Jari M. Böling

On control relevant criteria in H/sub /spl infin// identification

This paper proposes a technique for using control relevant criteria in H/sub /spl infin// identification. The work reported here has its background in a desire to understand the closed-loop versus open-loop issue in control relevant identification. The proposed technique has some features in common with the iterative closed-loop Schrama scheme, but is constructed so as to be able to obtain control relevant reduced complexity models also directly from open-loop data (for stable systems). It is demonstrated that the proposed technique solves, with the initial open-loop data only, the examples treated earlier in the literature using the iterative closed-loop Schrama scheme.

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-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.

Structural learning in artificial neural networks using sparse optimization

Sparse optimization have been applied to simultaneously estimate the weights and model structure of an artificial neural network.The problem has been formulates as an 0-norm optimization problem, which is approximatively solved with an iterative reweighting procedure.The proposed method reduces the complexity an artificial neural network by finding a sparse representation of it, i.e. a solution where as many weights as possible are equated to zero.The proposed algorithms have successfully been applied to several benchmark problems and to a case study for estimating waste heat recovery in ships. In this paper, the problem of simultaneously estimating the structure and parameters of artificial neural networks with multiple hidden layers is considered. A method based on sparse optimization is proposed. The problem is formulated as an 0-norm minimization problem, so that redundant weights are eliminated from the neural network. Such problems are in general combinatorial, and are often considered intractable. Hence, an iterative reweighting heuristic for relaxing the 0-norm is presented. Experiments have been carried out on simple benchmark problems, both for classification and regression, and on a case study for estimation of waste heat recovery in ships. All experiments demonstrate the effectiveness of the algorithm.

Multi-model control of a simulated pH neutralization process

Abstract A multi-model PID controller is developed and evaluated in a simulation study for a nonlinear pH neutralization process. The performance and robustness characteristics of the multi-model controller are compared to those for conventional PID controllers and an alternative ”multi-model interpolation” controller.

Control-relevant input excitation for system identification of ill-conditioned n × n systems with n > 2

Abstract The objective of this work is to generalize input excitation designs suggested for system identification of ill-conditioned 2 × 2 systems to cases with more than two inputs and outputs. The methods are evaluated using a four inputs-four outputs distillation column/stripper system as a case study. The performance of the various procedures is evaluated through the model fit and different plant-friendly indices. The obtained models, and thus the quality of the associated input excitations, are also evaluated through cross validations.

Robust H 2 Control Applied to an Ill-conditioned Distillation Column

Abstract Optimal H 2 (LQ) controllers with robustness to model uncertainties are designed and evaluated on a distillation column. The column is ill-conditioned and nonlinear, showing large variations of gain and dynamic response depending on the direction of the disturbance. Three approaches for achieving good H 2 performance subject to robustness are applied to the process. The first approach is a multimodel LQ controller design method based on a set of identified linear models which describe the process about the operating point. Further, two mixed H 2 / H ∞ controller design methods are applied to design controllers which achieve nominal and robust H 2 performance, respectively, subject to robustness expressed in terms of an H ∞ norm bound. All the controllers are tested experimentally on the distillation column. The experimental results are in line with the theoretical computations.

Subspace identification for MIMO systems in the presence of trends and outliers

Abstract In this paper we present a framework for subspace identification of multiple-input multipleoutput linear time-invariant systems from data corrupted by outliers and piece-wise linear trends. The subspace identification problem is formulated as a sparsity constrained rank minimization problem that is relaxed using the nuclear norm and the l 1 -norm. The proposed identification method has been validated on a simulated example and on a case study using data from a pilot-plant distillation column.