Showing papers in "International Journal of Control in 1975"
TL;DR: In this paper, a non-linear first-order reset element (FORE) is used to reduce the feedback loop transmission bandwidth of linear, minimum-phase plants with large parameter uncertainty.
Abstract: Feedback systems containing linear, minimum-phase plants with large parameter uncertainty may be designed to achieve specified performance tolerances over the entire range of parameter uncertainty. The principal ‘cost of feedback’ is in the feedback loop bandwidth, which is generally much larger than that of the system as a whole. This makes the system very sensitive to sensor noise and high-frequency parasitics. It is shown how a non-linear ‘first-order reset element’ (FORE) may be used to drastically decrease the feedback loop transmission bandwidth. One is logically led to FORE by simple, linear feedback frequency response concepts. The paper assumes that the primary design problem is to satisfy quantitative response tolerances to command inputs. However, disturbances at the plant are not neglected, but the specification on such disturbances is in the damping of the step response. An important feature of the non-linear design is that the system response to command inputs is almost exactly that of a lin...
276 citations
TL;DR: In this paper, the optimal control for a discrete-time linear system with quadratic criterion functional is derived for the case where the system parameters are subject to a discretetime, discrete-state Markov process.
Abstract: The optimal control for a discrete-time linear system with quadratic criterion functional is derived for the case where the system parameters are subject to a discrete-time, discrete-state Markov process. Utilization of the results is demonstrated in a numerical example using Samuelson's multiplier-accelerator macroeconomic model.
275 citations
TL;DR: In this paper, a new method of reduction is introduced, based on the Routh stability criterion and the Pade approximation technique, which may be applied to the reduction of single-input/single-output and multivariable systems.
Abstract: A new method of reduction is introduced, based on the Routh stability criterion and the Pade approximation technique The method may be applied to the reduction of single-input/single-output and multivariable systems The reduced-order models will always be stable if the high-order system is stable
250 citations
TL;DR: A new method of reduction in order of linear time-invariant systems is introduced that combines the desirable features of the time-moments and the modal methods of reduction based on the concept of Pade approximation about more than one point.
Abstract: A new method of reduction in order of linear time-invariant systems is introduced. It combines the desirable features of the time-moments and the modal methods of reduction. The methods is based on the concept of Pade approximation about more than one point. The reduced model derived by this method, retains the dominant modes (or any desirable modes) and fits the initial time-moments of the system The method is extended to the problem of reducing a high-order multivariable system described by its matrix transfer function. Several illustrative examples are discussed throughout the paper.
218 citations
TL;DR: The main part of this paper will cover stochastic adaptive controllers and the problem of dual control is given particular attention.
Abstract: There is a vast literature about adaptive (self-organizing, self-optimizing) control systems. The aim of this paper is to point out some of the main ideas. Since there exists good survey papers about several of the classes of adaptive controllers the main part of this paper will concentrate on recent developments. The paper will cover stochastic adaptive controllers. The problem of dual control is given particular attention.
188 citations
TL;DR: A sufficient condition for observability of non-linear time-variable systems is introduced which serves as a basis for the analysis of the structure of the decoupled closed-loop system.
Abstract: For non-linear time-variable systems a synthesis procedure for decoupling via state feedback is given. A sufficient condition for observability of non-linear time-variable systems is introduced which serves as a basis for the analysis of the structure of the decoupled closed-loop system. In this context a sufficient condition for the observability of a decoupled non-linear time-variable system is derived.
181 citations
TL;DR: In this paper, the collocation method meshed with non-linear programming techniques provides an efficient strategy for the numerical solution of optimal control problems, and good accuracy can be obtained for the state and the control trajectories as well as for the value of the objective function.
Abstract: The collocation method meshed with non-linear programming techniques provides an efficient strategy for the numerical solution of optimal control problems. Good accuracy can be obtained for the state and the control trajectories as well as for the value of the objective function. In addition, the control strategy can be quite flexible in form. However, it is necessary to select the appropriate number of collocation points and number of parameters in the approximating functions with care.
137 citations
TL;DR: In this paper, the problem of identifiability of processes using measurements obtained under closed loop operation is treated, where the feedback is time invariant, linear and noise free, and no external input signal is injected.
Abstract: The problem of identifiability of processes using measurements obtained under closed loop operation is treated. Single input-single output systems are considered. It is assumed that the feedback is time invariant, linear and noise free. It is also assumed that no external input signal is injected. Conditions, which are simultaneously necessary and sufficient for identifiability are derived. The results are illustrated by a few numerical examples.
124 citations
TL;DR: In this paper, it was shown that the essential mechanism employed by such a compensator is the multivariable analogue of pole-zero cancellation: the compensator supplies transmission zeros to cancel the unstable poles of the disturbance and reference signals.
Abstract: The problem is considered of designing compensators to regulate linear multivariable systems. It is shown that the essential mechanism employed by such a compensator is the multivariable analogue of pole-zero cancellation: the compensator supplies transmission zeros to cancel the unstable poles of the disturbance and reference signals. If the compensator is additionally required to function in the presence of small variations in system parameters then it must supply transmission zeros in greater multiplicity. Finally it is shown that the transmission zeros are generated by an ‘ internal model ’, incorporated in the compensator, of the dynamics of the disturbance and reference signals.
102 citations
TL;DR: In this paper, the problem of least-squares estimation of closed-loop systems is examined and the conditions for uniqueness and consistency of the estimates of the forward-path transfer function are determined.
Abstract: The problem of least-squares estimation of closed-loop systems is examined. The particular configuration considered is the single input-single output discrete linear system controlled by a linear, stationary feedback regulator. Results are obtained which determine the conditions for uniqueness and consistency of the least-squares estimates of the forward-path transfer function. In particular, it is shown that if two orthogonal unobservable noise sources are present, one in each path, the system is uniquely identifiable. When the feedback path is noise-free the uniqueness of the estimates is dependent upon the order of the regulator regression polynomials. The consistency of the estimates in the case of a white forward-path disturbance is assured provided that there is at least one delay term in the loop.
94 citations
TL;DR: In this paper, the problem of observing a plant state x(t) in the presence of unknown, inaccessible inputs which are acting on the plant is investigated and compared with results recently published by Meditch and Hostetter.
Abstract: Many practical applications of modern control theory lead to the problem of observing a plant state x(t) in the presence of unknown, inaccessible inputs which are acting on the plant. This paper traces some early works on that problem and compares those earlier results with results recently published in this Journal by Meditch and Hostetter (1974).
TL;DR: The problem of optimally locating a given number of Bensors for observing a general linear distributed parameter system is considered, and a computational algorithm is developed for determining the optimum set of measurement locations.
Abstract: The problem of optimally locating a given number of Bensors for observing a general linear distributed parameter system is considered. Measurements at the sensors are assumed to be available continuously in time, and the design criterion is minimization of a scalar measure of the covariance of the estimate error in the optimal linear filter. Necessary conditions for optimality are derived based on the formulation of a distributed parameter matrix minimum principle. A computational algorithm is developed for determining the optimum set of measurement locations. The algorithm is applied to the problem of optimally locating temperature sensors in a solid undergoing transient heat conduction.
TL;DR: This paper is concerned with the determination of suboptimal feedback laws for the linear systems with quadratic performance criteria and the Walsh functions approach to the solution of piecewise constant gains of optimal control is concentrated.
Abstract: This paper is concerned with the determination of suboptimal feedback laws for the linear systems with quadratic performance criteria. The time-varying gains are approximated by the piecewise constant gains which are naturally determined by using Walsh functions. An increase of the number of intervals of Walsh functions enables us to approximate the true optimal control more closely ; and a decrease of the number of intervals makes the implementation easier. Therefore the proposed method is simple in theory and flexible in practice. The beginning part of the paper, being tutorial in nature, is on Walsh functions, the middle part developes an operational method for solving state equations and the final part is concentrated on the Walsh functions approach to the solution of piecewise constant gains of optimal control.
TL;DR: The minimum-variance state-estimator for a class of linear distributed parameter systems with both process and measurement disturbances, is derived and a new algorithm is presented for the optimal simultaneous spatial allocation of sensors.
Abstract: The minimum-variance state-estimator for a class of linear distributed parameter systems with both process and measurement disturbances, is derived A new algorithm is presented for the optimal simultaneous spatial allocation of sensors The algorithm minimizes recursively the spatial integral of the covariance matrix of the error in the state estimates For time-invariant systems the algorithm leads to the minimization of the spatial integral of the steady-state error covariance matrix The influence of the system disturbances and measurement noise on these locations is discussed An illustrative example is given to demonstrate the numerical performance of the algorithm
TL;DR: In this paper, singular perturbation methods are used to demonstrate that the transfer function matrices of multivariable linear systems containing small parasitic elements have a distinctive structure which can be exploited in the design of controllers for this class by the application of frequency-domain methods.
Abstract: Singular perturbation methods are used to demonstrate that the transfer function matrices of multivariable linear systems containing small ‘parasitic’ elements have a distinctive structure which can be exploited in the design of controllers fur systems of this class by the application of frequency-domain methods.
TL;DR: In this paper, a method based upon the use of the Brunovsky canonical form (Brunovsky 1966) is presented for the design of controllers and full-order observers for a class of linear multivariable discrete-time plants with inaccessible state vectors.
Abstract: In this paper a method based upon the use of the Brunovsky canonical form (Brunovsky 1966) is presented for the design of controllers and full-order observers for a class of linear multivariable discrete-time plants with inaccessible state vectors
TL;DR: In this article, the influence of initial data on dynamic behaviour and stability properties of non-stationary systems is analyzed and new stability properties are discovered and defined as well as corresponding stability domains.
Abstract: The paper presents a refined analysis of the influence of initial data on dynamic behaviour and stability properties of non-stationary systems. As a result, new stability properties are discovered and defined as well as the corresponding stability domains. Furthermore, general necessary conditions are established for asymptotic stability of the unperturbed motion of these systems, the instantaneous asymptotic stability domain of which can be either time-invariant or time-varying and then possibly asymptotically contractive. It is shown that the classical Lyapunov stability conditions cannot be applied to the stability test as soon as the system instantaneous domain of asymptotic stability is asymptotically contractive. In order to investigate asymptotic stability of the motion in such cases novel criteria are established. Under the criteria the Eulerian derivative of a system Lyapunov function may be non-positive only and still guarantee asymptotic stability of the unperturbed motion The results ...
TL;DR: In this paper, a non-Lyapunov stability analysis of time-dependent non-linear large-scale systems of arbitrary order and structure is presented, which provides algebraic conditions for various types of practical and finite-time stability of the systems and provides information about trajectory bounds.
Abstract: Non-Lyapunov stability analysis of time-dependent non-linear large-scale systems of arbitrary order and structure presented in the paper develops algebraic conditions for various types of practical and finite-time stability of the systems and provides information about trajectory bounds. The stability properties are studied on products of time-varying sets. The conditions guarantee the corresponding stability property of the overall system to be implied by practical stability or finite-time stability of all subsystems. Moreover, under the conditions the overall system possesses the smiw settling time as its subsystems. Application of the aggregation-decomposition approach to the stability analysis reduces the dimension of the overall system aggregate matrix to the number of subsystems. Examples are worked out to illustrate results.
TL;DR: In this article, the structural properties of the decentralized time-invariant linear multivariable systems in connection with the problems of disturbance localization and output decomposition are investigated, and necessary and sufficient conditions of problem solvability are derived.
Abstract: The purpose of this paper is to investigate the structural properties of the decentralized time-invariant linear multivariable systems in connection with the problems of disturbance localization and output decomposition. In the first, the necessary and sufficient conditions under which the disturbance localization is possible, by applying local state feedback laws, are given. The conditions are also stated in both cases of ordinary (centralized) systems with imperfect state measurement and of those with output measurement. In the second, the problem of output decomposition in decentralized linear multivariable systems is proposed, and the necessary and sufficient conditions of problem solvability are derived.
TL;DR: In this paper, the authors explore the problem of maximizing the size of a region of asymptotic stability (RAS) over a class of Lyapunov functions (LF) in order to estimate the domain of attraction of a continuous or discontinuous (relay) system.
Abstract: This paper explores the problem of maximizing the size of a region of asymptotic stability (RAS) over a class of Lyapunov functions (LF) in order to estimate the domain of attraction of a continuous or discontinuous (relay) system. Analytic and numerical evidence shows that a subclass of LF may exist with multiple-tangency for the RAS problem, and can cause some serious convergence problems. Several systems are considered with two classes of LF for continuous and one class for relay systems.
TL;DR: In this article, a model reference adaptive controller for multivariable plants is designed using only input and output signals rather than the complete state vector, based on Liapunov's direct method, and the Meyer-Kalman-Yacubovich lemma.
Abstract: Model reference adaptive controllers for multivariable plants are designed using only input and output signals rather than the complete state vector. The design is based on Liapunov's direct method, and the Meyer-Kalman-Yacubovich lemma. State variable filters are employed to avoid differentiating output signals. Augmented error signals are used in deriving stable adaptive control laws which assure that the normally used response error signals approach zero asymptotically.
TL;DR: In this paper, sufficient conditions for the stochastic observability and controllability of non-linear systems are presented, and the mutual relation between observability with respect to controllabilities is discussed via sufficient conditions obtained above.
Abstract: The purpose of this paper is to present sufficient conditions for the stochastic observability and controllability of non-linear systems. First, the stochastic observability is defined and several theorems which give sufficient conditions of the stochastic observability are developed for an important class of non-linear systems. Secondly, the definition of stochastic controllability is also presented. By using the Lyapunov-like approach, sufficient conditions of the stochastic controllability are also shown. Finally, the mutual relation between the stochastic observability and controllability is discussed via sufficient conditions obtained above. For the purpose of supporting the theoretical aspects developed here, results of simulation studies are also demonstrated.
TL;DR: In this paper, an improved version of a previously published model for a drum boiler is presented, based on an improved model of the original drum boiler, which is used in this paper.
Abstract: This note gives an improved version of a previously published model for a drum boiler.
TL;DR: In this paper, a frequency domain approach is used for the design of decoupled control systems and necessary and sufficient conditions for the existence of proportional output feedback laws as well as a constructive procedure for finding these feedback laws are given.
Abstract: In this paper a frequency domain approach is used for the design of decoupled control systems. Necessary and sufficient conditions for the existence of proportional output feedback laws as well as a constructive procedure for finding these feedback laws are given. A simple relationship between the overall system transfer functions and the output feedback laws is derived.
TL;DR: In this paper, a new design procedure is presented for assigning closed-loop eigenvalues of multi-variable, linear systems using output feedback control, and the number of poles which can be assigned to arbitrary, distinct locations is given.
Abstract: A new design procedure is presented for assigning closed-loop eigenvalues of multi-variable, linear systems using output feedback control. Subject to certain mild restrictions, the number of poles which can be assigned to arbitrary, distinct locations is mill [m + r − 1, n], where m, r and n are the dimensions of the output, control and state vectors, respectively. The design procedure provides an extension of the results of Davison and Chatterjee (1971) and Jameson (1970) but allows a significantly larger number of eigenvalues to be assigned. The simplicity of the design procedure is demonstrated by a numerical example.
TL;DR: A survey of the early developments in the subject through to the most recent work of Jacobson and others in the establishment of necessary, sufficient, and necessary and sufficient conditions for optimality of singular extremals can be found in this article.
Abstract: Singular controls have appeared rather frequently in dynamic optimization problems during the last two decades. Although special methods have been effective in analysing these singular problems, it is only recently that a unifying theory has been developed. This survey paper traces the early developments in the subject through to the most recent work of Jacobson and others in the establishment of necessary, sufficient, and necessary and sufficient conditions for optimality of singular extremals.
TL;DR: An engineering solution to the problem of approximating a high-order linear system by a low-order model is suggested, which consists in formulating a quadratic error functional as a basic tool for the construction of a physically transparent and practically meaningful approximation criterion.
Abstract: An engineering solution to the problem of approximating a high-order linear system by a low-order model is suggested, which consists in formulating a quadratic error functional as a basic tool for the construction of a physically transparent and practically meaningful approximation criterion. For various different modes of operation analytical expressions for the evaluation of the functional as well as the gradients with respect to the unknown model parameters are given, which allows known gradient techniques to be applied for finding the optimal model parameters. In addition a representation for a general multivariate model, using only the minimal number of unknown parameters, is given.
TL;DR: In this article, the adaptive relay, control of single-input second-order systems is considered, where the controller dispenses with a learning (or identification) phase and does not organize itself through adaptive correction, but identifies a certain curve in the state space.
Abstract: The adaptive relay, control of single-input second-order systems is considered. The plant parameters are assumed constant, but unknown. The controller dispenses with a learning (or identification) phase and does not organize itself through adaptive correction, but identifies a certain curve in the state space. This curve is associated with sliding motion. The strategy is analysed for the double-integrator plant. The identical controller can be applied to other second-order plants. The system response is found to be close to the time-optimal response.
TL;DR: An iterative algorithm based on linear programming for solving the minimum-time minimum-effort discrete control problem for linear time-invariant systems is presented and some interesting properties of the iterative linear programming algorithm are shown.
Abstract: An iterative algorithm based on linear programming for solving the minimum-time minimum-effort discrete control problem for linear time-invariant systems is presented. The algorithm is based on transforming the minimum-effort problem to an equivalent linear programming one. Some interesting properties of the iterative linear programming algorithm are shown which result in reducing the computational time and storage memory required. Numerical examples are provided to indicate the efficiency of the proposed method.
TL;DR: In this article, the Luenberger observer is used for the state estimator of linear time-invariant control systems, but it cannot be applied directly to the plant which has varying parameters.
Abstract: The Luenberger observer is frequently used for the state estimator of linear time-invariant control systems However, it cannot be applied directly to the plant which has varying parameters This paper provides an observer for this problem whose structure is not affected by the varying parameters of the plant The results of this paper give the existence condition and the stability condition of such an observer and provide a direct design procedure The extension of this idea to the design of an unknown input observer is also presented