摘要:

A commonly used approximate discrete-time model for the estimation of the states of linear, continuous-time invariant processes is analysed. This analysis is performed by carefully defining and evaluating the true-error-covariance matrix of the estimate and by comparing it with what has been commonly believed to be the error covariance matrix. It is shown that there exists a class of unstable processes for which the former error-covariance matrix attains an unbounded norm, in spite of the fact that the norm of the other error-covariance matrix remains bounded. It is also shown that for another class of processes, the approximate model provides a particularly good estimation for short sampling periods. Based on the equations that govern the behaviour of the estimation-error covariance matrices, an alternative improved approximation is proposed that always leads to a true-error-covariance matrix with a bounded norm. Finally, following similar lines of analysis, it is shown that the approximate discrete-time models for the dual linear-quadratic regulation problem exhibit entirely different behaviour in that the cost may become unbounded even for stable continuous-lime processes

ISSN:0020-7179    

DOI:10.1080/00207178908953434

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Extension and partial parameter optimization are applied to a modified Smith predictor and controller, designed by de Paor( 1985) for a class of unstable processes having transfer functions of the form k1A exp(—sT)/B, where A is a monic, Hurwitz polynomial of degree (n — l) and the nth degree monic polynomial B has a single right half-plane root at s=λ It is found that for l = 1,2,3 asymptotic stability can be achieved for λ T> 1, which more than doubles the best result obtained earlier. For a specific process, responses are compared with those obtained using the optimum stability PI controller of de Paor and O'Malley (1989). The advantages of the optimized, modified predictor in terms of tightness of control and faster settling time are highlighted

ISSN:0020-7179    

DOI:10.1080/00207178908953435

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A primary role of feedback design is to enable a system to cope with the inevitable uncertainly associated with its description. Although it is often the case that we have at hand a practical description of both the size and structure of the expected uncertainty, simple multivariable design strategies which effectively incorporate this information have been slow to appear. A rigorous development of the uncertainly problem for linear multivariable feedback systems is presented utilizing the characteristic locus framework, and then a simple geometric alignment property is exploited in order to formulate a systematic design strategy, focusing on a PI implementation for the resulting controllers

ISSN:0020-7179    

DOI:10.1080/00207178908953436

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper relates the singular perturbation approximation technique for model reduction to the direct truncation technique if the system model to be reduced is stable, minimal and internally balanced. It shows that these two methods constitute two fully compatible model-reduction techniques for a continuous-time system, and both methods yield a stable, minimal and internally balanced reduced-order system with the same L∞-norm error bound on the reduction. Although the upper bound for both reductions is the same, the direct truncation method tends to have smaller errors at high frequencies and larger errors at low frequencies, while the singular perturbation approximation method will display the opposite character. It also shows that a certain bilinear mapping not only preserves the balanced structure between a continuous-time system and an associated discrete-time system, but also preserves the slow singular perturbation approximation structure. Hence the continuous-time results on the singular perturbation approximation of balanced systems are easily extended to the discrete-time case. Examples are used to show the compatibility and the differences in the two reduction techniques for a balanced system

ISSN:0020-7179    

DOI:10.1080/00207178908953437

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989. Particular attention is paid to relationships between definitions of such zeros and their theoretical development. Transmission, invariant, system, module, infinite and finite zeros are addressed, the latter subdivided into a hierarchical structure with respect to information considered in the definition process.

ISSN:0020-7179    

DOI:10.1080/00207178908953438

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We establish conjugation notion in discrete-time systems, first introduced into theH∞control theory of continuous-time systems by Kimura (1989). In discrete-time systems, conjugation is a very elementary operation on rational transfer functions that replaces some of their poles by their reflections with respect to the unit circle. With the aid ofJ-lossless conjugation conjugation by aJ.lossless system), it is shown that the parametrization of sub-optimal solutions ofH∞model-matching problems is reduced to a Lyapunov-type equation. The parametrization of all solutions is given in an extremely simple way. It is further proved that theJ-lossless conjugation of theH∞model-matching problem is a natural state-space representation of classical interpolation in discrete-time systems.

ISSN:0020-7179    

DOI:10.1080/00207178908953439

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Static optimization with linear equality constraints and separable structures is studied by using the mixed coordination method. The idea is to relax equality constraints via Lagrange multipliers, and create a hierarchy where the Lagrange multipliers and part of the decision variables are selected as high-level variables. The method was proposed about ten years ago with a simple high-level updating scheme. We show that the solution of the high-level problem is a saddle point, and the simple updating scheme has a linear convergence rate under appropriate conditions. To obtain faster convergence, the modified Newton method is adopted at the high level. There are two difficulties associated with this approach. One is how to obtain the hessian matrix in determining the Newton direction, since second-order derivatives of the objective function with respect to all high-level variables are needed. The second is when to stop in performing a line search along the Newton direction, as the high-level problem is a maxmini problem looking for a saddle point. In this paper, the hessian matrix is obtained by using a kind of sensitivity analysis. The line search stopping criterion, on the other hand, is based on the norm of the gradient vector. Extensive numerical testings show that our approach performs much better than the simple high-level updating scheme. Since the low level consists of a set of independent subproblems, this method is well suited for parallel implementation in solving large-scale problems. Simulated parallel-processing results show that our method outperforms the one-level Lagrange relaxation method for all the test problems. Furthermore, since convexification terms can be added while maintaining the separability of low-level subproblems, the method is very promising for non-convex problems.

ISSN:0020-7179    

DOI:10.1080/00207178908953440

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In this paper we treat the problem of inducing local sliding regimes on non-linear smooth surfaces defined in the state space of general non-linear controlled systems. A suitable notion of relative degree is found to be of crucial importance in establishing the most salient properties of non-linear systems undergoing sliding motion. The relevance of sliding modes in several control problems as complementary ‘outer loop’ feedback is examined

ISSN:0020-7179    

DOI:10.1080/00207178908953441

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Recently, for discrete-event systems modelled by automata, Ramadge and Wonham (1987 a, b) have proposed two control techniques called ‘supervisory control’ and ‘state feedback logic’. If control specifications are given in terms of predicates on the set of states, both techniques are applicable. This paper discusses the relationship between these techniques. It is shown that the language accepted by the discrete-event system with maximally permissive feedback is equal to the supremal controllable language if the predicate is control invariant. Moreover, it is shown that the predicate is control invariant if there exists a controllable language with a certain condition on the set of reachable states, but the converse does not hold in general

ISSN:0020-7179    

DOI:10.1080/00207178908953442

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The non-singular transformation that completely decouples a weakly coupled linear system under non-restrictive conditions is defined. The transformation matrices are obtained from two algebraic matrix equations. Algorithms that efficiently generate solutions to these equations are derived. The proposed transformation also completely decouples the corresponding Lyapunov matrix differential equation.

ISSN:0020-7179    

DOI:10.1080/00207178908953443

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor