Showing papers in "IEEE Transactions on Applications and Industry in 1964"
TL;DR: A general and unique approach to the analysis and synthesis of control systems in the parameter plane is presented which may be advantageously applied to the design of linear continuous systems, sampled-data systems, nonlinear systems, and systems with distributed parameters.
Abstract: A general and unique approach to the analysis and synthesis of control systems in the parameter plane is presented which may be advantageously applied to the design of linear continuous systems, sampled-data systems, nonlinear systems, and systems with distributed parameters This paper is concerned with the application of the method to linear continuous systems As a simple and rapid procedure for factoring characteristic polynomials in the parameter plane, the proposed method permits the designer to maintain control over salient characteristics of both transient and frequency responses The introduction of the Chebyshev functions greatly facilitates the procedure and makes it suitable for simulation on either analog or digital computers In the design procedure, all graphical and analytical operations are performed in the real domain
65 citations
TL;DR: In this paper, an extension of the Lur'e stability function to a class of discrete-time systems which may contain saturation-type nonlinear elements is presented which demonstrate the improved stability inequalities available from this function.
Abstract: This paper presents an extension of the Lur'e stability function to a class of discrete-time systems which may contain saturation-type nonlinear elements. Examples are presented which demonstrate the improved stability inequalities available from this function.
37 citations
TL;DR: This work has shown that when the state of a control system is represented as a pattern, learning to make the control decisions actually becomes the same as learning to classify the patterns.
Abstract: Adaptive or self-optimizing systems utilize feedback principles to achieve automatic performance optimization. These principles have been applied to both control systems and adaptive logic structures. The Adaline (adaptive linear threshold element) is essentially the same as an adaptive sampled-data system with quantized input and output signals. A digital controller made of adaptive neurons comprises a pattern-recognizing control system. When the state of a control system is represented as a pattern, learning to make the control decisions actually becomes the same as learning to classify the patterns.
36 citations
32 citations
TL;DR: The proposed analysis procedure is based upon the describing functions defined for both pure and damped sinusoidal signals and permits the designer to obtain information about the effects on absolute and relative stability of adjusting system parameters or varying the initial signal level.
Abstract: The stability and self-excited oscillations of nonlinear feedback control systems are investigated in the parameter plane with respect to both the system parameters and the initial conditions. The proposed analysis procedure is based upon the describing functions defined for both pure and damped sinusoidal signals and, therefore, permits the designer to obtain information about the effects on absolute and relative stability of adjusting system parameters or varying the initial signal level. Control systems with two non-linearities and with amplitude- and frequency-dependent describing functions may be designed advantageously. The method is particularly useful when the describing function appears as a variable pole of relevant transfer functions. The procedure requires no block-diagram manipulations, and it is suitable for the application of computer techniques.
27 citations
25 citations
TL;DR: This paper presents parameter-plane analysis and synthesis of sampled-data linear control systems and the introduction of the Chebyshev functions makes the procedure ideal for simulation on a digital computer.
Abstract: This paper presents parameter-plane analysis and synthesis of sampled-data linear control systems. Just as in the continuous system case,1 the proposed method permits the designer to obtain readily the information about the effects on both the absolute and relative stability of adjusting system parameters. Since the characteristic equations in the parameter plane can be factored in a straightforward manner for various values of system parameters, the salient characteristics of system response may be advantageously designed by the presented procedure. The introduction of the Chebyshev functions makes the procedure ideal for simulation on a digital computer. Also, all analytical and graphical operations are performed in the real domain.
25 citations
TL;DR: The generalization provides a general graphical method for synthesis of linear systems, which can be applied whenever it is required to examine how the zeros of an algebraic equation are affected by a change in its coefficients.
Abstract: A main limitation of Mitrovi's graphical method for analysis and synthesis of linear control systems lies in the fact that only the last two coefficients of the characteristic equation are considered as variables. This paper presents a generalization of the mentioned method, by which it is possible to designate that arbitrary pairs of coefficients be considered variable. The generalization provides a general graphical method for synthesis of linear systems, which can be applied whenever it is required to examine how the zeros of an algebraic equation are affected by a change in its coefficients. The generalized method achieves the same degree of simplicity as does the method in its primary form.
24 citations
TL;DR: The design of an adaptive controller is described which, in conjuction with a numerical control system, extends the process measurement to the actual tool-work interface and adjusts the process input parameters so as to optimize cutting performance.
Abstract: As presently practiced, metal cutting is a relatively inefficient process. The equations relating input parameters and the finished product are mainly empirical, and they are applicable only over limited ranges and conditions. A particularly significant problem is the machining of recently developed high-strength materials for the aerospace industry. Present numerical control systems cannot achieve optimum machining because the feedback loops are closed only around the dimensional position of the tool and workpiece. This paper describes the design of an adaptive controller which, in conjuction with a numerical control system, extends the process measurement to the actual tool-work interface and adjusts the process input parameters so as to optimize cutting performance. The system can be programmed to optimize a selected performance criterion such as cost while applying constraints on other factors such as surface finish and machine horsepower.
21 citations
TL;DR: The objective of this paper is to introduce the formulation of a control problem, called the ``basic control problem,'' then to derive from it a concept of adaptation, and to show how self-organizing subsystems can be used in the design stage or in on-line operation to solve the basic control problem.
Abstract: The objective of this paper is first to introduce the formulation of a control problem, called the ``basic control problem,'' then to derive from it a concept of adaptation. Furthermore, the paper shows how self-organizing subsystems can be used in the design stage or in on-line operation to solve the basic control problem. The discussion is conceptual; its objective is to indicate possible new avenues for research in control and adaptation, and no attempt is made towards mathematical formalization of the proposed ideas.
18 citations
TL;DR: In this article, a set of performance limitations for a class of minimal fuel satellite attitude control where the control torque is amplitude constrained is developed. Butts et al. considered both the fixed and free terminal time problems, and derived conditions for controllability and minimal fuel controLLability using quantity of fuel and control time as parameters.
Abstract: A set of performance limitations is developed for a class of minimal fuel satellite attitude controls where the control torque is amplitude constrained. Both the fixed and free terminal time problems are considered. Conditions for controllability and minimal fuel controllability are derived using quantity of fuel and control time as parameters. The results are compared with those of a similar system where the control torques have been idealized to impulses.
TL;DR: The derivation of the estimates assumes that the power spectrum has no zeros, and is based on well-known results in the theory of autoregressive schemes, and can be easily implemented by a digital computer for use in an adaptive loop.
Abstract: This paper describes a method for identifying the parameters of a class of power spectra. In contrast to conventional methods of spectral analysis, the method assumes a particular form for the power spectrum and gives direct estimates of unknown parameters. Thus the method is faster than ordinary spectral analysis and can be easily implemented by a digital computer for use in an adaptive loop. The derivation of the estimates assumes that the power spectrum has no zeros, and is based on well-known results in the theory of autoregressive schemes. Some ways of extending the results to the case where zeros are present in the spectrum are suggested. The method can also be used as a prewhitening technique in conjunction with ordinary spectral analysis.
TL;DR: In this article, a series-saturating reactor is added to the armature circuit of a rectifier-motor system to improve the dynamic characteristics of the rectifier.
Abstract: Rectifier performance with the low-inductance counter electromotive force (emf) load of a large d-c motor may be some-what different than the more conventional performance resulting from a highly inductive load. If, at low average values, the current is not continuous but flows in pulses, both the static and the dynamic characteristics of the rectifier-motor system are affected. In the case of a main drive motor for a hot strip mill stand, mill performance may be impaired by the dynamic characteristics associated with discontinuous current flow. One means of over-coming this is the addition of a series-saturating reactor to the armature circuit.
TL;DR: The method of linear programming described here is well suited to the design of open-loop or closed-loop sampled-data control systems with deterministic inputs.
Abstract: The method of linear programming described here is well suited to the design of open-loop or closed-loop sampled-data control systems with deterministic inputs. Linear equations are written to express the errors at sampling instants in terms of the undetermined coefficients of the over-all pulse transfer function. Other linear equations are written to impose any desired limits on errors or on coefficients. A solution is found which maximizes an objective function. The design method is explained and the results of a practical example are given.
TL;DR: In this paper, the double integral plant y(t) = u(t), |u(t)|?1, the control u (t) is determined which, in the time interval [0, T], forces the state of the plant to zero, minimizes the fuel consumed, as measured by? 0 T|u (t)|dt, and results in a response time T which does not exceed a prespecified multiple of the minimum time.
Abstract: Given the double integral plant y(t)=u(t), |u(t)|?1, the control u(t) is determined which, in the time interval [0, T], forces the state of the plant to zero, minimizes the fuel consumed, as measured by ? 0 T|u(t)|dt, and results in a response time T which does not exceed a prespecified multiple of the minimum time. A design of the nonlinear controller necessary is included.
TL;DR: In this paper, intentional nonlinear passive compesation is used to stabilize dry friction nonlinearity in a system with small ramp inputs by increasing the damping by a derivative control which becomes saturated for high ramp rates.
Abstract: Systems having dry friction nonlinearity can be stabilized by introducing intentional nonlinear passive compesation. For small ramp inputs it is necessary to increase the damping by a derivative control which becomes saturated for high ramp rates. To decrease the steady-state error at high ramp rates and achieve stability, a dead zone before the integrator is used. A scheme for an input adaptive system is also presented in this paper.
TL;DR: A new phase-plane diagram represents the electric space heating-cooling process controlled by a 2-position system as well as the cycling of the controlled process, under conditions of dynamic equilibrium, by the T-T diagram.
Abstract: The simplest forms of 2-position discontinuous temperature control systems for the electric space heating-cooling process are described. Simple and complex forms of the controlled process are represented by block diagrams. It is shown that secondary feedback can compensate for a control element's nonlinearities. The secondary feedback conditions for optimum compensation, and the effects of overcompensation, are discussed. An actuating signal equation is derived which represents the control system. Description is given of a new technique for predicting the behavior of a proposed control system by displaying the actuating signal equation in three dimensions. The need for overriding commands is outlined, and their introduction into the system via the primary feedback loop is explained. A new overriding command system, for room-vacancy and night-shutdown events, is introduced. Description is given of a new analog for the discontinuously controlled electric space heating-cooling process. The analog is simple to handle, but represents the process with a degree of accuracy sufficient for research and development purposes. From the analog, a control equation for the discontinuously controlled process is formulated. Mention is made of the desirability of basing the reference input on information other than the command.
TL;DR: In this paper, a new criterion is presented which is applicable to a broad class of linear systems defined by linear n-dimensional ordinary vector-matrix differential equations; for this criterion only the coefficient matrices of the differential equation need to be known.
Abstract: A linear system is completely controllable if for any initial state a control can be found to take the state of the system to the origin of the state space. Present criteria for testing linear systems for controllability require knowing the weighting function matrix of the linear system. In this paper a new criterion is presented which is applicable to a broad class of linear systems defined by linear n-dimensional ordinary vector-matrix differential equations; for this criterion only the coefficient matrices of the differential equation need to be known.
IBM1
TL;DR: Quasi-continuous temperature control is needed when electric space heating is applied to temperature-dependent processes, and quasi-continuously systems have economic and operating advantages over many continuous systems.
Abstract: Quasi-continuous temperature control is needed when electric space heating is applied to temperature-dependent processes. In such applications, multiposition systems cannot supply the accurate control often required, and quasi-continuous systems have economic and operating advantages over many continuous systems. The reference input of a quasi-continuous system can be a trimmed, optimized, open-loop command derived from the incoming and outgoing quality levels of the process. Feedforward correction for process lag, and overriding commands, can easily be incorporated into such systems. Quasi-continuous characteristics contain a number of discontinuities. Time can be saved by representing these characteristics by a continuous profile. A multitude of intermediate values of manipulated variable can be obtained by new and inexpensive methods. When the heating load must remain intact, phase-discontinuity methods can be used which approximate level-discontinuity control. For fast response processes, phase-controlled SCR's (silicon-controlled rectifiers) can be used. The T-T (temperature-time) diagrams have limitations as representations of quasi-continuously controlled processes. Time domain information can be obtained from the phase plane where quasi-continuous performance resembles a spiral. Nonlinearities can be advantageously introduced into quasi-continuous profiles. Performance is improved by derivative feedback. It is possible to predict quasi-continuous system behavior by means of a 3-dimensional actuating-signal display.
TL;DR: In this article, it is shown that the control u =?x(t)/?x (t)? drives any initial state to zero in such a manner that the response time, the consumed fuel, and a linear combination of time and control energy are minnimized.
Abstract: Given the system x?(t)=A(t)x(t)+u(t),where A(t)=?A?(t) and ?u(t)??1, it will be shown that the control u=?x(t)/?x(t)? drives any initial state to zero in such a manner that the response time, the consumed fuel, and a linear combination of time and control energy are minnimized. The theory is applied to the optimum angular velocity cotrol of a tumbling space body.
TL;DR: Three different methods are developed for calculating various moments of the system variables of a linear system, represented by matrix equation x = Ax, which are especially useful for high-order systems.
Abstract: In this paper, three different methods are developed for calculating various moments of the system variables of a linear system, represented by matrix equation x = Ax. A transformation Q is developed which transforms the system matrix A into a special matrix R. Liapunov function V is considered as V = x t Q t Qx and it facilitates evaluation of various moments ? 0 ? tmx2dt These methods are especially useful for high-order systems. Examples are included to explain each method.
TL;DR: The gap between nonlinear control theory and the discontinuous control of electric space heating and cooling is outlined, and the choice of the temperature transducer for use as a primary feedback element is examined.
Abstract: The historical background of electric space heating and cooling, and automatic temperature control, is summarized, and developments since world war II outlined. The advantages of discontinuous control systems are traced from recent investigations into the control of temperature in electric space heating, and the gap between nonlinear control theory and the discontinuous control of electric space heating and cooling is outlined. The representation of the controlled process by block diagram is discussed in detail. The choice of the temperature transducer for use as a primary feedback element is examined. The suitability of nonlinear elements for line voltage control is discussed. The snap-acting switch is treated as a discontinuous control element. A control equation is quoted combining the primary feedback element, the control element, and the process. The action of this control equation is illustrated.
Journal Article•
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TL;DR: An attempt is made here to lay foundations for a control theory based on a plan of attack utilized by human organizations for centuries; namely, notions of division of labor and co-ordination.
Abstract: The optimal control of complex multivariable systems poses a great many problems for the control engineer. Among the most difficult of these is the computational problem. An attempt is made here to lay foundations for a control theory based on a plan of attack utilized by human organizations for centuries; namely, notions of division of labor and co-ordination. The usefulness of these concepts is examined via a number of mathematical models.
TL;DR: The controlled system has the transfer function G(s)=K/(s-λ1T) and the control input is u(t), |u(t)|≤1, and the out put is y(t).
Abstract: The controlled system has the transfer function G(s)=K/(s-? 1 )(s-? 2 ). The control input is u(t), |u(t)|?1, and the out put is y 1 (t). the control which forces any initial state y 1 (0), ? 1 (0) to the terminal state y 1 (T), ? 1 ,(T), such that -K/? 1 ? 2 ?y 1 (T)?K/? 1 ? 2 , ? 1 (T)=0, and which minimizes the fuel, F(T)=? 0 T |u(t)|dt is determined. The phase plane is divided into three sets G - , G + , and G 0 ; if the state is in G - then u(t)=?1 is used; if the state is in G + , then u(t)=+1 is used; if the state is in G 0 , then u(t)=0 is used.
TL;DR: In this article, a new method for analyzing and predicting the behavior of a multiposition temperature control system by displaying its actuating signal equation in three dimensions is introduced, and a new display method is outlined for simultaneously portraying the phase-plane and time-domain performance of such processes.
Abstract: Three new schemes for 3-position temperature control are described. A new method is introduced for analyzing and predicting the behavior of a multiposition temperature control system by displaying its actuating signal equation in three dimensions. Two new methods of predicting or analyzing the behavior, in the phase plane and time domain, of the multiposition temperature-controlled electric space heating process are described. Expressions are derived for the evaluation of the important performances indexes and figures of merit of such multiposition controlled processes. A new display method is outlined for simultaneously portraying the phase-plane and time-domain performance of such processes. Cycling characteristic diagrams are shown for 3-position controlled electric space heating processes with two alternative magnitudes of the intermediate value of manipulated variable. New 4-position temperature control schemes are described; and their cycling characteristic is shown for the control of the electric space heating processes. The application of these new techniques to other fields of control, and their limitations, are mentioned.
TL;DR: In this article, the transfer function is represented by a gain constant and ratio of two rational polynomials of s, where s is Laplace variable, and the coefficients vary in an unknown fashion but rather slowly.
Abstract: One of the most important problems facing a control engineer today is to find a simple and satisfactory method for determining the transfer function of an unknown time-varying control system. In this paper the transfer function is represented by a gain constant and ratio of two rational polynomials of s, where s is Laplace variable. The gain constant and the coefficients in the polynomials vary in an unknown fashion but rather slowly. A method is developed whereby as many independent signals are developed as the number of unknown coefficients. These signals are used to determine the unknown coefficients in a straightforward manner.
TL;DR: A procedure which applies the generalized Mitrovic method and the steepest descent approach to the automatic analog solution of algebraic equations and the plotting of root loci and its use of general-purpose analog computing equipment is presented.
Abstract: This paper presents a procedure which applies the generalized Mitrovic method and the steepest descent approach to the automatic analog solution of algebraic equations and the plotting of root loci. The significance of the procedure is its simplicity and its use of general-purpose analog computing equipment.
TL;DR: A compensation design method is proposed, which not only secures a desired location for the dominant roots on the s plane, but also satisfies conditions concerning the dominance of these dominant roots to the varying plant parameters.
Abstract: A compensation design method is proposed, which not only secures a desired location for the dominant roots on the s plane, but also satisfies conditions concerning the sensitivity of these dominant roots to the varying plant parameters. Examples are solved and verified on the analog computer.