摘要:

A design methodology for observers and controllers for a class of single-input, single-output non-linear systems is developed. A non-linear observer form is defined, and a corresponding observer using non-linear observer gains is specified. The resulting error dynamics, which are non-linear, are asymptotically stable for a proper choice of those gains and bounded inputs and outputs. A non-linear controller form is defined and a corresponding controller, which results in linear closed-loop dynamics with arbitrary eigenvalue placement, is devised. Transformations from the class of interest to the defined forms are derived. In the observer case, the transformation to the observer form and the non-linear entries in the state matrix of that form can be determined separately, leading to a system of linear partial-differential equations—a major simplification. In the controller case, a simple, well-known system of linear partial-differential equations is obtained. The efficacy of the developed methodology is shown, by employing a non-linear, third-order model of a vehicle's longitudinal dynamics in the design process. Both here, and in other simulations, the latter results in a considerable improvement over a linearization/classical-design approach—especially in situations where the nonlinear effects are pronounced. Moreover, it has definite advantages over parameter scheduling, especially for systems where the non-linearities are functions of many state variables, resulting in a large number of operating points.

ISSN:0020-7179    

DOI:10.1080/00207178808906221

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Full-order observers have n integrators (or n delayors in the discrete-time case) that must be assigned ‘initial-condition values’ prior to the beginning of operation. However, the issue of how best to choose (design) those initial-condition values has apparently been completely ignored in control engineering textbooks. As a consequence, observer initial conditions in industrial applications are usually set to zero, by default. In this paper it is shown that there exists a welldefined, easily computed, physically realizable optimum choice for observer initial-condition values. When these optimum initial conditions are used, rather than ‘zero’ initial conditions, a significant improvement in the observer's ‘start-up error transients’ may result. A numerical example is worked out to illustrate this performance improvement.

ISSN:0020-7179    

DOI:10.1080/00207178808906222

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The tracking of a specified nominal output within an arbitrary error bound in the presence of uncertainties is formulated in terms of topological neighbourhoods in the function spaces L2k[0, ∞). A class of uncertain multi-input multi-output nonlinear systems is considered and design criteria are developed for so-called ‘tracking in the sense of spheres’ The design criteria are essentially of a ‘quantitative pole-placement’ form with the induced L2-norm as the measure of performance. For the special case of single-input single-output systems with a sector bounded non-linearity, a circle-type geometric interpretation of the design criteria is given. The applicability of the design criteria for the SISO case is illustrated by synthesizing a controller for a second-order system.

ISSN:0020-7179    

DOI:10.1080/00207178808906223

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A direct method for solving variational problems using Fourier series is presented. An operational matrix of integration is first introduced and is utilized to reduce a variational problem to the solution of algebraic equations. Illustrative examples are also given.

ISSN:0020-7179    

DOI:10.1080/00207178808906224

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Fractional representation methods for finite-dimensional linear time-invariant (FDLTI) systems have been developed in an algebraic framework of principal ideal domains. The concept of coprime fractional representations has been generalized to discrete-time non-linear systems by Hammer (1985, 1987), by viewing the Bezout identity as the basis of the definition of coprimeness. In this paper, we view the role of (right) coprime fractional representation in representing the set of all stable input-output pairs of a (possibly unstable) non-linear system. This notion of coprimeness is shown to be equivalent to that of FDLTI systems. Using coprime fractional representations of non-linear systems, we obtain a characterization of the stability of non-linear feedback systems. This characterization is similar to that obtained in the case of FDLTI systems. We also obtain a parameterization of all non-linear and time-varying stabilizing controllers for linear (possibly time-varying) plants which has the same form as the Youla parameterization for FDLTI systems.

ISSN:0020-7179    

DOI:10.1080/00207178808906225

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Decentralized compensation of large-scale power systems has the appealing feature that local substations may be controlled by a small subset of state or output variables. In this paper, the problem of decentralized control by discrete-time compensation is addressed. By formulating the dynamics of each subsystem and including the interaction terms with other subsystems, a performance measure is constructed, based upon local desired system performance. This resulting controller is optimal, even if the subsystems are strongly coupled. An example using a 10-machine power system is provided to illustrate the improvement of the system response to faults when compared to classical excitation control.

ISSN:0020-7179    

DOI:10.1080/00207178808906226

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Various discrete-time representations of a class of stochastic distributed parameter systems for optimal state estimator design are proposed and their properties are examined. Four different types of discrete-time models are considered: the first is an exact model by means of Green's function technique and the other three are approximate models by forward-, backward- and forward-averaging-differences in time. It is found that the forward-difference approximation leads to an unstable discrete-time model while the remaining three preserve the stability of the original distributed parameter systems. In addition, unlike the lumped-parameter systems, the state estimator based on the discrete-time model derived from forward-difference is proven to be unstable. An illustrative numerical example for a simple diffusion process is given.

ISSN:0020-7179    

DOI:10.1080/00207178808906227

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

We investigate certain questions concerning the periodic structure of the matrix Riccati differential equation with constant coefficients. A closed-form expression for the periodic solutions is obtained for both the cases involving distinct or repeated eigenvalues in the associated linear hamiltonian system. Previous results are extended by establishing that periodic solutions are bounded if and only if the span of their range does not intersect the orthogonal complement of the controllable subspace of the associated linear system.

ISSN:0020-7179    

DOI:10.1080/00207178808906228

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not ‘too’ coloured, as when a positive-real condition on the noise mode is satisfied. Moreover, the whiter the noise environment the more robust are the algorithms. This paper shows that for linear regression signal models, the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates. Indeed, there are guaranteed attractive convergence rates independent of the process noise colour. No positive-real condition is imposed on the noise model.

ISSN:0020-7179    

DOI:10.1080/00207178808906229

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

This paper studies the problem of controlling discrete-event systems as formulated by Ramadge and Wonham (1987). An optimal D-supervisor is introduced, which requires a minimal number of switchings (i.e. enabling and disabling controllable events). A complete characterization of such controllers as well as a procedure for its construction is given. An example to illustrate the result is also included.

ISSN:0020-7179    

DOI:10.1080/00207178808906230

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor