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Identifiability of linear dynamic networks typically depends on the presence and location of external (excitation or disturbance) signals, in relation to the topology of the parametrized network model set. For closed-loop identification, it is known that switching (non-parameterized) controllers can also provide excitation, thereby rendering the model set identifiable. In this paper, we derive verifiable conditions for network identifiability of the non-switching modules in presence of (non-parameterized) switching modules. These conditions generalize the classical result in closed-loop identification towards network identification. Furthermore, verifiable path-based conditions for identifiability in a generic sense are developed on the graph of the network model set.

The exploitation of subsurface hydrocarbon reservoirs is achieved through the control of production and injection wells (i.e., by prescribing time-varying pressures and flow rates) to create conditions that make the hydrocarbons trapped in the pores of the rock formation flow to the surface. The design of production strategies to exploit these reservoirs in the most efficient way requires an optimization framework that reflects the nature of the operational decisions and geological uncertainties involved. This paper introduces a new approach for production optimization in the context of closed-loop reservoir management (CLRM) by considering the impact of future measurements within the optimization framework. CLRM enables instrumented oil fields to be operated more efficiently through the systematic use of life-cycle production optimization and computer-assisted history matching. Recently, we have proposed a methodology to assess the value of information (VOI) of measurements in such a CLRM approach a-priori, i.e. during the field development planning phase, to improve the planned history matching component of CLRM. The reasoning behind the a-priori VOI analysis unveils an opportunity to also improve our approach to the production optimization problem by anticipating the fact that additional information (e.g., production measurements) will become available in the future. Here, we show how the more conventional optimization approach can be combined with VOI considerations to come up with a novel workflow, which we refer to as informed production optimization. We illustrate the concept with a simple water flooding problem in a two-dimensional five-spot reservoir and the results obtained confirm that this new approach can lead to significantly better decisions in some cases. © 2019, The Author(s).

We are concerned with the efficiency of stochastic gradient estimation methods for large-scale nonlinear optimization in the presence of uncertainty. These methods aim to estimate an approximate gradient from a limited number of random input vector samples and corresponding objective function values. Ensemble methods usually employ Gaussian sampling to generate the input samples. It is known from the optimal design theory that the quality of sample-based approximations is affected by the distribution of the samples. We therefore evaluate six different sampling strategies to optimization of a high-dimensional analytical benchmark optimization problem, and, in a second example, to optimization of oil reservoir management strategies with and without geological uncertainty. The effectiveness of the sampling strategies is analyzed based on the quality of the estimated gradient, the final objective function value, the rate of the convergence, and the robustness of the gradient estimate. Based on the results, an improved version of the stochastic simplex approximate gradient method is proposed based on UE(s2) sampling designs for supersaturated cases that outperforms all alternative approaches. We additionally introduce two new strategies that outperform the UE(s2) designs previously suggested in the literature.

Adopting a dynamic network viewpoint allows one to analyze and identify subsystems of a complex interconnected system. When studying a network of dynamic systems, it is important to know if significant nonlinear behavior is present in a dynamic network under study and where the nonlinearity is located in the network. This work extends the Best Linear Approximation framework from the closed-loop to the networked setting. The framework is illustrated using a practical step-by-step estimation and analysis procedure. It is shown how nonlinear behavior can be quantified and located in a dynamic network using this framework.

In this paper, we discuss the model predictive control algorithms that are tailored for uncertain systems. Robustness notions with respect to both deterministic (or set based) and stochastic uncertainties are discussed and contributions are reviewed in the model predictive control literature. We present, classify and compare different notions of the robustness properties of state of the art algorithms, while a substantial emphasis is given to the closed-loop performance and computational complexity properties. Furthermore, connections between (i) the theory of risk and (ii) robust optimization research areas and robust model predictive control are discussed. Lastly, we provide a comparison of current robust model predictive control algorithms via simulation examples illustrating closed loop performance and computational complexity features.

The paper describes a commutation method used for the active compensation of the deformation of the magnetically levitated mover of a planar motor. The single-stage double layer planar motor under consideration comprises a stator with two coil arrays and a mover with permanent magnets, and is designed to perform positioning tasks with high accuracy. To minimize the deformation of the light-weight moving structure, which is exposed to a large force during actuation, its flexible behavior is considered in the commutation of the machine. The commutation decouples the rigid-and flexible-body modes and calculates the required currents in the coils to produce a desired force and torque, as well as the modal force to control the flexible modes deformation. To decouple the flexible modes in the commutation, the relation from coil current to deformation is required, which is obtained by the coupling of a mechanical model and electromagnetic model of the motor. Using a 25-axis laser interferometer system, the deformation of the mover is measured and the relation from coil current to modal deformation is experimentally validated. In a second experiment, the deformation reduction of the magnetically levitated translator is demonstrated.

In many practical applications it might be desirable to excite only point at a time in an interconnection of multiple dynamic subsystems (e.g. large-scale system). Therefore multiple experiments need to be combined to successfully identify one or more subsystems in the network of subsystems. This papers illustrates how the identification of a linear subsystem of a dynamical network containing one or more nonlinear subsystems can result in biased estimates when multiple experiments are combined using the Best Linear Approximation (BLA) based approach.

Flow pattern analysis in a spiral Helix reactor is conducted, for the application in the commercial surfactant production. Step change response curves (SCR) were obtained from numerical tracer experiments by three-dimensional computational fluid dynamics (CFD) simulations. Non-reactive flow is simulated, though viscosity is treated as variable in the direction of flow, as it increases during the reaction. The design and operating parameters (reactor diameter, number of coils and inlet velocity) are varied in CFD simulations, in order to examine the effects on the flow pattern. Given that 3D simulations are not practical for fast computations needed for optimization, scale-up and control, CFD flow model is reduced to one-dimensional axial dispersion (AD) model with spatially variable dispersion coefficient. Dimensionless dispersion coefficient (Pe) is estimated under different conditions and results are analyzed. Finally, correlation which relates Pe number with Reynolds number and number of coils from the reactor entrance is proposed for the particular reactor application and conditions.

Summary Ensemble optimization (referred to throughout the remainder of the paper as EnOpt) is a rapidly emerging method for reservoir-model-based production optimization. EnOpt uses an ensemble of controls to approximate the gradient of the objective function with respect to the controls. Current implementations of EnOpt use a Gaussian ensemble of control perturbations with a constant covariance matrix, and thus a constant perturbation size, during the entire optimization process. The covariance-matrix-adaptation evolutionary strategy is a gradient-free optimization method developed in the “machine learning” community, which also uses an ensemble of controls, but with a covariance matrix that is continually updated during the optimization process. It was shown to be an efficient method for several difficult but small-dimensional optimization problems and was recently applied in the petroleum industry for well location and production optimization. In this study, we investigate the scope to improve the computational efficiency of EnOpt through the use of covariance-matrix adaptation (referred to throughout the remainder of the paper as CMA-EnOpt). The resulting method is applied to the waterflooding optimization of a small multilayer test model and a modified version of the Brugge benchmark model. The controls used are inflow-control-valve settings at predefined time intervals for injectors and producers with undiscounted net present value as the objective function. We compare EnOpt and CMA-EnOpt starting from identical covariance matrices. For the small model, we achieve only slightly higher (0.7 to 1.8%) objective-function values and modest speedups with CMA-EnOpt compared with EnOpt. Significantly higher objective-function values (10%) are obtained for the modified Brugge model. The possibility to adapt the covariance matrix, and thus the perturbation size, during the optimization allows for the use of relatively large perturbations initially, for fast exploration of the control space, and small perturbations later, for more-precise gradients near the optimum. Moreover, the results demonstrate that a major benefit of CMA-EnOpt is its robustness with respect to the initial choice of the covariance matrix. A poor choice of the initial matrix can be detrimental to EnOpt, whereas the CMA-EnOpt performance is near-independent of the initial choice and produces higher objective-function values at no additional computational cost.

In an earlier study, two hierarchical multi-objective methods were suggested to include short-term targets in life-cycle production optimization. However, this earlier study has two limitations: (1) the adjoint formulation is used to obtain gradient information, requiring simulator source code access and an extensive implementation effort, and (2) one of the two proposed methods relies on the Hessian matrix which is obtained by a computationally expensive method. In order to overcome the first of these limitations, we used ensemble-based optimization (EnOpt). EnOpt does not require source code access and is relatively easy to implement. To address the second limitation, we used the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to obtain an approximation of the Hessian matrix. We performed experiments in which water flood was optimized in a geologically realistic multilayer sector model. The controls were inflow control valve settings at predefined time intervals. Undiscounted net present value (NPV) and highly discounted NPV were the long-term and short-term objective functions used. We obtained an increase of approximately 14 % in the secondary objective for a decrease of only 0.2–0.5 % in the primary objective. The study demonstrates that ensemble-based hierarchical multi-objective optimization can achieve results of practical value in a computationally efficient manner

In this work, the application of tensor methodologies for computer-assisted history matching of channelized reservoirs is explored. A tensor-based approach is used for the parameterization of petrophysical parameters to reduce the dimensionality of the parameter estimation problem. Building on the work of Afra and Gildin (2013); Afra et.al. (2014); Afra and Gildin (2016), permeability fields of multiple model realizations are collected in a tensor form which is subsequently decomposed to derive a low-dimensional representation of the dominant spatial structures in the models. This representation then is used to estimate an identifiable reduced set of parameters using an ensemble Kalman filter (EnKF) strategy. This approach is attractive for the parameter estimation of permeabilities because it increases the ability to represent channelized structures in the updates resulting in an improved predictive capacity of the history-matched models. In particular, channel continuity is better preserved than with a Principal Component Analysis (PCA) parameterization.

This paper presents an output feedback nonlinear model-based control approach for optimal operation of industrial batch crystallizers. A full population balance model is utilized as the cornerstone of the control approach. The modeling framework allows us to describe the dynamics of a wide range of industrial batch crystallizers. In addition, it facilitates the use of performance objectives expressed in terms of crystal size distribution. The core component of the control approach is an optimal control problem, which is solved by the direct multiple shooting strategy. To ensure the effectiveness of the optimal operating policies in the presence of model imperfections and process uncertainties, the model predictions are adapted on the basis of online measurements using a moving horizon state estimator. The nonlinear model-based control approach is applied to a semi-industrial crystallizer. The simulation results suggest that the feasibility of real-time control of the crystallizer is largely dependent on the discretization coarseness of the population balance model. The control performance can be greatly deteriorated due to inadequate discretization of the population balance equation. This results from structural model imperfection, which is effectively compensated for by using the online measurements to confer an integrating action to the dynamic optimizer. The real-time feasibility of the output feedback control approach is experimentally corroborated for fed-batch evaporative crystallization of ammonium sulphate. It is observed that the use of the control approach leads to a substantial increase, i.e., up to 15%, in the batch crystal content as the product quality is sustained.

In piezoelectric positioning systems the achievable bandwidth is often limited by weakly damped resonant modes. System performance may be improved by avoiding the excitation of these modes. If sufficient mechanical damping is present this can be done by shifting resonant modes towards anti-resonant modes through manipulation of the mechanical boundary conditions. In a second approach the anti-resonances may be shifted towards the resonances by the application of modal actuation. Using this method the excitation of the second and higher order modes can be avoided by adjusting the distribution of actuation forces. This paper investigates and compares the application of modal control techniques in systems that are based on piezoelectric tube actuators such as atomic force microscopes.

Linear parameter-varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different representations it appears that the time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. Therefore, representations used previously to define and specify LPV systems are not equal in terms of dynamics. In order to construct a parametrization-free description of LPV systems that overcomes these difficulties, a behavioral approach is introduced that serves as a basis for specifying system theoretic properties. LPV systems are defined as the collection of trajectories of system variables (like inputs and outputs) and scheduling variables. LPV kernel, input-output, and state-space system representations are introduced with appropriate equivalence transformations.

Dynamic optimization is applied for throughput maximization of a semi-industrial batch crystallization process. The control strategy is based on a non-linear moment model. The dynamic model, consisting of a set of differential and algebraic equations, is optimized using the simultaneous optimization approach in which all the state and input trajectories are parameterized. The resulting problem is subsequently solved by a non-linear programming algorithm. The optimal operation is realized by manipulation of the heat input to the crystallizer such that a maximal allowable crystal growth rate is maintained in the course of the process. Effective control of the crystal growth rate in batch crystallization processes is often crucial to avoid product quality degradation. To be able to effectively track the maximum crystal growth rate, the optimal heat input profile is computed on-line using the current system states that are estimated by an extended Luenberger-type observer based on CSD measurements. The feedback structure of the control framework enables the optimizer to reject process uncertainties and account for plant-model mismatch. It is demonstrated that the application of the proposed on-line optimization strategy leads to a substantial increase, i.e. 30%, in the amount of crystals produced at the batch end, while the product quality requirements are fulfilled. © 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Currently systematic design of actuation (operational degrees of freedom) for process systems is not possible because (i) the required domain knowledge has not been identified and (ii) it is unclear how to explore the relation between actuation and operational improvement. This paper proposes geometry and flux equations as the required domain knowledge. It is explained that the relation between actuation and operational improvement should be explored in an optimal control setting. By means of an example (distillation) it is illustrated that a spatial actuation extension may result in considerable operational improvement.

Municipal solid waste combustion (MSWC) plant operators are currently under an increasing pressure to optimize the economic performance of their plants. A route with high potential for optimizing this performance is by improving the performance of the MSWC plant combustion control system, which typically is of the PID-type. In this paper, motivated by the industrial need to improve the overall economic MSWC plant performance, a model based approach is taken to optimize this control system, using recently derived black and white box MSWC plant models. More specific, from a closer analysis of the dynamics of these models a new PID-type of MSWC plant combustion control strategy is derived. It is shown that this new control strategy has improved setpoint tracking properties compared to PID-type of combustion control strategies typically encountered in the industry. As a result, a significant improvement of the economic performance of an MSWC plant will be obtained when replacing such a control strategy for the new one. However, no improvement of the disturbance rejection properties of existing PID-type of combustion control strategies has been observed with the new control strategy, which would also lead to a significant improvement of the economic performance of an MSWC plant, indicating that other, non-PID, types of combustion control strategies are required for that.

In the framework of Linear Parameter-Varying (LPV) systems, controllers are commonly designed in continuous-time, but implemented on digital hardware. Additionally, LPV system identification is formulated exclusively in discrete-time, needing structural information about the plant, which is often provided by first principle continuous-time models. These imply that LPV system discretization is an important issue for both system identification and controller implementation. Discretization approaches of LPV state-space systems are introduced and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling of the input-output signals and the scheduling parameter of the system. Criteria to choose appropriate sampling times with the investigated methods are also presented.

When the number of data used for an identification experiment is small, the data contain transient effects and these effects contribute to the accuracy of the identified model. Consequently, when designing the optimal input signal for an identification experiment in the case of small data set, these transient effects have to be taken into account. In this paper, we present a methodology for optimal experiment design which, unlike other approaches such as the asymptotic approach, takes explicitly the transient effects into account. This paper is restricted to model structures that are linear in the parameter and to multisine input signals.

A measurement-based statistical verification approach is developed for systems with partly unknown dynamics. Grey-box systems, which are specified as a model class, are subject to identification experiments that enable accepting or rejecting system properties expressed as formulae in a linear-time logic with a given confidence. We employ a Bayesian framework for the computation of the confidence level and for the design of experiments to increase the confidence. The experiment design is formulated as a stochastic optimal control problem, which solvable via dynamic programming. Applied to linear control systems, this work enables efficient data-driven verification of partly-known dynamics with controllable non-determinism (inputs) and noisy output observations. A numerical case study concerning the safety of a dynamical system is used to elucidate this approach.

Closed-loop reservoir management (CLRM) is a combination of life-cycle optimization and computer-assisted history matching. The application of the CLRM framework to real field cases can be computationally demanding. An even higher computational load results from procedures to assess the value of information (VOI) in CLRM. Such procedures, which are performed prior to field operation, i.e. during the field development planning (FDP) phase, require extreme amounts of simulations. Therefore, we look for alternatives to reduce this computational cost. In particular we compare various clustering techniques to select a limited number of representative members from an ensemble of reservoir models. Using K-means clustering, multi-dimensional scaling and tensor decomposition techniques, we test the effectiveness of different dissimilarity measures such as distance in parameter space, distance in terms of flow patterns and distance in optimal sets of controls. As a first step towards large-scale application we apply several of these measures to a VOI-CLRM exercise using a simple 2D reservoir model which results in a reduction of the necessary number of forward reservoir simulations from millions to thousands.

Over the past few years, dynamic optimization of reservoir flooding using optimal control theory has received significant attention. Various studies have shown that dynamic (time-varying) injection and production settings can yield a higher Net Present Value (NPV) than conventional reactive settings. In these studies, the optimization procedure itself is always gradient-based, where the gradients are obtained with an adjoint formulation. However, the shape of the optimal injection and production settings is generally not known beforehand. The main contribution of this paper is to investigate why and under what conditions reservoir flooding problems can be expected to have bang-bang (on–off) optimal solutions. A major practical advantage of bang-bang controls is that they can be implemented with simple on–off valves. Furthermore, there are sufficient optimality conditions that are tailor-made for bang-bang solutions, meaning we can actually check whether a solution is locally optimal or not. These results are illustrated by a water flooding example of a 3-dimensional reservoir in a fluvial depositional environment, modeled with 18.553 grid blocks. The valve settings of 8 injection and 4 production wells are optimized over the life of the reservoir, with the objective to maximize NPV. It turns out that optimal settings are sometimes bang-bang, and sometimes bang-bang in combination with so-called singular arcs. For the latter situations, however, bang-bang solutions are found that are only slightly suboptimal.

Improving the operation is an attractive option for the process industry to deal with increased competition. In this paper a general dynamic optimization framework is proposed that aims to improve plantwide operation in an economic sense. The term general means that it is based on dynamic operation in which any operational constraints can be accommodated. One would expect economic optimization to utilize all available degrees of freedom. However it is shown that this is normally not the case, so this leaves the possibility open to do further optimization.

Current state-of-the-art correct-by-design controllers are designed for full-state measurable systems. This work extends the applicability of correct-by-design controllers to partially observable linear, time-invariant (LTI) models. Towards the certification of the synthesised controllers, approximate simulation relations are leveraged to attain a quantification for the accuracy of introduced approximations. Additionally, the robustness of the approach allows the extension to models with the presence of probabilistic disturbances on state transitions and on output measurements. In a case study from smart buildings we evaluate the new output-based correct-by-design controller on a physical system with limited sensor information.

This work develops a measurement-driven and model-based formal verification approach, applicable to systems with partly unknown dynamics. We provide a principled method, grounded on reachability analysis and on Bayesian inference, to compute the confidence that a physical system driven by external inputs and accessed under noisy measurements, verifies a temporal logic property. A case study is discussed, where we investigate the bounded- and unbounded-time safety of a partly unknown linear time invariant system.

Least-costly experiment design has received ample attention over the past decades, and efficient numerical algorithms that can compute optimal excitation spectra for linear models have been found. The interpretation of such spectra, however, has received far less attention. We restrict ourselves to uni-parametric models, for which an analytical solution to the experiment design problem is derived. This solution enables us to address, among other things, the following questions: What determines the frequency and amplitude of the excitation signal? Does the optimal frequency depend on the location(s) that the parameter occupies in the transfer function? With the optimal signal, is a closed-loop identification experiment cheaper than an open-loop one?

A measurement-based statistical verification approach is developed for systems with partly unknown dynamics. These grey-box systems are subject to identification experiments which, new in this contribution, enable accepting or rejecting system properties expressed in a linear-time logic. We employ a Bayesian framework for the computation of a confidence level on the properties and for the design of optimal experiments. Applied to dynamical systems, this work enables data-driven verification of partly-known system dynamics with controllable non-determinism (inputs) and noisy output observations. A numerical case study concerning the safety of a dynamical system is used to elucidate this data-driven and model-based verification technique.

This paper considers the use of spatial-temporal (tensor) decompositions for the compact representations of saturation patterns in reservoir models. Reservoir flow patterns, in the sense of evolution of saturation patterns over time, can be considered to drive the economic performance of reservoirs as they drive the ultimate recovery. This makes the reservoir flow pattern a natural dissimilarity measure between models in the context of production optimization. We show that the application of multilinear algebra techniques allows the construction of low-complexity representations of the essential saturation patterns. The reservoir flow patterns are stored in large-scale multidimensional arrays, and tensor decompositions can be effectively used to describe the spatial-temporal behavior of the reservoir flow patterns. The dimensionality of the reservoir flow patterns can be substantially reduced, showing that a small number of spatial-temporal basis functions are required to characterize the dominant features. When applying the tensor decompositions to flow profiles of an ensemble of realizations they can be used for clustering models with similar dynamical properties, by allowing a fast calculation of a flow-relevant dissimilarity measure between realizations. For large ensembles of realizations they can lead to considerable computational advantages in (robust) optimization. This is illustrated by using a gradient-based technique to maximize Net Present Value (NPV) in water flooding for an ensemble of realizations. Besides in reducing ensemble sizes the resulting tools have potential use in constructing reduced order models.

International audience; All approaches to optimal experiment design for control have so far focused on deriving an input signal (or input signal spectrum) that minimizes some control-oriented measure of plant/model mismatch between the nominal closed-loop system and the actual closed-loop system, typically under a constraint on the total input power. In practical terms, this amounts to finding the (constrained) input signal that minimizes a measure of a control-oriented model uncertainty set. Here we address the experiment design problem from a “dual” point of view and in a closed-loop setting: given a maximum allowable control-oriented model uncertainty measure compatible with our robust control specifications, what is the cheapest identification experiment that will give us an uncertainty set that is within the required bounds? The identification cost can be measured by either the experiment time, the performance degradation during experimentation due to the added excitation signal, or a combination of both. Our results are presented for the situation where the control objective is disturbance rejection only.

This paper extends previous work on value of information (VOI) assessment in closed-loop reservoir management (CLRM) to estimate the added value of performing multiple measurements along the producing life of the reservoir. The new procedure is based on the workflow from our previous paper which allows to quantify the VOI of a single observation under geological uncertainty. Here we show that, by modifying that workflow slightly, it is possible to assess the value of a series of measurements without a prohibitive increase in computational costs. The approach is illustrated with two cases based on a simple water flooding problem in a two-dimensional five-spot reservoir: the first one, in which we assess the value of a series of production measurements, and the second one, in which we estimate the additional value of water front positions tracked by an interpreted time-lapse seismic survey. We believe that our proposed workflow is a complete methodology to estimate the VOI in a CLRM context because we take into account that the production strategy is updated periodically after new information has been assimilated in the models. However, future work will be required to reduce the computational load to allow for the application of the workflow to real field cases.

We consider robust ensemble-based (EnOpt) multi-objective production optimization of on-off inflow control devices (ICDs) for a sector model inspired on a real-field case. The use of on-off valves as optimization variables leads to a discrete control problem. We propose a re-parameterization of such discrete controls in terms of switching times, i.e. we optimize the time at which a particular valve is either open or closed. This transforms the discrete control problem into a continuous control problem which can be efficiently handled with the EnOpt method. Additionally this leads to a significant reduction in the number of controls which is expected to be beneficial for gradient quality when using approximate gradients. We consider an ensemble of sector models where the uncertainty is described by different permeability, porosity, net-to-gross and initial water saturation fields. The controls are the ICD settings over time in the three horizontal injection wells, with approximately 15 ICDs per well. Different optimized strategies resulting from different initial strategies were compared. We achieved a mean 4.2% increase in expected NPV at a 10% discount rate compared to a traditional pressure maintenance strategy. Next, we performed a sequential bi-objective optimization, and achieved an increase of 9.2% in the secondary objective (25% discounted NPV to emphasize short-term production gains) for a minimal decrease of 1% in the primary objective (0% discounted NPV to emphasize long-term recovery gains), as averaged over the 100 geological realizations. The workflow was repeated for alternative numbers of ICDs showing that having fewer control options lowers the expected value for this particular case. The results demonstrate that ensemble-based optimization workflows are able to produce improved robust recovery strategies for realistic field sector models against acceptable computational cost. Copyright © 2015 Society of Petroleum Engineers.

In iterative schemes of identification and control one of the particular and important choices to make is the choice for a model uncertainty structure, capturing the uncertainty concerning the estimated plant model. This is typically done in some norm-bounded form, in order to guarantee robust stability and/or robust performance when redesigning the controller. Structures that are used in the recent literature encompass e.g. gap metric uncertainty, coprime factor uncertainty, and the Vinnicombe gap metric uncertainty. In this paper we study the effect of these choices when our aim is to maximize the (re)tuning freedom for a present controller (in terms of a norm-bounded perturbation) under conditions of robust stability. Particular attention will be given to the representation of plant uncertainty and controller tuning freedom in terms of Youla parameters. In the problem formulation considered here the so-called double Youla parametrization provides a norm-bounded set of robustly stabilizing controllers that is larger than corresponding sets that are achieved by using any of the other uncertainty structures. Copyright & 2002 IFAC

We present a novel optimal experiment design method that is applicable to linear time-invariant systems regulated by unknown, nonlinear and implicitly-defined controllers. Current methods require an explicit expression for the controller in order to construct the optimal excitation spectrum. Consequently, these are limited to linearly-controlled systems. The identification scheme suggested in this paper circumvents the aforementioned requirement by ensuring that the excitation signal remains unnoticed by the controller, i.e., the identification data is gathered in an open-loop fashion. Our theoretical analysis is complemented with a numerical study on a six-parameter, single-input single-output linear system controlled by an MPC. We find that our method generates least-costly excitation signals which deliver identified models that lie close to the true system whilst honoring quality constraints, validating the novel optimal experiment design framework.

In this paper a realization theory and associated algorithms are presented for the construction of minimal realizations on the basis of a sequence of expansion coefficients in a generalized orthonormal basis. Both the exact and the partial realization problem are addressed and solved, leading to extended versions of the classical Ho-Kalman algorithm.In the construction of the realization algorithms, fruitful use is made of a system analysis in the transform domain, being induced by the choice of basis functions. The resulting algorithms can also be applied in approximate realization and in system approximation.

This paper deals with the problem of obtaining a plant nominal model and its error uncertainty bound when a batch of plant models is provided. While the selection of model set structure is essential and probably depends on the model intended application, in this paper it is assumed that a nominal model is perturbed by its error through a homographic transformation. A necessary and sufficient condition is obtained for a nominal model to be suboptimal. Moreover, an algorithm is proposed to obtain a nominal model which is suboptimal and has a low complexity. Furthermore, the extraction of structured nominal model errors is discussed. The efficiency of the proposed model set determination algorithm is verified through the application to the simultaneous spiral control of two compact disc players.

In this paper a framework for an iterative procedure of identification and robust control design is introduced wherein the robust performance is monitored during the subsequent steps of the iterative scheme. By monitoring the performance via a model-based approach, the possibility to guarantee performance improvement in the iterative scheme is being employed. In order to monitor achieved performance (for a present controller) and to guarantee robust performance (for a future controller), an uncertainty set is used where the uncertainty structure is chosen in terms of model perturbations in the dual Youla parametrization. This uncertainty structure is shown to be particularly suitable for the control performance measure that is considered. The model uncertainty set can be identified by an uncertainty estimation procedure on the basis of closed-loop experimental data. To obtain performance robustness, robust control design tools are used to synthesise controllers on the basis of the identified uncertainty set.

In spite of large uncertainties in the actual reservoir structure, structural parameters of a reservoir model are usually fixed during history matching and only the flow properties of the model are allowed to vary. This often leads to unlikely or even unfeasible property updates and possibly to a poor predictive capability of the model. In those cases it may be expected that updating of the structural parameters will improve the quality of the history match. Preferably such structural updates should be implemented in the static (geological) model, and not just in the dynamic (flow) model. In this paper we use a gradient-based history matching method to update structural properties of the static model. We use an adjoint method to efficiently compute the derivatives of the data mismatch with respect to grid block porosities in the dynamic model and convert the corresponding volume changes to structural updates (layer thicknesses) in the static model. This method is suitable for structural updating of large scale reservoir models using production data and/or time-lapse seismics or other spatially distributed data. The method is tested on a 3D synthetic model, where time-lapse as well as production data have been used to update depth of the reservoir’s bottom horizon. We obtained significant improvements in the history match quality and the predictive capability of the model.

Ensemble optimization (referred to throughout the remainder of the paper as EnOpt) is a rapidly emerging method for reservoirmodel-based production optimization. EnOpt uses an ensemble of controls to approximate the gradient of the objective function with respect to the controls. Current implementations of EnOpt use a Gaussian ensemble of control perturbations with a constant covariance matrix, and thus a constant perturbation size, during the entire optimization process. The covariance-matrix-adaptation evolutionary strategy is a gradient-free optimization method developed in the "machine learning" community, which also uses an ensemble of controls, but with a covariance matrix that is continually updated during the optimization process. It was shown to be an efficient method for several difficult but small-dimensional optimization problems and was recently applied in the petroleum industry for well location and production optimization. In this study, we investigate the scope to improve the computational efficiency of EnOpt through the use of covariance-matrix adaptation (referred to throughout the remainder of the paper as CMA-EnOpt). The resulting method is applied to the waterflooding optimization of a small multilayer test model and a modified version of the Brugge benchmark model. The controls used are inflow-control-valve settings at predefined time intervals for injectors and producers with undiscounted net present value as the objective function. We compare EnOpt and CMA-EnOpt starting from identical covariance matrices. For the small model, we achieve only slightly higher (0.7 to 1.8%) objective-function values and modest speedups with CMAEnOpt compared with EnOpt. Significantly higher objective-function values (10%) are obtained for the modified Brugge model. The possibility to adapt the covariance matrix, and thus the perturbation size, during the optimization allows for the use of relatively large perturbations initially, for fast exploration of the control space, and small perturbations later, for more-precise gradients near the optimum. Moreover, the results demonstrate that a major benefit of CMAEnOpt is its robustness with respect to the initial choice of the covariance matrix. A poor choice of the initial matrix can be detrimental to EnOpt, whereas the CMA-EnOpt performance is near-independent of the initial choice and produces higher objectivefunction values at no additional computational cost.

Identification of low-order linear multiinput/multiouput models can lead to accurate descriptions of the dynamic behavior of a continuous crystallization process. While open-loop experiments exhibit an oscillating crystal size distribution, improved experimental conditions can be established through stabilization of the process with a simple single-loop feedback controller. The resulting closed-loop identification problem is studied using low-order linear multivariable input–output models. Two closed-loop identification methods are applied, one of which was recently introduced to provide accurate approximate models in general closed-loop process configurations. Identification and validation data are obtained from an evaporative pilot crystallizer, and the identified models are validated in terms of time- and frequency-domain responses. A fourth-order, three-input three-output model is shown to describe accurately the process dynamics. The results are compared with a linearized and reduced first-principles model.

Trends in the power system's development, such as increased demand response or penetration of renewable energy, indicate that in the future, power system will experience significant daily changes in their physical properties. Time frames of energy economics and physical processes start to overlap. These changes require proper secondary controller tuning, for which high-quality up-to-date models are needed. The main contribution of this paper, we utilize the information on the energy market outcome, which is known in advance, to identify the dynamics of a control area relevant for the secondary control (SC) design/tuning. By rethinking the interconnected power systems in the system identification framework, and exploiting the developed theory, a consistent model of a control area is obtained within a few hours. This is sufficient to follow the daily changes in the system dynamics. It is expected that a controller based on a better model adapts to the daily changes in power system dynamics, and moreover, is capable of improving the system performance. Several illustrative examples confirm that the use of market based signals in the identification process is an important step that helps getting accurate models.

In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l/sub 2sup n/. To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients. >

A least squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions. The basis functions are orthogonal in H 2 and generalize the pulse, Laguerre and Kautz bases. One of their important properties is that when chosen properly they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only few coefficients to be estimated. Explicit bounds are derived for the bias and variance errors that occur in the parameter estimates as well as in the resulting transfer function estimates.

This paper discusses the approximate and feedback relevant parametric identification of the radial servo system present in a Compact Disc player. In this application the problem of approximate identification based on data from closed loop experiments will be analyzed to find a finite dimensional linear time invariant discrete time model, suitable for model-based control design. The feedback relevant identification in this paper is based on the algebraic theory of fractional representations, which has lead to a framework for equivalent open loop identification of (normalized) coprime plant factors and a manageable approximate transfer function estimation of the feedback controlled plant. A mixed worst-case/probabilistic approach to model uncertainty quantification is used to construct an upper bound on the uncertainty of the normalized coprime factors being estimated. Both the nominal model and the uncertainty description are used to design an enhanced robust controller.

International audience; This paper presents in a new unified way, optimal instrumental variable methods for identifying discrete-time transfer function models when the system operates in closed-loop. The conditions for the optimal design of prefilters and instruments depending on common model structures are analyzed and different approaches are developed according to whether the controller is known or not. The performance of the proposed approaches is evaluated by Monte-Carlo analysis in comparison with other alternative closed-loop estimation methods.

Hypothesis testing is a classical methodology of making decisions using experimental data. In hypothesis testing one seeks to discover evidence that either accepts or rejects a given null hypothesis H0. The alternative hypothesis H1 is the hypothesis that is accepted when H0 is rejected. In hypothesis testing, the probability of deciding H1 when in fact H0 is true is known as the false alarm rate, whereas the probability of deciding H1when in fact H1is true is known as the detection rate (or power) of the test. It is not possible to optimize both rates simultaneously. In this paper, we consider the problem of determining the data to be used for hypothesis testing that maximize the detection rate for a given false alarm rate. We consider in particular a hypothesis test which is relevant in functional magnetic resonance imaging (fMRI).

In many areas of signal, system and control theory orthogonal functions play an important role in issues of analysis and design. In this paper it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems, and that compose an orthonormal basis for the signal space l 2 n . To this end use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of e.g. the Laguerre functions and the pulse functions, related to the use of the delay operator, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit thcsp generalized basis functions to increase the speed of convergence in a series expansion, i.e. to obtain a good approximation by retaining only a finite number of expansion coefficients.

In this paper a procedure is presented to obtain an estimate of the transfer function of a linear system together with a confidence interval, using only limited a priori information. By applying Bartlett's procedure of periodogram averaging to the non-parametric empirical transfer function estimate, and by employing a periodic input signal, the statistics of the resulting estimate asymptotically can be obtained from the data. The model error consists of two parts: a probabilistic part, due to the stochastic noise disturbance on the data, and a deterministic part, due to the bias in the estimate. The latter is explicitly bounded with a deterministic error bound, while the former asymptotically results from a F distribution. For this analysis only minor assumptions are made on the distribution of the noise.

In this paper, we introduce a two-phase flow model which describes the motion of two incompressible fluids. The proposed model is governed by nonlinear partial differential algebraic equations (PDAEs) with open initial-boundary conditions. The well-posedness of the boundaries is analyzed using characteristic curves, which leads to development of a boundary actuation structure that is suitable for a control design. A particular emphasis is placed on a possible coordinate transformation that can reduce the problem to a set of partial differential equations (PDEs) without algebraic constraints. The boundary actuation strategy is presented using linearized model equations and tested on a numerical example for a quasi steady-state situation.

In high speed AFMs the vertical axis of the sample positioning stage requires high bandwidth feedback control. In these systems the dynamics of the piezoelectric actuator, its support structure and load play a dominant role in the design of the feedback loop. System performance can be increased by avoiding the excitation of resonant modes of the piezoelectric actuator by modal actuation. In this approach, the piezoelectric actuator is modified to render modes close to the controller bandwidth uncontrollable. Due to its static hardware implementation robustness issues may emerge due to varying loads used for AFM imaging. This paper focusses on performance robustness of modal filters due to load variation.

In order to accurately identify linear parameter-varying (LPV) systems, order selection of LPV linear regression models has prime importance. Existing identification approaches in this context suffer from the drawback that a set of functional dependencies needs to be chosen a priori for the parametrization of the model coefficients. However in a black-box setting, it has not been possible so far to decide which functions from a given set are required for the parametrization and which are not. To provide a practical solution, a nonnegative garrote approach is applied. It is shown that using only a measured data record of the plant, both the order selection and the selection of structural coefficient dependence can be solved by the proposed method.