Output tracking in multivariable nonlinear systems

Hirschorn, R.M.

doi:10.1109/tac.1981.1102658

Cited by 77 publications

(24 citation statements)

References 5 publications

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“…Different type of problems can be distinguished based on the structure imposed to the set of the desired trajectories. The most highly structured situation is when this set is finite [9] . If the class of desired trajectories can be described by an exosystem, i.e., an autonomous, noninitialized set of differential equations with an output, then the problem is called the regulator or servomechanism problem [10], [13].…”

Section: Problem Formulationmentioning

confidence: 99%

Tracking of continuous LPV systems using dynamic inversion

Balas

Bokor

Szabó

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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This paper investigates the problem of output tracking by dynamic system inversion for linear parameter varying (LPV) systems, where the system matrix depends affinely from the parameters. The proposed method does not suppose that the full state vector is measured and it is based on a dynamic inversion approach with error feedback. A dynamic inversion based solution applying an observer instead of the inverse dynamics is also given.

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Section: Problem Formulationmentioning

confidence: 99%

Tracking of continuous LPV systems using dynamic inversion

Balas

Bokor

Szabó

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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“…The problem of asymptotic tracking and disturbance rejection of a linear multivariable system subject to unmeasurable disturbances has been studied by many authors (see, e.g., Grasselli and Nicolo 1971a.b, 1976, Young and Willems 1972, Wonham 1974, Davison and Goldenberg 1975, Francis and Wonham 1975a, b,c, Davison 1976, Francis 1977, Staats and Pearson 1977, Desoer and Wang 1978, Basile et al 1987, possibly considering the robust output regulation and/or tracking under perturbations of 'physical' parameters affecting the description of the system Longhi 1991 a,b, Grasselli et al 1993), and contributions were given even for the case of linear periodic systems (Grasselli et al 1979, Grasselli and Lampariello 1981, Cdaneri 1990, Grasselli and Lough 1991, and non-linear systems (Hirschorn 1981, Hirschorn and Davis 1987, Isidori 1989, Isidori and Byrnes 1990, Tornambe 1991.…”

Section: T Introductionmentioning

confidence: 99%

“…For non-linear systems, the first approaches were the insertion of the inverse of the system in the closed-loop system (Hirschorn 1981), and input-output linearization (Isidori 1989). The main problem with the actual implementation of these algorithms is the assumption that the system is minimum phase: obviously, such a condition is not necessary .…”

Section: T Introductionmentioning

confidence: 99%

Global output tracking for a class of single-input single-output non-linear systems

Tornambè

1994

International Journal of Systems Science

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“…The most highly structured situation is when this set is finite [15] . If the class of desired trajectories can be described by an exosystem, i.e., an autonomous, noninitialized set of differential equations with an output, then the problem is called the regulator or servomechanism problem [16], [19].…”

Section: Problem Formulationmentioning

confidence: 99%

“…According to (15) the expression of the required input to track a desired output signal z d is given by the dynamic systemη…”

Section: Inversion Based Open-loop Designmentioning

confidence: 99%

Reference Tracking for Wiener Systems Using Dynamic Inversion

Szabó

Gáspár

Bokor

Proceedings of the 2005 IEEE International Symposium On, Mediterrean Conference on Control and Automation Intelligent Control,

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This paper investigates the problem of reference tracking for systems defined by a Wiener model. The proposed method does not suppose that the full state vector is measured and it is based on a dynamic inversion approach with error feedback. It is assumed however,that the inverse of the nonlinear part can be constructed. As an example a tracking control of a pressurizer is also provided. I. PROBLEM FORMULATIONWiener models have the capability of approximating, with arbitrary accuracy, any fading memory nonlinear time invariant system. For Wiener models, see Figure I, the system has a linear part Σ, followed by a nonlinear memoryless subsystem, i.e.,ẋ(1)They have been successfully used to model several nonlinear systems encountered in the process industry, in chemistry, pH control systems, distillation columns or processes where the measurement device has a nonlinear characteristics.Fig. 1. Wiener model Several methods have been proposed in the literature for the identification of Wiener models (see for instance [5], [32], [9], [28], [29], [20], [1], [10], [12], for some classical identification methods for Wiener models). The problem consists in estimating the nonlinear characteristic of the memoryless subsystem and recovering the impulse response of the linear one from input-output observations of the whole system. The main difficulty is caused by the fact that the inner system signal is not measured.By a particular choice of parametrization of the linear subsystem and the inverse of the nonlinearity, it is possible to formulate an error criterion where the parameters enter quadratically. This error criterion may be minimized using linear regression, quadratic programming or the total least squares method. This initial estimate may then be used in the numerical minimization of the prediction error criterion.There are a lot of papers dealing with the control design based on Wiener model structure, e.g. [21], [13], [14], [30], [31]. Usually, for controller design purposes the static nonlinearities are removed by an inversion, however, the inverse of the nonlinearity can be delivered by the identification algorithm, too. The special way in which the nonlinearity enters the Wiener model can be exploited by transforming it into uncertainty. The result will be an uncertain linear model, which enables to use for example robust linear MPC techniques, see [8], [25], [6].In the present paper, we study the reference tracking problem of a Wiener system. The problem of (asymptotic) tracking consists in finding a compensator such that the closed-loop system is internally stable and for any desired trajectory y d the output of the closed-loop system (asymptotically) approaches y d .Different type of problems can be distinguished based on the structure imposed to the set of the desired trajectories. The most highly structured situation is when this set is finite [15] . If the class of desired trajectories can be described by an exosystem, i.e., an autonomous, noninitialized set of differential equations with an output, then the...

show abstract

Output tracking in multivariable nonlinear systems

Cited by 77 publications

References 5 publications

Tracking of continuous LPV systems using dynamic inversion

Tracking of continuous LPV systems using dynamic inversion

Global output tracking for a class of single-input single-output non-linear systems

Reference Tracking for Wiener Systems Using Dynamic Inversion

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