed and comparisons to other interior approaches and related problem formulations are discussed.

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Robust Process Control by Dynamic Stochastic Programming

Steinbach

2004

Proc Appl Math and Mech

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Unnecessarily conservative behavior of standard process control techniques can be avoided by stochastic programming models when the distribution of random disturbances is known. In an earlier study we have investigated such an approach for tank level constraints of a distillation process. Here we address techniques that have accelerated the numerical solution of the large and expensive stochastic programs by a factor of six, and then present a refined optimization model for the same application. IntroductionIn [3] we have proposed a multistage stochastic programming extension of model predictive control techniques to allow for the explicit incorporation of uncertainty via scenario trees. As a concrete example, we have studied the separation of methanol and water in a continuously running process where the inflow into a buffer tank is assumed to be random with known distribution. The objective is to minimize the total energy consumption over a given planning horizon under hard level constraints at the buffer tank; an alternative approach with probabilistic level constraints has been studied in [5]. The model investigated in [3] is a tracking problem that decouples uncertainty from the process dynamics: the stochastic on-line problem minimizes the expected quadratic deviation from a nominal deterministic operation profile that is determined off-line. For the numerical solution of the linear-quadratic multistage stochastic programs we rely on a primal-dual interior method in combination with a tree-sparse KKT solver for the highly structured Newton step subproblems [10].The current paper presents two techniques that are crucial for maximum efficiency in solving the stochastic on-line problem (and thus for future application to models with higher complexity): a problem reformulation enforcing relatively complete recourse, and a software tool generating custom code for the tree-sparse KKT solver, given a specific problem class. Finally we discuss a natural replacement of the tracking approach by an integrated optimization of uncertainty and process dynamics. Stochastic Tracking ModelConsider a planning horizon of T periods in discrete time, t = 0, 1, . . . , T, and a scenario tree with vertex set V. Let L t ⊆ V denote the level set of nodes at time t and L ≡ L T the set of leaves. Further let 0 ∈ L 0 denote the root, j ∈ L t the "current" node, i ≡ π(j) ∈ L t−1 its unique predecessor (if t > 0), and S(j) ⊆ L t+1 its set of successors. We also need sets V * = V \ {0}and V t = t τ=0 L τ , and finally the node probabilities p j > 0, j ∈ V. As in [3], let ξ t denote the tank inflow volume during (t − 1, t),f t the target extraction during (t, t + 1), and f t the actual extraction. The decision variables, y t = (x t , u t ), consist of the tank filling volume x t as state (with desired final valuex T ), and the local tracking error as control, u t = f t −f t . These quantities are random variables with realizations ξ j

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A Multistage Stochastic Programming Approach in Real-Time Process Control

Cited by 3 publications

References 11 publications

Robust speed estimation and control of an induction motor drive based on artificial neural networks

Robust speed estimation and control of an induction motor drive based on artificial neural networks

Tree-sparse convex programs

Robust Process Control by Dynamic Stochastic Programming

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