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Showing papers in "International Journal of Control in 1980"


Journal ArticleDOI
TL;DR: The sign function of a square matrix can be defined in terms of a contour integral or as the result of an iterated map as discussed by the authors, which enables a matrix to be decomposed into two components whose spectra lie on opposite sides of the imaginary axis.
Abstract: The sign function of a square matrix can be defined in terms of a contour integral or as the result of an iterated map $. Application of this function enables a matrix to be decomposed into two components whose spectra lie on opposite sides of the imaginary axis. This has application in reduction of linear systems to lower order models and in the solution of the matrix Lyapunov and algebraic Riccati equations.

430 citations


Journal ArticleDOI
TL;DR: In this paper, the authors provide a mathematical framework for building reliable control using less reliable controllers, which is based upon the decentralized control schemes used so far for synthesizing reliable control systems subject to perturbations in the plant interconnection structure.
Abstract: The objective of this paper is to provide a mathematical framework for building reliable control using less reliable controllers The new ingredient in the design is the multiple control system which provides the necessary redundancy for reliability enhancement in control systems subject to controller failures The proposed reliability design is based upon the decentralized control schemes used so far for synthesizing reliable control systems subject to perturbations in the plant interconnection structure

286 citations


Journal ArticleDOI
TL;DR: The paper shows how the refined IV procedure can be extended in various important directions and how it can provide the basis for the synthesis of optimal generalized equation error (GEE) algorithms for a wide class of stochastic dynamic systems.
Abstract: This is the final paper in a series of three which have been concerned with the comprehensive evaluation of the refined instrumental variable (IV) method of recursive time-series analysis. The paper shows how the refined IV procedure can be extended in various important directions and how it can provide the basis for the synthesis of optimal generalized equation error (GEE) algorithms for a wide class of stochastic dynamic systems. The topics discussed include the estimation of parameters in continuous-time differential equation models from continuous or discrete data; the estimation of time-variable parameters in continuous or discrete-time models of dynamic systems ; the design of stochastic state reconstruction (Wiener-Kalman) filters direct from data ; the estimation of parameters in multi-input, single output (MISO) transfer function models ; the design of simple stochastic approximation (SA) implementations of the refined IV algorithms ; and the use of the recursive algorithms in self-adaptive (self...

273 citations


Journal ArticleDOI
TL;DR: In this article, the Smith dead-time compensator controllers are used to provide necessary conditions for practical stability and sufficient conditions guaranteeing certain sensitivity and relative stability properties of SISO systems.
Abstract: The special stability properties of SISO systems incorporating Smith dead-time compensator controllers are investigated. It is shown that the conventional approach to the design of such systems may lead to practical instabilities. Necessary conditions for practical stability and sufficient conditions guaranteeing certain sensitivity and relative stability properties are stated and proven. The inaccuracies in the models are measured by means of an ' ignorance function '. Sufficient conditions expressed in terms of this function, from which conservative estimates on allowed mismatches in the models may be found, are stated. Illustrative examples demonstrating the main results are presented.

202 citations


Journal ArticleDOI
TL;DR: In this article, a means to assess the value of each component of a large-scale system, when the total cost is a quadratic function, is provided, and a cost decomposition of the system has several important uses.
Abstract: A means is provided to assess the value or 'cst' of each component of a large scale system, when the total cost is a quadratic function. Such a 'cost decomposition' of the system has several important uses. When the components represent physical subsystems which can fail, the 'component cost' is useful in failure mode analysis. When the components represent mathematical equations which may be truncated, the 'component cost' becomes a criterion for model truncation. In this latter event component costs provide a mechanism by which the specific control objectives dictate which components should be retained in the model reduction process. This information can be valuable in model reduction and decentralized control problems.

174 citations


Journal ArticleDOI
TL;DR: In this article, a method to design optimal experiments for parameter estimation in distributed systems is given, where the design variables considered are the boundary perturbation and the spatial location of measurement sensors.
Abstract: A method to design optimal experiments for parameter estimation in distributed systems is given. The design variables considered are the boundary perturbation and the spatial location of measurement sensors. The design criterion used is the determinant of Fisher's information matrix. It is shown that suitable choice of these variables leads to improved parameter accuracy. Two examples are used to illustrate this method. The first example is concerned with sensor location for estimating the velocity of propagation and the damping coefficient of a vibrating string. The second example is concerned with the estimation of the thermal diffusivity and radiation constant for a heat diffusion process. It is also shown that the design philosophy can be applied to a wide class of systems described by partial differential equations.

134 citations


Journal ArticleDOI
TL;DR: In this paper, a synthesis procedure for stabilizing a single input-output plant with uncertainty in the gain factor by means of single-loop feedback with an asymptotically stable control and feedback sensor is presented.
Abstract: Using interpolation methods for holomorphic functions from the unit disc to itself we drive a synthesis procedure for stabilizing a single input-output plant with uncertainty in the gain factor by means of single-loop feedback with an asymptotically stable control and feedback sensor. We moreover give an algorithm for obtaining the optimum design.

128 citations


Journal ArticleDOI
TL;DR: In this paper, a scheme for synthesizing an intelligent controller is given, and then it is applied to the case of a simple system, by which the superiority of the intelligent controller becomes clear.
Abstract: Integral controllers designed for various state determined systems, which are subject to constant disturbances and large initial conditions, very often turn out to be unsatisfactory, The overshoot becomes large and the speed of response may not be fast enough even when optimum (in some sense) feedback gains are employed. One euro for such problems is the use of ‘ intelligent’ integral controllers. A scheme for synthesizing an ‘ intelligent ’ controller is given, and then it is applied to the case of a simple system, by which the superiority of the ‘ intelligent’ integral control becomes clear.

125 citations


Journal ArticleDOI
TL;DR: In this article, a combined method making use of the advantages of the stability-equation method and the continued-fraction method for reducing high order single-input/single-output systems and multivariate systems is presented.
Abstract: A combined method making use of the advantages of the stability-equation method and the continued-fraction method for reducing high order single-input/single-output systems and multivariate systems is presented. The reduction procedure is simple and computer-oriented. The reduced model is guaranteed to be stable if the original system is stable.

125 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a simple proof that an optimum Li(jω) lies on its ψi(ω) for each ω∊[0, ∞).
Abstract: In quantitative feedback synthesis, the objective is to satisfy assigned performance tolerances over given ranges of plant uncertainty and external disturbances. In such linear and non-linear problems, whether single, multiple-loop or multivariable, the synthesis techniques result in frequency-domain bounds ψi(ω) in the complex plane, on the loop transmission functions Li(jω). This paper presents a simple proof that an optimum Li(jω) lies on its ψi(ω) for each ω∊[0, ∞). Also, a numerical technique is presented for deriving any desired approximation to the optimum.

121 citations


Journal ArticleDOI
TL;DR: In this paper, a class of linear shift-invariant discrete systems satisfying a two-time-scale property is defined and a model satisfying this property is given, where a pair of explicitly invertible block diagonalizing transformations are used to obtain reduced order fast and slow models analogous to the continuous singularly perturbed case.
Abstract: A class of linear shift-invariant discrete systems satisfying a two-time-scale property is defined and a model satisfying this property is given. A pair of explicitly invertible block diagonalizing transformations are used to obtain reduced order fast and slow models analogous to the continuous singularly perturbed case. A deadbeat approximation to the fast modes results in a reduced order slow model, and a ‘ boundary layer ’ error in the original fast states. For control law design, the dual nature of these block diagonalizing transformations allows partial or total eigenvalue placement for fast and/or slow modes based on feedback designs for the reduced order slow and fast models.

Journal ArticleDOI
TL;DR: In this article, a digital control system to control a double inverted pendulum on a cart is presented, where the cart is placed on an inclined rail and is to be kept in position at a given reference point.
Abstract: A digital control system to control a double inverted pendulum on a cart is presented, where the cart is placed on an inclined rail and is to be kept in position at a given reference point. The controller design is based on linear servo control theory and can control the cart position of the inverted pendulum, eliminating the effect of the rail incline. Theoretical analyses of the pendulum and of the control system are given.

Journal ArticleDOI
TL;DR: In this article, necessary and sufficient conditions for existence and uniqueness of hermitian solutions of the algebraic n×n matrix Riccati equation (D≥0,C∗=C,(A, D) controllable) are obtained.
Abstract: Necessary and sufficient conditions for existence and uniqueness of hermitian solutions of the algebraic n×n matrix Riccati equation (D≥0,C∗=C,(A, D) controllable) are obtained. The conditions are formulated in terms of the spectral structure of a certain 2n × 2n matrix. A description is also given of the set of solutions in a geometrical language of invariant subspaces which are neutral with respect to a certain indefinite scalar product. This technique is then applied to provide some results on existence and uniqueness of solutions which are not necessarily hermitian. The problem is also approached (when Dz;> 0)via a related unilateral equation. for Z where K1 ∗ equals K1, K0 ∗ equals K0

Journal ArticleDOI
Michio Kono1
TL;DR: In this paper, the stabilization of the linear periodic discrete-time system through the use of linear periodic state-variable feedback has been studied and it is shown that complete reachability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of the eigenvalues to Y(τ, 0) by choosing a suitable state feedback.
Abstract: This paper considers the stabilization of the linear periodic discrete-time system through the use of linear periodic state-variable feedback. Let the transition matrix of the closed-loop system be Y(t, s). Then the stability of the closed-loop system depends on eigenvalues of Y(τ,0), where τ is period. It is shown that complete reachability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of the eigenvalues to Y(τ, 0) by choosing a suitable state feedback.

Journal ArticleDOI
TL;DR: The purpose of this correspondence is to draw attention to significant extensions of the results presented by Verghese, et al. as mentioned in this paper, which were obtained after the above paper was written, and are described in more detail in the following papers.
Abstract: The purpose of this correspondence is to draw attention to significant extensions of the results presented by Verghese, et al. (1979). These extensions were obtained after the above paper was written, and are described in more detail in Verghese (1978) and Verghese and Kailath (1979).

Journal ArticleDOI
TL;DR: In this article, two methods are developed by which control systems that are non-linear in the state variables but linear in the inputs may be approximated by bilinear systems in the neighbourhood of a steady state.
Abstract: Two methods are developed by which control systems that are non-linear in the state variables but linear in the inputs may be approximated by bilinear systems in the neighbourhood of a steady state. For both methods the approximations can be made successively more accurate at the expense of higher dimensionality, and can be a considerable improvement over the linear approximation. The resulting dimensionalities are determined as functions of the accuracy. Illustrative examples are given, and finally the two models are compared. Both are found to have considerable merit.

Journal ArticleDOI
TL;DR: In this article, a method for the design of linear state feedback laws for bilinear systems is presented, using a Liapunov approach, a class of stabilizing feedback amplifier matrices is constructed, depending on three positive definite weighting matrices which can be selected freely.
Abstract: A method for the design of linear state feedback laws for bilinear systems is presented. Using a Liapunov approach, a class of stabilizing feedback amplifier matrices is constructed, depending on three positive definite weighting matrices which can be selected freely. The computation of the amplifiers requires the solution, by successive approximations, of an algebraic Riccati equation for which a positive definite solution must be found. The relative magnitudes of the weighting matrices, expressed in terms of scaling factors, constitute the main design parameters. The influence of these parameters on some important dynamic characteristics of the system is analysed, thus allowing to adapt the parameter choice to the specifications of the design.

Journal ArticleDOI
TL;DR: In this paper, the self-tuning regulator of Astrom and Wittenmark and its derivatives are discussed and the stability properties are analyzed using standard input-output concepts. And convergence with probability of certain mean-square errors of interest is shown to be a consequence of input output stability of a related system.
Abstract: The self-tuning regulator of Astrom and Wittenmark and its derivatives are discussed. The stability properties are analysed using standard input-output concepts. Convergence with probability one of certain mean-square errors of interest is shown to be a consequence of input-output stability of a related system and the martingale convergence theorem.

Journal ArticleDOI
TL;DR: In this article, a new canonical form for a class of non-linear time-varying systems is introduced, which allows control design by pole assignment in a very systematic and clear way.
Abstract: A new canonical form for a class of non-linear time-varying systems is introduced. It allows control design by pole assignment in a very systematic and clear way. Under certain conditions a system can be transformed to this special form by a nonlinear time-varying transformation. These conditions define a sufficient criterion for controllability in the large, a new aspect of the controllability concept for non-linear systems.

Journal ArticleDOI
TL;DR: In this article, earlier results for feedback stabilization of linear systems and for Kalman filters and regulators are generalized, with proofs being in fact more direct than those explored earlier, and they are shown to be correct.
Abstract: When stabilizing linear discrete-time finite dimensional systems in control and estimation either optimally or suboptimally, technical difficulties arise in the conventional stability theories for coping with state transition matrices which are permitted to be singular or with eigenvalues arbitrarily small. In overcoming these difficulties, earlier results for feedback stabilization of linear systems and for Kalman filters and regulators are generalized in this paper, with proofs being in fact more direct than those explored earlier.

Journal ArticleDOI
TL;DR: In this paper, several theorems related to the mapping of eigenvalues under accelerated sign function algorithms are developed together with a consistent metric for measuring the distance of eigvalues from their ultimate destination.
Abstract: Applications of the matrix sign function to solving Lyapunov and Riccati equations and to other systems theory calculations are reviewed and the spectral implications of its definition discussed, Tho disadvantages of reduced order formulations are presented. Several theorems related to the mapping of eigenvalues under accelerated sign function algorithms are developed together with a consistent metric for measuring the distance of eigenvalues from their ultimate destination. After listing the desirable properties of an accelerated map, several previous attempts at acceleration are analysed and the fundamental reasons for their degree of success or otherwise determined. An optimally accelerated method and another rapidly convergent one are then developed. All of the methods are compared on two 28 x 28 examples arising from a Lyapunov and a Riccati equation. Finally, global and higher order convergence of the three successfully accelorated algorithms are proved.

Journal ArticleDOI
TL;DR: In this paper, an application of the theory of polynomial models to the study of some natural objects in geometric control theory is described, and a geometric characterization of feedback irreducibility is derived.
Abstract: This paper describes an application of the theory of polynomial models to the study of some natural objects in geometric control theory. In particular, it utilizes the correspondence between factorization of polynomial matrices and invariant subspaces to obtain, by the use of Toeplitz operators, a polynomial characterization of (A, B) invariant subspaces as well as those included in her C. A geometric characterization of feedback irreducibility is rederived.

Journal ArticleDOI
TL;DR: In this paper, the problem of tracking a reference variable from a given class is considered for discrete-time linear single-input-output plants, where the plant and the reference are both described by an input/output relation, such as a difference equation, and the objective is to track exactly in a minimum time.
Abstract: The problem of tracking a reference variable from a given class is considered for discrete-time linear single-input-output plants. The plant and the reference are both described by an input/output relation, such as a difference equation, and the objective is to track exactly in a minimum time. This dead-beat servo problem is solved hero by applying polynomial techniques. The optimal control law is shown to contain both feed-back and feed-forward terms and it is obtained by solving two linear polynomial equations. The entire design procedure is remarkably simple and efficient.

Journal ArticleDOI
TL;DR: A new algorithm is presented for the optimal reduction of multi-input, multi-output, time invariant linear systems and it is shown that the algorithm has the ability to determine the correct underlying canonical structure of the optimal reduced order system.
Abstract: A new algorithm is presented for the optimal reduction of multi-input, multi-output, time invariant linear systems. It is self-contained and requires no external minimization routines. Using an example it is shown that the algorithm has the ability to determine the correct underlying canonical structure of the optimal reduced order system. The reduction of a ninth order boiler model and an eleventh order nuclear reactor model are presented.

Journal ArticleDOI
Rein Luus1
TL;DR: Model reduction for reducing a high-order transfer function to one of low order is based on minimizing the deviations in frequency response throughout the frequency range of interest as mentioned in this paper, and several examples are used to illustrate the procedure and to test the viability of such an approach to model reduction.
Abstract: Model reduction for reducing a high-order transfer function to one of low order is based on minimizing the deviations in frequency response throughout the frequency range of interest. Several examples are used to illustrate the procedure and to test the viability of such an approach to model reduction.

Journal ArticleDOI
TL;DR: In this article, a measurement selection criterion is derived with the objective of minimizing the sensitivity of the state estimates to the disturbances, and an interesting parallel is discussed to the dual problem of controllability of a system when the state...
Abstract: Slowly-varying persistent unmeasured disturbances, i.e. disturbances which allow the process to exhibit quasi steady-state behaviour most of the time, are very common in process-control systems. The inferential control schemes employing the well-known state-reconstruction methods (Luenberger observer, Kalman filter) are unable to cope with such disturbances and have been demonstrated to lead to large errors. The augmentation of the state vector has been proposed as a means for overcoming these difficulties. This paper shows that this procedure yields in general (i.e. always when the number of disturbances exceeds the number of measurements) problems of structural observability and suggests an optimal way to resolve them. As a consequence of this approach a measurement selection criterion is also derived with the objective of minimizing the sensitivity of the state estimates to the disturbances. An interesting parallel is discussed to the dual problem of controllability of a system when the state ...

Journal ArticleDOI
TL;DR: In this article, necessary and sufficient conditions for the stabilization of an /-input, m-output, time invariant, linear and minimal system while block decoupling it by state feedback and a constant non-singular input transformation are determined.
Abstract: Necessary and sufficient conditions arc determined for the stabilization of an /-input, m-output, time invariant, linear and minimal system while block decoupling it by state feedback and a constant non-singular input transformation. The fixed poles of the block decoupled system are related to a subset of the transmission zeros of tho uncompensated system nnd a method is presented for assigning arbitrarily all the non-fixed poles of the compensated system. Finally, the observability of the block decoupled system is examined.

Journal ArticleDOI
TL;DR: In this paper, a new algorithm for solving the Lyapunov matrix equation X − A∗XA = Q is proposed, which is purely algebraic and does not involve the calculation of the characteristic polynomial of A or reduction to a canonical form.
Abstract: A new algorithm for solving the Lyapunov matrix equation X − A∗XA = Q is proposed. The method proceeds by reducing to a special case for which an explicit formula is given. The technique is purely algebraic (i.e. involves no iteration), but does not involve the calculation of the characteristic polynomial of A or reduction to a canonical form. If Q is symmetric and the matrices are of type n × n, the number of multiplications and divisions required is about 4n4. Two simple devices are given whereby the technique can be extended to a wider class of linear matrix equations.

Journal ArticleDOI
TL;DR: A composite stabilizing feedback controller using a full-order observer is synthesized from the separate observer-based controllers, the mutually independent gains of which do not require knowledge of the small singular perturbation parameter.
Abstract: The dynamic feedback control for a class of singularly perturbed linear time-varying systems with inaccessible state is considered through a separate observer-based controller design for two lower-dimensional subsystems in two different time-scales A composite stabilizing feedback controller using a full-order observer is synthesized from the separate observer-based controllers, the mutually independent gains of which do not require knowledge of the small singular perturbation parameter

Journal ArticleDOI
TL;DR: In this paper, the infinite zero structure of completely controllable and observable linear multi-variable systems which give rise to square, non-singular, strictly proper transfer function matrices is investigated via the polynomial matrix approach to the solution of the decoupling problem.
Abstract: The infinite zero structure of completely controllable and observable linear multi-variable systems which give rise to square, non-singular, strictly proper transfer function matrices is investigated via the polynomial matrix approach to the solution of the decoupling problem. In the process various connections between infinite zeros, their degrees and geometric and polynomial matrix ideas are demonstrated. The asymptotic behaviour of closed loop eigenvectors under high gain output feedback is also examined.