Multipurpose deadbeat controllers for multivariable systems

A simple and direct deadbeat control design algorithm for discrete-time multivariable systems is introduced. Our brief was to synthesize a realizable controller to achieve the following objectives: (1) input-output decoupling, (2) deadbeat tracking of any prespecified class of changeable deterministic reference signals and (3) changeable deterministic disturbances rejection where the changeable reference signals and disturbances can be different at each channel. Since the internal stability requirement is satisfied, our design algorithm can easily handle both unstable and non-minimum phase systems. Some constraints on the transfer function are also derived to make sure that the derived controller is realizable. Since all solutions can be described in parametric form, some of the performance criteria can be combined.     

Output deadbeat control discrete-time multivariate systems

An algorithm is presented to compute output deadbeat controls for linear multivariable systems. The algorithm, based on quadratic optimization with no cost on control (cheap control), is numerically stable and covers the most general cases. The resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback. The central part of the algorithm is the construction of the nonunique state-cost matrix. Two alternatives are presented having different complexities and resulting in solutions having different properties     

On output deadbeat control of discrete-time multivariable systems

A necessary extension to the output deadbeat control algorithm of M.R. Marrani et al. (see ibid., vol.AC-34; p.644-8 (1989)) is presented. This extension is shown to provide particular theoretical insights when dealing with the case of a system with multiple stable transmission zeros. It is numerically straightforward to implement. Once the zeros have been calculated, the state zero directions can be determined independently. This method has particular advantages when dealing with the case of a plant with multiple stable transmission zeros     

Design of linear multivariable discrete-time tracking systems incorporating error-actuated dynamic controllers

Jn this paper, the method of entire eigenstructure assignment (Bradshaw and Porter 1978 a) is applied to the design of linear multivariable discrete-time tracking systems incorporating error-actuated dynamic controllers. The method is illustrated by designing an crror-aetuated dynamic controller which causes the output of a second-order discrete-time plant to track a constant command input in the presence of an unmeasurable constant disturbance input.     

Asymptotic properties of linear multivariable discrete-time tracking systems incorporating fast-sampling error-actuated controllers

In this paper, the asymptotic properties of tracking systems incorporating linear multivariable plants which are amenable to fast-sampling error-actuated control (Bradshaw and Porter 1980) are characterized in terms of the eigenstructure of the closed-loop plant matrices. It is shown that the closed-loop eigenstructure is such that the tracking behaviour of systems incorporating fast-sampling error-actuated controllers designed in accordance with the synthesis technique of Bradshaw and Porter (1980) is increasingly dominated by the modes associated with characteristic roots of the form λ=l+σ as the sampling frequency is increased and that increasingly ‘tight’ control is therefore achieved. These theoretical results are illustrated in the case of a closed-loop system incorporating a third-order plant and a fast-sampling error-actuated controller by the presentation of the computed closed-loop eigenstructure and of the results of computer simulation studies.     

Design of linear multivariable discrete-time tracking systems incorporating fast-sampling decentralized error-actuated controllers

In this paper, the class of linear multivariable continuous-time plants which are amenable to fast-sampling decentralized error-actuated control is characterized in terms of the relatively prime polynomial matrix factors of the transfer function matrices of such plants. It is shown that this characterization greatly facilitates the design of fast-sampling decentralized error-actuated controllers, and the resulting synthesis technique is illustrated by designing such a controller for a third-order plant. with two inputs and two outputs.     

Deadbeat algorithms for output controllers in discrete-time multivariable systems

This paper studies the problem of designing output deadbeat controllers to force the state of discrete-time multivariable systems to zero in a finite number of samples. Two algorithms are considered. The first is based on the fact that the closed-loop eigenstructure assignable by output feedback is constrained by the requirement that the left and right eigenvectors must be in certain subspaces. In the second algorithm, the output gain matrix is computed through the optimization of certain parameters of the controller, while maintaining its structural constraints. Computer programs have been developed to realize the two algorithms and examples are given to illustrate the feasibility of the techniques.     

Robust controllers for uncertain linear multivariable systems

This paper is addressed to three distinct yet related topics in the design of controllers for imprecisely known linear multivariable systems. In the first part, it is supposed that the plant to be stabilized is subject to additive or multiplicative uncertainties, and necessary and sufficient conditions are derived for the existence of a controller that stabilizes all plants within this band of uncertainty. In the second part, in contrast with the first part, it is supposed that the number of unstable poles of the plant to be stabilized is not precisely known. The type of plant uncertainty is the so-called “stable-factor” uncertainty, and necessary and sufficient conditions are given for robust stabilization. In the third part, the model of uncertainty is a ball in the space of rational matrices metrized by the so-called graph metric, and sufficient conditions for robust stabilization are derived.     

All covariance controllers for linear discrete-time systems

The authors characterize the set of covariances that a linear discrete-time plant with a specified-order controller can have. The controllers that assign such covariances to any linear discrete-time system are given explicitly in closed form. The freedom in these covariance controllers is explicit and is parameterized by two orthogonal matrices. By appropriately choosing these free parameters, additional system objectives can be achieved without altering the state covariance, and the stability of the closed-loop system is guaranteed     

Dynamic controllers in linear multivariable systems

The theory of pole assignment in multivariable stationary linear systems using a controller of given order is reassessed. Novel proofs, both simpler and more general than hitherto are given, enabling efficient design algorithms to be formulated. Examples of such algorithms are worked out.     

Output deadbeat control of nonlinear discrete-time systems withone-dimensional zero dynamics: global stability conditions

Output deadbeat control in one step is considered for a class of discrete-time systems described by a nonlinear single-input/single-output recursive representation. Global stability conditions are established for the particular subclass of systems with one-dimensional zero dynamics. The results are illustrated with applications to polynomial and neural dynamical systems     

Nilpotency properties of linear multivariable discrete-time disturbance-rejection systems

In this paper the nilpotency properties of deadbeat linear multivariable discrete-time disturbance-rejection systems incorporating full-order or reduced-order observers for plants with accessible or inaccessible statea are investigated. The theory is illustrated by the presentation of the results of computer simulation studies which indicate that the presence of an observer affects only the transient behaviour of deadbeat discrete-time disturbance-rejection systems and that the use of a reduced-order observer results in markedly superior transient behaviour than the use of a full-order observer.     

线性离散时滞系统的输出反馈耗散控制

考虑线性离散时滞系统的二次型耗散控制问题,设计动态输出反馈使闭环系统渐近稳定且严格二次型耗散.先将系统严格二次型耗散性转化为线性矩阵不等式的可解性,得到了系统渐近稳定且严格二次型耗散的条件.然后讨论输出反馈耗散控制问题,给出了控制器的存在条件,总结出了控制器的综合方法、步骤.所得结果可为离散时滞系统的无源控制和H∞控制提供统一框架,也为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

Design of linear multivariable discrete-time tracking systems for plants with inaccessible states

In this paper a basis is developed for the systematic design of linear multivariable discrete-time tracking systems for plants with inaccessible states, which thus extends the results for discrete-time plants with accessible states previously obtained by Bradshaw and Porter (1975). The design method is illustrated by the presentation of the results of computer simulation studies.     

Multipurpose controllers for multivariable systems

The primary purpose of this paper is to outline a new procedure for designing controllers which simultaneously achieve a variety of desired design goals in deterministic, unity feedback, linear multivariable systems. More specifically, we will present a new algorithm for the systematic design of a "three-part" multivariable controller which simultaneously ensures: 1) a noninteractive or decoupled closed-loop design, 2) complete and arbitrary closed-loop pole placement, which implies desired (single-loop) transient performance as well as closed-loop stability, 3) zero steady-state errors between the plant outputs and any nondecreasing deterministic inputs, 4) complete steady-state output rejection of nondecreasing deterministic disturbances, and 5) robustness with respect to stability, disturbance rejection, and zero error tracking for rather substantial plant parameter variations. Our development will employ the more "modern" (Laplace-transformed) differential operator approach for controller synthesis, which involves transfer matrix factorizations and the manipulation of polynomial matrices in the Laplace operators.     

Robust stability for linear discrete-time systems with structured perturbations

The robust stability problems of linear discrete-time systems with structured perturbations are considered. The necessary and sufficient condition of interval stability is given and the maximal bound of robust stability is presented for systems with a non-negative or non-positive nominal system matrix. Further, it is shown that the given necessary and sufficient condition and the given maximal robust bound are still valid for time-varying perturbations and nonlinear perturbations.     

The stability of linear multivariable systems

A general criterion is presented for establishing the stability of a multivariable system from the stability of the simplified system consisting of its diagonal elements. This new criterion includes all known criteria of stability based on the diagonal system elements such as Rosenbrock's (1974), Nwokah's (1980) anil Koussiouris's (1980). For the class of matrices satisfying this criterion an equivalent result in terms of eigenloci can also be stated     

Unknown input observability for discrete-time linear multivariable systems and its application

A new concept of the unknown input observability, namely (r, s ; K) observability, for discrete-time linear multivariable systems is introduced. This concept is an extension of the conventional unknown input observability and reconstructibility. Necessary and sufficient conditions for the (r, s ; K) observability of the given system are derived by introducing a new unobservable subspace and presenting algorithms for obtaining the subspace. It is also shown that these new concepts are closely related to the existence condition of a dead-beat observer for a decentralized control system.     

A general stability theorem for linear discrete-time systems

The strongest sufficient conditions for constraining zeros to be on or within a circular region in thezplane in terms of weighted absolute norms are derived using elementary geometry. It is shown that the weighted L1norm yields the strongest result.     

Design of linear multivariable continuous-time tracking systems incorporating error-actuated controllers

In this paper, the controllability results of Porter and Bradshaw (1974) are applied to the dosign of linear multivariable continuous-time tracking systems incorporating plants with inaccessible states for which appropriate error-actuated controllers exist. The design method is illustrated by the presentation of the results of computer simulation studies