Kurt E. Häggblom

Control structure analysis by partial relative gains

A new procedure for analysis and selection of decentralized control structures is presented. In addition to the relative gain array (RGA) for the entire open-loop system, the RGA for the system under partial control is considered. This partial relative gain (PRG) provides necessary conditions for integral controllability and integrity. The PRG also solves the variable pairing problem more reliably than the conventional RGA, which may fail for systems larger than 2/spl times/2.

Combined internal model and inferential control of a distillation column via closed-loop identification

Abstract A procedure for designing distillation control systems with spe cified nominal properties is presented. The desired behaviour of the control system for both setpoint changes and disturbances in the feed flow rate and the feed composition can be specified. Both types of specifications can be handled because the disturbances can be inferred from the behaviour of the inventory control system. The control system is realized as a combined internal model and inferential control (CIMIC) system. A disturbance rejecting and decoupling (DRD) control structure is obtained as a special case. The performance of the control system is demonstrated experimentally on a pilot-scale distillation column. For comparison, experiments with pure internal model control (IMC) are also illustrated. A preliminary model of the distillation column was determined from step tests carried out in open-loop operation, but the final model used in the control system designs was obtained via a control-relevant closed-loop identification.

Multivariable uncertainty estimation based on multi-model output matching

Abstract This paper describes a procedure for deriving norm-bounded output-multiplicative uncertainty descriptions for a multi-input multi-output system by matching the output of an uncertainty model to the outputs of a set of known models. It is assumed that the set of models has been obtained through system identification. The objective is to determine the least conservative uncertainty description such that all known experimental data can be reconstructed by the uncertainty model. Both unstructured and diagonal uncertainty are considered as well as various structures of the uncertainty weight matrix. For the case with no a priori information, it is shown that a nonconservative uncertainty description can be obtained by minimizing the magnitude of the determinant of the uncertainty weight matrix subject to the output-matching condition. The procedure is illustrated by estimation of uncertainty weights and design of μ -optimal controllers for a distillation column.

Derivation and selection of norm-bounded uncertainty descriptions based on multiple models

A method for determining a norm-bounded unstructured uncertainty description from a set of linear models is presented. The method yields multiple-input, multiple-output shaping filters which are suitable for -based analysis or controller synthesis. The method can be applied to so-called model matching, where uncertainty descriptions are obtained from a set of linear models. Another approach is to use so-called output matching, which utilises outputs of the models in the set. First, necessary and sufficient conditions for uncertainty shaping filters to capture a multimodel set are given. Then, an approach for non-conservative filter design by optimizing a closed-loop criterion is proposed. It is highlighted by a design example, where additive, input-multiplicative and output-multiplicative uncertainty models are compared. The example illustrates the impact of the choice of uncertainty model and the structure of the shaping filter on the resulting conservatism caused by the uncertainty description.

Application of robust and multimodel control methods to an ill-conditioned distillation column

A set of linear models of an ill-conditioned two-product distillation column is used for controller design. A number of controller design methods are studied, each with the aim of achieving sufficient robustness and performance by using the description of plant variations and uncertainties provided by the model set. The investigated methods comprise multimodel H2 optimal control, mixed H2/H∞ control with nominal H2 performance, mixed H2/H∞ control with robust H2 performance, mixed-sensitivity loop shaping using structured-singular-value synthesis, robust loop shaping according to Glover and McFarlane, multivariable IMC and optimally tuned decentralized PI control. The controllers obtained by the various design methods are tested by a series of setpoint change experiments on the pilot-scale distillation column. The experimental results are reported and the different control methods are evaluated and compared with respect to obtained performance. Design issues are briefly discussed.

Control Structures, Consistency, and Transformations

The operation of a multivariable process like a distillation column has to satisfy several control objectives. Typical objectives are to ensure the stability of the process, to produce specified products, and to optimize the operation economically. As the various objectives may be of quite different importance and normally require control actions at different time rates, it is usually desirable to decompose the full system into a number of subsystems according to the objectives.

Control-relevant identification of an ill-conditioned distillation column

Identification for control of an ill-conditioned system requires special techniques. The directionality of such a system should be taken into account in the design of identification experiments. This requires some prior information about the system. In distillation, information about the directionality properties can be obtained from certain flow gains, which are easy to determine in practice. Based on such information, the plant can be explicitly excited in its high- and low-gain directions. In the paper, a pilot-scale distillation column is identified by this approach at two different operating points. The models obtained are superior to models determined via traditional step tests. In this case, the former satisfy integral controllability requirements, while the latter do not.Identification for control of an ill-conditioned system requires special techniques. The directionality of such a system should be taken into account in the design of identification experiments. This requires some prior information about the system. In distillation, information about the directionality properties can be obtained from certain flow gains, which are easy to determine in practice. Based on such information, the plant can be explicitly excited in its high- and low-gain directions. In the paper, a pilot-scale distillation column is identified by this approach at two different operating points. The models obtained are superior to models determined via traditional step tests. In this case, the former satisfy integral controllability requirements, while the latter do not.

Integral controllability and integrity for uncertain systems

It is well known that the relative gain array (RGA) and the determinant of the gain matrix provide useful information about integral controllability and integrity (e.g., failure tolerance), which are important issues in decentralized control. The RGA also gives information about robustness with respect to modeling errors and input uncertainty. Almost exclusively only nominal models have been considered in previous studies and applications of these methods. Not until recently have there been attempts to consider model uncertainty more explicitly. However, the methods proposed in these studies tend to find uncertainty bounds that are too wide. In this paper a more accurate procedure based on sensitivity analysis is developed for studying the effect of model errors. Independent gain uncertainty as well as more structured uncertainty can be handled. The method is well suited for deriving tight bounds on the tolerable uncertainty.

DATA-BASED UNCERTAINTY MODELING BY CONVEX OPTIMIZATION TECHNIQUES

Abstract A procedure based on convex optimization techniques for deriving norm-bounded uncertainty models for MIMO systems is presented. The procedure is developed for unstructured additive uncertainty models, but in principle this is no limitation since any uncertainty model of LFT type can be transformed into such a model. The models are determined by matching to process data available in the form of frequency responses of a set of individual models or sets of input-output data. Conditions for the existence of solutions to the data-matching problems are defined by LMIs. Uncertainty models that tightly match the data are obtained by minimizing an ellipsoidal uncertainty region. An application to distillation is included.

Control structure selection via relative gain analysis of partially controlled systems

A new procedure based on the Relative Gain Array (RGA) is proposed for screening of control structures. In addition to the RGA for the full open-loop system, the RGA for the system under partial control is considered. This Partial Relative Gain (PRG) provides necessary conditions for integral controllability and integrity. The PRG also solves the variable pairing problem in decentralized control more reliably than the conventional RGA, which may fail or be ambiguous for systems larger than 2×2. Furthermore, it can be inferred from the PRG when block-decentralized control should be considered.