Showing papers in "International Journal of Control in 1981"
TL;DR: In this paper, the effects and uses of applying linear feedback to continuous time descriptor systems are studied and structural changes resulting from feeding back the slow and fast parts of the trajectory separately are characterized.
Abstract: The effects and uses of applying linear feedback to continuous time descriptor systems are studied. Structural changes resulting from feeding back the slow and fast parts of the trajectory separately are characterized. It is shown that under certain conditions related to controllability the poles of the slow subsystem may be shifted arbitrarily and the impulsive behaviour of the fast subsystem may be eliminated.
245 citations
TL;DR: In this article, several stability conditions with an extremely simple form are provided for single linear systems with time delays, and these results are extended to the composite linear systems which exist in each subsystem and in the interconnections between subsystems.
Abstract: Easy ways to test the stability of systems involving time delays have been sought. In this paper, several stability conditions with an extremely simple form are provided. First, some criteria for single linear systems with time delays are presented. Then these results are extended to the composite linear systems with time delays which exist in each subsystem and in the interconnections between subsystems. Among these criteria, those which are expressed by scalar inequalities also permit us to assess the transient behaviour of systems.
221 citations
TL;DR: In this paper, the authors discuss the practical implications of an extended self-tuning property, which allows the designer to make arbitrary assumptions concerning the disturbance dynamics, and propose a simple pole-assignment selftuner which combines servo-tracking and regulatory closed-loop criteria.
Abstract: This article concerns the practical implications of an extended self-tuning property. The extension represents a refinement of existing asymptotic self-tuning properties, in the sense that it allows the designer to make arbitrary assumptions concerning the disturbance dynamics. The important practical consequence of this is that a simple pole-assignment self-tuner may now be designed which combines servo-tracking and regulatory closed-loop criteria. In the pure regulation case a priori parametrization of the noise dynamics can be used to aid convergence of the self-tuning algorithm. In addition, an implicit pole-assignment regulator is easily formulated from the extended self-tuner.
135 citations
TL;DR: In this article, the mathematical form associated with an oscillatory system lends itself to a complete modal analysis that can be written in closed form, and this available modal structure and the controllability measures are combined to yield a design approach for optimal placement of actuators in oscillatory systems.
Abstract: Oscillatory systems provide a good linear description of large flexible space structures. Considering the problem of controllability measures for these systems leads to a design approach for actuator placement in such systems. It is shown that the mathematical form associated with an oscillatory system lends itself to a complete modal analysis that can be written in closed form. This available modal structure and the controllability measures are combined to yield a design approach for optimal placement of actuators in oscillatory systems.
123 citations
TL;DR: An adaptive control method to track desired trajectories which are described by arbitrary task-oriented coordinates is proposed, which requires neither a knowledge of parameters of the system nor complicated calculations, and is easy to implement on a microcomputer.
Abstract: It is in general difficult to control the motion of mechanical manipulators by the usual deterministic control methods in a wide range of work spaces, because of complex non-linearities of dynamics and parameter uncertainty. This paper proposes an adaptive control method to track desired trajectories which are described by arbitrary task-oriented coordinates. Since the method requires neither a knowledge of parameters of the system nor complicated calculations, it is easy to implement the control law on a microcomputer. The effectiveness of the proposed method is verified by several simulation results. In particular, an adaptive control law compensating an acceleration term is shown to be very effective for fast motions.
118 citations
TL;DR: In this article, the authors apply the operational properties of block-pulse functions to the analysis and optimal control of time-varying linear systems with quadratic performance index.
Abstract: Succinct and clear-sighted operational properties of block-pulse functions are fully applied to the analysis and optimal control of time-varying linear systems with quadratic performance index. Piecewise constant solutions equally distributed, which are simple in form and convenient for use or implementation, are consequently obtained. Another advantage of this method is that any positive integer can be chosen as the number of sub-intervals, whereas in the case of Walsh function approximation the choice can only be made from 2, 4, 8, 16, 32, and so on. The algorithms developed in the paper are illustrated by appropriate examples.
111 citations
TL;DR: In this article, the theory of observability and deterministic observers for linear time systems with delays has been studied for the case of point delays which are commensurable; however, most of the results can be generalized to the situation with distributed delays and to the ease with noncommensurate delays.
Abstract: New results on the theory of observability and deterministic observers for linear time.invariant systems with delays are presented. The results have been established only for the case of point delays which are commensurable ; however, most of the results can be generalized to the situation with distributed delays and to the ease with non-commensurate delays.
107 citations
TL;DR: It is shown that when a recursive least squares estimation scheme is used, the feedback employed can be expressed simply in terms of the estimated system parameters.
Abstract: This paper employs a state space system description to provide a pole placement scheme via state feedback. It is shown that when a recursive least squares estimation scheme is used, the feedback employed can be expressed simply in terms of the estimated system parameters. To complement the state feedback approach, a method employing both state feedback and linear output feedback is discussed. Both methods arc then compared with the previous output polynomial type feedback schemes.
86 citations
TL;DR: In this article, the Mihailov stability criterion is used to improve the Pade approximation method for linear model reduction, and the stability of the reduced model is assured if the original system is stable.
Abstract: This paper uses the property of the Mihailov stability criterion to improve the Pade approximation method for linear model reduction. Therefore the stability of the reduced model is assured, if the original system is stable. This method provides several different reduced models depending upon the constant k 2 to be chosen. It is rather simple, computationally very straightforward, and can be used for multi-input multi-output systems and unstable systems. Finally this paper introduces a method for estimating the order of the reduced model, and gives a possibility for solving the model reduction problem over a desired low-frequency interval. Numerical examples and comparison among different reduced models are given.
85 citations
TL;DR: In this article, a complete classification of almost (A, B) -invariant, almost controllability and controllable subspaces is derived in terms of matrix pencil invariants.
Abstract: The equivalence between the algebraic, matrix pencil, characterization of the sub-spaces of the ‘ extended ’ geometric theory and their dynamic characterization 13 established. As a result, a complete classification of Almost ( A, B) -invariant, ( A, B) -invariant, Almost controllability and controllability subspaces is derived in terms of matrix pencil invariants. The frequency propagation aspects of infinite spectrum ( A, B)-invariant subspaces are investigated and it is shown that they are limits of closed-loop eigenspaces with arbitrarily largo eigenvalues. Finally, the importance of the infinite frequency subspaces in the study of the asymptotic behaviour of the closed-loop eigenspaces and eigenvalues under scalar gain output feedback is discussed.
78 citations
TL;DR: In this paper, the Laguerre operational matrices for the integration and differentiation of a Laguero vector whose elements are Lagueria polynomials are generalized to fractional calculus for investigating distributed systems.
Abstract: The Laguerre operational matrices for the integration and differentiation of a Laguerre vector whose elements are Laguerre polynomials are generalized to fractional calculus for investigating distributed systems. The generalized operational matrices corresponding to 8, 1/8, 8/√(82+1) and exp (−8/(8+1)) are derived as examples. Comparison of the Laguerre series approximate inversions of irrational Laplace transforms with exact solutions is very satisfactory.
TL;DR: In this article, the closed-loop representation of a jointly stationary vector (y, u)-proccss was studied and conditions were derived on the closed loop models for the joint process model to be stable and minimum phase.
Abstract: Stable constant linear closed-loop systems relating an input vector u to an output vector u and vice versa produce a jointly stationary (y, u)-procoss. On the other hand it is often natural to split up a stationary vector random process z into component vectors yand u, and to examine the closed-loop relations between y and u. This paper presents a number of new results on the spectral factorization and the closed-loop representation of a jointly stationary vector (y, u)-proccss. Conditions are derived on the closed-loop models for the joint process model to bo oE minimal degree, stable and minimum-phase. Relations between different joint process models producing the same spectrum φyu(z)are established.
TL;DR: In this paper, a design oriented methodology is presented for the construction of low-order, sub-optimal, output feedback compensators, which is suboptimal in the sense that it retains an l-dimensional eigenspace from a reference optimal state-feedback linear quadratic regulator problem.
Abstract: A design oriented methodology is presented for the construction of low-order, suboptimal, output feedback compensators. The design is suboptimal in the sense that it retains an l-dimensional eigenspace from a reference optimal state-feedback linear quadratic regulator problem. If r is the number of outputs, then for fixed l > r, it is known that the design requires a dynamic compensator of dimension l — r. The parameters of the compensator are determined by the solution of an associated output feedback pole placement problem. Using iterative, dyadic pole placement, a procedure is given which determines the solution of this problem, without a priori assumptions on the dimension of the compensator. The design is also extended to the class of stabilizable systems, and the resulting compensator is shown to possess a separation property.
TL;DR: In this article, the characteristic quasipolynomial for a linear differential-difference system is replaced by a regular polynomial to which standard stability tests for finite dimensional systems can be applied.
Abstract: The characteristic quasipolynomial for a linear differential-difference system is replaced by a regular polynomial to which standard stability tests for finite dimensional systems can be applied. The Routh-Hurwitz stability test is then used to determine necessary and sufficient conditions for asymptotic stability of time-delay systems independent of the length of the delay.
TL;DR: This paper deals with a formal description of ill-defined processes (fuzzy systems) by the use of fuzzy relational equations and indices of each method make it possible to express the quality of each of them.
Abstract: This paper deals with a formal description of ill-defined processes (fuzzy systems) by the use of fuzzy relational equations. It is pointed out that fuzzy relational equations form a generalized version of the difference equations widely considered in control theory. Some equivalence between these two kinds of description is presented. Basic problems of fuzzy systems e.g. identification, prediction, sensitivity and stability are shown and numerical algorithms are given. Indices of each method are introduced (especially the degree of fuzziness, the sensitivity index) which makes it possible to express the quality of each of them.
TL;DR: In this paper, the design of MRAC for achieving independent tracking and regulation objectives with a unique equilibrium point in the controller parameter space is presented, where the stability of the system and boundness of various variables do not require any positivity condition.
Abstract: The design of MRAC for achieving independent tracking and regulation objectives with a unique equilibrium point in the controller parameter space is presented. The corresponding schemes can use either an explicit reference model or an implicit reference model. The design is done from a stability point of view by extending an appropriate control configuration used for the case of known plant parameters. The result of the design is a simple control scheme using a linear constant feedforward controller and a non-linear feedback controller. The stability of the system and boundness of various variables do not require any positivity condition. The performances of the control structure in tracking and regulation are evaluated by simulations.
TL;DR: In this article, the dead-beat control of linear periodic discrete-time systems subject to periodic disturbances is studied and necessary and sufficient conditions are given for the existence of a linear periodic controller such that both output deadbeat control under periodic disturbances, and state dead-beast control under no disturbance, are performed.
Abstract: In this paper the dead-beat control of linear periodic discrete-time systems subject to periodic disturbances is studied. Necessary and sufficient conditions are given for the existence of a linear periodic controller such that both output dead-beat control under periodic disturbances, and state dead-beat control under no disturbance, are performed. Moreover synthesis procedures of the controller, as well as of state dead-beat observers, are given, which can be applied also to a class of bilinear systems.
TL;DR: In this paper, a generalized minimum-variance controller is proposed to stabilize non-minimum phase plants in a self-tuning control law, which results in an unstable closed-loop system in this situation.
Abstract: A now minimum-variance type of control law is derived for use in self-tuning control schemes where the plant is non-minimum phase. The controller has some of the features of the minimum-variance controller and is related to the generalized or λ minimum-variance controller which includes control weighting terms. The controller has the advantage that when the control-weighting scalar tends to zero the system is assured of being asymptotically stable. The generalized minimum-variance controller, employed in the self-tuning control law, results in an unstable closed-loop system in this situation. The controller may also be used to stabilize plants which are both unstable and non-minimum phase (the closed-loop system corresponding to the generalized minimum variance controller may be unstable for all values of the weighting scalar in this situation)
TL;DR: In this paper, a solution of the disturbance decoupling problem for non-linear systems is given, where the main difference between this and related works in the field is the construction of a now state-dependent basis for the inputs.
Abstract: The paper gives a solution of the disturbance decoupling problem for non-linear systems. The main difference between this and related works in the field is the construction of a now state-dependent basis for the inputs.
TL;DR: In this paper, the least square parameter estimator is combined with the minimum variance regulator for the estimated model to produce a bilinear self-tuning regulator ''BLSTR'' and it is found that though the estimation may be biased, under certain assumptions, the BLSTR will converge to minimum variance control law.
Abstract: Discrete single-input single-output bilinear systems with constant parameters are considered. First, the minimum variance regulator for known parameters is determined. Then the least squares parameter estimation method is applied and is seen to have certain desirable properties. Finally, the least squares parameter estimator is combined with the minimum variance regulator for the estimated model to produce a bilinear self-tuning regulator «BLSTR’. It is found that though the estimation may be biased, under certain assumptions, the BLSTR will converge to the minimum variance control law.
TL;DR: In this paper, a realization procedure is presented that brings a polynomial system matrix of a non-proper multivariable system to generalized state-space form, such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained.
Abstract: This paper contains three main results. Firstly, a realization procedure is presented that brings a polynomial system matrix of a non-proper multivariable system to generalized state-space form, such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained. Secondly, new definitions are proposed for poles, zeros and decoupling zeros at infinity of a general polynomial system matrix. As a third result, a theorem of Rosenbrock (1974 e) on the redundancy of LCR multiports is generalized to include the decoupling zeros at infinity.
TL;DR: In this article, the problem of optimal design of experiments for identification of distributed systems described by a linear, parabolic partial differential equation is considered, and conditions for optimality of the experiment design are derived.
Abstract: The problem of optimal design of experiments for identification of distributed systems described by a linear, parabolic partial differential equation is considered. Conditions of an experiment, which consists of the spectral density of a stochastic input signal and a probability measure corresponding to positions of sensors, are chosen such as to maximize the accuracy of a finite number of the system's eigenvalue estimates. Conditions for optimality of the experiment design are derived. In particular, it is shown that the optimal input consists of a finite number sinusoids and optimal positions of the sensors can be found analytically in some eases, Application of the results is illustrated in case of a vibrating system.
TL;DR: In this article, a quantitative synthesis theory based on Schauder's fixed point theorem for uncertain multiple input-output feedback systems is presented, by means of a detailed 3×3 problem with large plant uncertainty, including open-loop instability and some non-minimum-phase plant elements.
Abstract: A recent paper presented a quantitative synthesis theory based on Schauder's fixed point theorem, for uncertain multiple input-output feedback systems. This paper is devoted to practical design execution, by means of a detailed 3×3 problem with large plant uncertainty, including open-loop instability and some non-minimum-phase plant elements. The outstanding features of the theory are : 1. The quantitative nature of the assigned tolerances on the nine closed-loop system response functions. In this problem four are specified basically non-interacting and the other five interacting. 2, The design problem is translated into separate quantitative single-loop problems, each with plant uncertainty, external disturbances and closed-loop tolerances derived from the original problem. The solutions for these single-loop problems are guaranteed to solve the original multivariable problem, whose system characteristic equation need never be examined. 3. There is developed a systematic means of (a) optimization of the ...
TL;DR: In this article, an algorithm is presented for obtaining a minimal-order state-space realization of a strictly proper rational function matrix, which can also be used to compute the observability indices of any given state space system.
Abstract: In this paper, an algorithm is presented for obtaining a minimal-order state-space realization of a strictly proper rational function matrix. The algorithm can also be used to compute the observability indices of any given state-space system. A controllable but unobservable state-space realization of the given rational function matrix is first obtained, by inspection. The algorithm then performs a sequence of simple coordinate transformations on the state vector of the system. The coordinate transformation matrices are orthogonal and are easily constructed from the system matrices. Each coordinate transformation operates on submatrices (of the state-space system matrices) of lower dimension than the preceding one. The sequence of coordinate transformations terminates after at most v 1 + 1 transformations, where v 1, is the maximal observability index of the state-space model. The observability indices of the system are also determined at this time. The transformed system matrices are obtained in a form wh...
TL;DR: In this paper, a method for model reduction is proposed which minimizes the equation error and yields a stationary exact model, where the desired state variables or their physically meaningful linear combinations are reproduced.
Abstract: A method for model reduction is proposed which minimizes the equation error and yields a stationary exact model. With this model, the desired state variables, or their physically meaningful linear combinations, are reproduced. This approach to the reduction problem leads to linear equations; thus no search routines are needed. Moreover, a time-varying weighting matrix is introduced, so that even unstable linear time-invariant models can be reduced. Especially, the characteristics of very low order reduced models depend highly on the weighting matrix. The reduction for a distillation column of the 45th-order is carried out.
TL;DR: In this article, a generalized minimum variance strategy is proposed for self-tuning control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters.
Abstract: The control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters is discussed. A strategy using a generalized cost-function is first presented. A multivariable self-tuning regulator based on this generalized minimum variance strategy is then proposed. It uses a recursive multiple least squares estimator and a linear matrix controller obtained directly from the estimates. The algorithm can be considered as a multivariable generalization of Clarke's self-tuning controller.
TL;DR: In this paper, an algorithm to perform the assignment by output feedback of an almost arbitrary set of eigenvalues for a class of linear time-invariant multivariable control systems with direct feedthrough is presented.
Abstract: An algorithm to perform the assignment by output feedback of an almost arbitrary set of eigenvalues for a class of linear time-invariant multivariable control systems with direct feedthrough is presented. This algorithm is a development of an earlier one proposed by the author for systems without feedthrough. Only the ordinary procedures of linear algebra are required for its implementation and the* proof given of the feasibility and validity of the algorithm includes a proof of the existence of the appropriate control law.
TL;DR: In this paper, the authors defined the transmission zeros as the limit points of the spectrum as the feedback gain increases to infinity, and a simple criterion which characterizes the transmission zero, different from the system operators spectrum, is found.
Abstract: The transmission zeros, for a class of distributed parameter systems, are defined as the limit points of the spectrum as the feedback gain increases to infinity. A simple criterion, which characterizes the transmission zeros, different from the system operators spectrum, is found. The case, when the transmission zeros belong to the spectrum, is also discussed. The presented theory is clarified with an example.
TL;DR: In this paper, the authors introduced a measure for the degree of dependence of the state variables on the high-order dominant eigenvalues, which can be used to find an appropriate decomposition yielding a good low-order model, and also to get an indication of the order of the reduced model.
Abstract: Singular perturbation techniques for order reduction are based on decomposing the high-order system into two parts. Approximation of the high-order system dynamics by the low-order model is mainly dependent on this partition. This paper introduces a measure for the degree of dependence of the state variables on the high-order dominant eigenvalues. By means of this measure it is not only possible to find an appropriate decomposition yielding a good low-order model, but also to get an indication of the order of the reduced model. Two illustrative examples demonstrate the main results.
TL;DR: In this paper, a general non-linear exponential observer for non-linearly perturbed nonlinear systems is presented, which is done by using the nonlinear variation of constants formula.
Abstract: A general non-linear exponential observer is presented for non-linearly perturbed nonlinear systems. This is done by using the non-linear variation of constants formula.