Elling W. Jacobsen

Performance limitations in decentralized control

Abstract In decentralized control of multivariable systems, the system is decomposed into a number of subsystems and individual controllers are designed for each subsystem. Advantages of such decomposition include reduced modelling requirements and ease of implementation. However, a potential disadvantage is a reduction in achievable control performance due to restricted controller structure. In this paper we consider performance limitations from non-minimum phase transmission zeros in decentralized control. In particular, we derive conditions on when closing the loop around one subsystem moves transmission zeros of other subsystems across the imaginary axis. Such zero crossings may occur regardless of the existence of non-minimum phase behavior in the open-loop system, and may, therefore, represent performance limitations specific to the use of decentralized controllers.

Identification of small scale biochemical networks based on general type system perturbations.

New technologies enable acquisition of large data‐sets containing genomic, proteomic and metabolic information that describe the state of a cell. These data‐sets call for systematic methods enabling relevant information about the inner workings of the cell to be extracted. One important issue at hand is the understanding of the functional interactions between genes, proteins and metabolites. We here present a method for identifying the dynamic interactions between biochemical components within the cell, in the vicinity of a steady‐state. Key features of the proposed method are that it can deal with data obtained under perturbations of any system parameter, not only concentrations of specific components, and that the direct effect of the perturbations does not need to be known. This is important as concentration perturbations are often difficult to perform in biochemical systems and the specific effects of general type perturbations are usually highly uncertain, or unknown. The basis of the method is a linear least‐squares estimation, using time‐series measurements of concentrations and expression profiles, in which system states and parameter perturbations are estimated simultaneously. An important side‐effect of also employing estimation of the parameter perturbations is that knowledge of the systems steady‐state concentrations, or activities, is not required and that deviations from steady‐state prior to the perturbation can be dealt with. Time derivatives are computed using a zero‐order hold discretization, shown to yield significant improvements over the widely used Euler approximation. We also show how network interactions with dynamics that are too fast to be captured within the available sampling time can be determined and excluded from the network identification. Known and unknown moiety conservation relationships can be processed in the same manner. The method requires that the number of samples equals at least the number of network components and, hence, is at present restricted to relatively small‐scale networks. We demonstrate herein the performance of the method on two small‐scale in silico genetic networks.

On the dynamics of integrated plants—non-minimum phase behavior

Abstract Recycling of material and or energy in chemical plants imposes a feedback mechanism which is known to move the poles of the plant. In this paper the effect of recycling on the zero dynamics is considered, and it is shown that the feedback effect imposed by recycling also may move the zeros of control relevant transfer-functions. Sufficient conditions for the existence of non-minimum phase transmission zeros caused by the presence of recycling are derived. The conditions may be evaluated based on steady-state information about the individual units only, and are hence particularly well suited for incorporation in a process design environment. The derived results are illustrated through application to the design of a reactor-separator system.

Chaotic dynamics in homogeneous tubular reactors with recycle

This note presents a bifurcation analysis of the homogeneous tubular reactor with recycle and shows that the presence of recycle also may cause more complex behaviour, including chaotic behaviour.

Structural robustness of biochemical network models-with application to the oscillatory metabolism of activated neutrophils.

Sensitivity of biochemical network models to uncertainties in the model structure, with a focus on autonomously oscillating systems, is addressed. Structural robustness, as defined here, concerns the sensitivity of the model predictions with respect to changes in the specific interactions between the network components and encompass, for instance, uncertain kinetic models, neglected intermediate reaction steps and unmodelled transport phenomena. Traditional parametric sensitivity analysis does not address such structural uncertainties and should therefore be combined with analysis of structural robustness. Here a method for quantifying the structural robustness of models for systems displaying sustained oscillations is proposed. The method adopts concepts from robust control theory and is based on adding dynamic perturbations to the network of interacting biochemical components. In addition to providing a measure of the overall robustness, the method is able to identify specific network fragilities. The importance of considering structural robustness is demonstrated through an analysis of a recently proposed model of the oscillatory metabolism in activated neutrophils. The model displays small parametric sensitivities, but is shown to be highly unrobust to small perturbations in some of the network interactions. Identification of specific fragilities reveals that adding a small delay or diffusion term in one of the involved reactions, likely to exist in vivo, completely removes all oscillatory behaviour in the model.

Identifying feedback mechanisms behind complex cell behavior

The FNAL Email System is the primary point of entry for email destined for an employee or user at Fermilab. This centrally supported system is designed for reliability and availability. It uses multiple layers of protection to help ensure that: (1) SPAM messages are tagged properly; (2) All mail is inspected for viruses; and (3) Valid mail gets delivered. This system employs numerous redundant subsystems to accomplish these tasks.Interactions among genes, proteins, and metabolites generate most of the central functions of the living cell. These interactions take place in highly complex biochemical networks, often involving hundreds of components and reactions. Exposing the connection between the individual components, such as genes, and the overall behavior of the network requires a systems approach based on dynamic models of the network. In this article, the author illustrates how a simple linear systems analysis can be used to analyze the role of various components in generating complex dynamic behavior in biochemical networks. The approach is used to identify the most important proteins and mutual interactions involved in the cell cycle in frog eggs and sustained oscillations of glycolysis in yeast. The approach is applicable to large-scale network models that can be developed in the near future based on high throughput data on a genomic and proteomic scale.

On the use of reduced order models in bifurcation analysis of distributed parameter systems

Bifurcation theory provides a powerful tool for analyzing the nonlinear dynamic behavior of process systems. However, although the theory in principle applies to lumped as well as distributed parameter processes, it is in practice necessary to reduce the order of distributed (partial differential equations, PDE) models prior to application of the theory. As shown in this paper, simply applying some ad hoc discretization method such as finite differences or finite elements, can result in spurious bifurcations and erroneous predictions of stability. To enable detection of such anomalities, and to aid in the selection of a proper model order, we propose a method for estimating the error introduced by the model reduction. Apart from simply providing a label of confidence in the results of the bifurcation analysis, the estimated error can be used to improve the quality of the reduced order model. For this purpose we propose a method based on dynamically moving the discretization mesh such as to minimize the discretization error. The proposed method is based on principles from feedback control, and is both very simple and highly robust compared with existing so-called moving mesh methods. As an application we consider bifurcation analysis of a heat-integrated fixed-bed reactor.

Approximate characteristics of a moving temperature front in a fixed-bed catalytic reactor

Abstract The study deals with a nonstationary process of mass and heat transfer accompanied by a chemical reaction occurring in a catalytic reactor. Based on the assumptions of the ‘ideal thermal front’ in the reactor, approximate solutions are obtained for the equations that describe the process. Thus, relations are derived which define the principal properties of the thermal front, namely its propagation velocity in the bed and the maximum temperature of the front. The above relations express these properties in terms of dimensionless numbers that characterise the chemical reaction taking place in the reactor and the operating parameters of the vessel. Good agreement is found between the front properties as calculated using the approximate formulae and those yielded by the integration of the complete model equations, i.e. the exact values. A method is proposed for determining approximate temperature profiles in the bed, which is by far simpler and less time-consuming than the integration of a complete set of partial differential equations. Both the formulae derived and the method proposed for calculating the temperature profiles along the bed may be useful in the design of reactors with the periodic reversal of the feed mixture. They enable the effect to be analysed of the various operating parameters upon the propagation velocity of the thermal front and its maximum temperature, without resorting to tedious and time-consuming trial and error methods that require repeated integration of the model equations.

Kinetic perturbations as robustness analysis tool for biochemical reaction networks

Models of biochemical reaction networks can be decomposed into a stoichiometric part and a kinetic part. The stoichiometric part describes the structural mass flows while the kinetic part describes how the flow rates vary with substrate concentrations and regulatory interactions. Herein a method for analyzing the robustness of biochemical networks with respect to perturbations of the kinetic part is proposed. In particular, we consider a class of perturbations that modify the local kinetic slopes while leaving the reaction flow rates in steady state unchanged. A method for computing the associated robustness radii for perturbations of single or multiple kinetic slopes is devised. The corresponding non-robust perturbations can be implemented in the original nonlinear model through specific parameter variations described by the perturbation class. The proposed method is illustrated through application to the Huang-Ferrell model of MAPK signaling cascades. In particular, we compute the smallest kinetic perturbations that translate the nominal utltrasensitive response into a bistable and oscillatory response, respectively. The results are highly relevant since MAPK cascades are conserved pathways known to produce bistability as well as sustained oscillations depending on the context in which they operate.

Selecting control configurations for performance with independent design

An important task in the design of decentralized control systems for multivariable plants is the choice of the structure of interconnections between manipulated variables and controlled outputs, i.e. the control configuration. Most tools available for this task, such as the RGA, address mainly the stability properties of the overall system. In this paper we focus on performance, and consider in particular the problem of selecting control structures that enable a desired performance to be achieved through independent tuning of the subsystems. We show that, for this task, the common assumption of perfect control within the bandwidths of the subsystems is a poor one. Based on this, a new measure of interactions, the decentralized relative gain (dRG), is proposed. Finally, it is stressed that the effect of interactions on the magnitude as well as on the phase lag of the subsystems should be considered when selecting control configurations for performance.