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Control Theory and Applications, IEE Proceedings -

Issue 5 • Date Sep 2001

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Displaying Results 1 - 12 of 12
  • Zero-placement approach to the design of sliding surfaces for linear multivariable systems

    Page(s): 333 - 339
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (554 KB)  

    A method is introduced for sliding-surface design for multivariable linear systems based on the placement of the transfer function transmission zeros from the control signal to the (fictitious) output which specifies the sliding surface. The design procedure uses the Luenberger feedback canonical form with input normalisation, which in turn is calculated using numerically reliable orthogonal transformations from the SLICOT library View full abstract»

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  • Constructing networks of continuous-time velocity-based models

    Page(s): 397 - 405
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (588 KB)  

    A conventional local model (LM) network consists of a set of affine local models blended together using appropriate weighting functions. Such networks have poor interpretability since the dynamics of the blended network are only weakly related to the underlying local models. In contrast, velocity-based LM networks employ strictly linear local models to provide a transparent framework for nonlinear modelling in which the global dynamics are a simple linear combination of the local model dynamics. A novel approach for constructing continuous-time velocity-based networks from plant data is presented. Key issues including continuous-time parameter estimation, correct realisation of the velocity-based local models and avoidance of the input derivative are all addressed. Application results are reported for a highly nonlinear simulated continuous stirred tank reactor process View full abstract»

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  • Identification of fuzzy models with the aid of evolutionary data granulation

    Page(s): 406 - 418
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (1029 KB)  

    The identification of fuzzy rule-based systems is considered. By their nature, these fuzzy models are geared toward capturing relationships between information granules-fuzzy sets. The level of granularity of fuzzy sets helps establish a required level of detail that is of interest in the given modelling environment. The form of the information granules themselves (in particular their distribution and type of membership functions) becomes an important design feature of the fuzzy model, contributing to its structural as well as parametric optimisation. This, in turn, calls for a comprehensive and efficient framework of information (data) granulation, and the one introduced in the study involves a hard C-means (HCM) clustering method and genetic algorithms (GAs). HCM produces an initial collection of information granules (clusters) that are afterwards refined in a parametric way with the aid of a genetic algorithm. The rules of the fuzzy model assume the form `if x1 is A and x2 is B and ··· and xn is W then y=φ (x1 , x2, ···, xn, param)' and come in two forms: a simplified one that involves conclusions that are fixed numeric values (that is, φ is a constant function), and a linear one where the conclusion part (φ) is viewed as a linear function of inputs. The parameters of the rules are optimised through a standard method of linear regression (least square error method). An aggregate objective function with weighting factor used in this study helps maintain a balance between the performance of the model for training and testing data. The proposed identification framework is illustrated with the use of two representative numerical examples View full abstract»

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  • Genetic algorithm approach to designing finite-precision controller structures

    Page(s): 377 - 382
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (671 KB)  

    The parameters of a digital control design usually need to be rounded when the controller is implemented with finite precision arithmetic. This often results in degradation of the closed loop performance and reduced stability margins. This paper presents a multi-objective genetic algorithm based approach to designing the structure of a finite-precision second-order state space controller implementation, which can simultaneously minimise some set of performance degradation indices and implementation cost indices. The approach provides a set of solutions that are near Pareto-optimal, and so allows the designer to trade-off performance degradation against implementation cost. The method is illustrated by the design of the structure of a PID controller for the IFAC93 benchmark problem View full abstract»

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  • Poles and zeros of α-β and α-β-γ tracking filters

    Page(s): 370 - 376
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (560 KB)  

    Discrete transfer functions for the α-β and α-β-γ Kalman tracking filters are presented. Filters for the update, as well as the prediction, estimates are considered. Root loci for the poles and zeros are presented, parameterised in the manoeuvring index. Closed-form solutions for the α-β-γ gains are given as functions of the manoeuvring index View full abstract»

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  • Box-Jenkins model LQG controller: design and performance

    Page(s): 419 - 429
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (791 KB)  

    The relationship between the variances of the input and output variables of a Box-Jenkins model control system under the linear quadratic Gaussian control law is obtained. This relationship is generalised to the relationships between the statistics of the input and output variables under this control law. Formulae to calculate these statistics are derived. The statistics are the auto-covariances and cross-covariances of the two input and output variable time series driven by the same Gaussian white noise. The statistics can be used to assess control loop performance View full abstract»

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  • Robust optimal guaranteed cost control for 2D discrete systems

    Page(s): 355 - 361
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (581 KB)  

    The guaranteed cost control problem is studied for a class of 2D discrete uncertain systems in the Fornasini-Marchesini state space setting. The uncertainty is assumed to be norm-bounded. Based on the guaranteed cost controller for 1D differential/difference systems, the notion of the guaranteed cost control problem for 2D discrete systems is proposed. The problem is to design both a static-state feedback controller and a dynamic output feedback controller such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach. A parametrised characterisation of the guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. Furthermore, a convex optimisation problem is formulated to select the optimal guaranteed cost controller which minimises the upper bound of the closed-loop cost function View full abstract»

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  • Identification of processes with direction-dependent dynamics

    Page(s): 362 - 369
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (773 KB)  

    The identification of systems which have different dynamics when the output is increasing compared with those when the output is decreasing is considered. The dynamics in each direction will be assumed to be linear. It is shown that when such systems are perturbed by pseudorandom binary signals based on maximum length sequences, there are coherent patterns in the input-output crosscorrelation function, but there is no coherent pattern in either the gain response or the phase response in the frequency domain. The crosscorrelation terms are developed in detail for a process with first-order dynamics in the two directions, perturbed by a maximum length binary (MLB) signal and the results are confirmed by simulation. Similar theoretical expressions and simulation results are given for such a process perturbed by an inverse-repeat signal based on an MLB signal. The crosscorrelation function patterns obtained using an MLB signal are not present when other classes of pseudorandom binary signals are used. The linear dynamics for the process perturbed by an MLB signal and its corresponding inverse-repeat MLB signal are estimated, and found to agree more closely with the theoretical value when the latter type of signal is used. The theory cannot be readily extended to processes with direction-dependent dynamics of higher order, but simulation results presented for such second-order processes show that the departure from linearity can still be detected from the crosscorrelation function when an MLB perturbation signal is used View full abstract»

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  • Robust stability of singularly perturbed state feedback systems using unified approach

    Page(s): 391 - 396
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (547 KB)  

    A method for the decomposition of unified state-feedback singularly perturbed systems is presented. Based on the small-gain theorem, a sufficient condition for robust stability is derived such that the composite state feedback renders the closed-loop singularly perturbed system asymptotically stable. With this method there is no need to consider two different approaches for continuous-time and discrete-time domains. An example illustrates the methodology View full abstract»

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  • Robust PI and PID controller design in delta domain

    Page(s): 350 - 354
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (634 KB)  

    A simple unified tuning method for PI and PID delta-domain controllers for SISO plants is developed. The method can shape the nominal stability, transient performance, static accuracy and control signal. A problem of how to satisfy the robust closed-loop stability and performance is also addressed. The method leads to a parameterised set of controllers that provide the required stability margin for a maximally achievable closed-loop bandwidth in the presence of unstructured plant uncertainties. The developed methodology can be employed as a design tool in a systematic multiobjective optimisation, where in view of the diversity of conflicting goals that must be simultaneously achieved, some trade-off mechanisms should be taken into account. Numerical examples illustrating the method are given View full abstract»

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  • LMI-based quadratic stability analysis for hierarchical fuzzy systems

    Page(s): 340 - 349
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (772 KB)  

    The quadratic stability issue in a hierarchical fuzzy system is investigated and a Takagi-Sugeno (TLS) type hierarchical fuzzy controller is proposed to regulate the nth order linear SISO plant with the bounded time-varying uncertainties or nonlinearities. The proposed T-S type hierarchical fuzzy controller is made up of n-1 2D T-S type fuzzy controllers and allows for the simple closed dynamics in the diagonal norm-bound linear differential inclusions (DNLDI) formulation. For this closed dynamics, the stability condition in linear matrix inequalities (LMI) form is presented. Then, based on the stability condition, a method for finding the maximum stable ranges of the T-S type hierarchical fuzzy controller gains is proposed. To illustrate the performance of the proposed method, a third order simple example is given View full abstract»

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  • New efficient frequency domain algorithm for H approximation with applications to controller reduction

    Page(s): 383 - 390
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (706 KB)  

    New frequency domain computational schemes for the weighted and unweighted H norm system approximation problems are introduced. The schemes are applicable in both continuous and discrete-time cases. The new algorithm is used to obtain reduced order controllers for a well known control problem View full abstract»

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