Showing papers on "Control theory published in 1969"

In-the-large stability of relay and saturating control systems with linear controllers

Abstract: It is shown that when the plant of a relay control system consists of a pure integrators, with n ≥ 3, and the control signal proceding the relay is a linear combination of state coordinates, the system is unstable in-the-large for all values of the controller coefficients. The same result holds if the relay is replaced by a. saturator. The method used is to prove that (except for a degenerate case) state trajectories exist which go to infinity. This method enables more general systems to be treated than those discussed in a previous paper, which demonstrated the existence of a periodic solution. Plants not consisting of pure integrators are also considered. The question of when it is worthwhile to incorporate non-linearities in the controller is discussed.

Theory of Manual Vehicular Control

Abstract: The analytical basis of manual vehicular control theory is a combination of feedback systems analysis and mathematical models for human operators engaged in control tasks. Simplified representations for the operator-system combination are provided by the 'crossover model', which is described in detail. The system dynamics and average performance of the crossover model system are developed. With these as bases, case studies are presented to illustrate the types of result which can be obtained from application of the operator-vehicle control theory. Two aircraft control examples illustrate the use of the theory and its empirical correlates to estimate operator dynamic characteristics, system performance, pilot ratings, pilot commentary, design implications, and some experimental guidelines. A driver automobile example is presented to illustrate the use of the theory in structuring the key guidance and control features of the driver's visual field. A comprehensive bibliography of operator-vehicle system analysis applications is also provided.

The Human as an Optimal Controller and Information Processor

Abstract: A mathematical model of the instrument-monitoring behavior of the human operator is developed. The model is based on the assumption that the operator behaves as an optimal controller and information processor, subject to his inherent physical limitations. The resulting model depends explicitly on the control task and the control actions. Provision is made for the ability to obtain information from the peripheral visual field. There are no restrictions on signal coupling. The specific characteristics of the operator's visual sampling behavior are predicted by solving a nonlinear, deterministic optimization problem. A two-axis compensatory tracking example is investigated, and the results exhibit the general characteristics expected of a human operator performing a similar task.

A Model for Human Controller Remnant

Abstract: A model for human controller remnant is postulated in which remnant is considered to arise from an equivalent observation noise vector whose components are linearly independent white noise processes. Extensive analysis of data obtained from simple manual control systems verifies that this model structure holds over a wide range of input amplitudes and bandwidths, vehicle dynamics, and display locations. When the display is viewed foveally, the component noise processes are proportional to the variances of the displayed quantities. This constant of proportionality is independent of input parameters and of vehicle dynamics.

Linear and Nonlinear Models of the Human Controller

Abstract: This paper presents a review of recent studies of the human controller both in psychology and in control engineering. Theoretical and technological problems in the study of skilled behaviour are first discussed, and the desirable constraints upon any “model” are outlined. The foundations of linear continuous modelling of the human controller and experimental data on the validity and utility of linear models are then reviewed. The evidence for non-linear and discontinuous behaviour in the human controller is then outlined, and studies of non-linear models based on modern optimal and sampled-data control theory are then presented.

Learning Control Systems

Abstract: In designing an optimal control system, if all the a priori information about the controlled process (plant-environment) is known and can be described deterministically, the optimal controller is usually designed by deterministic optimization techniques. If all or a part of the a priori information can only be described statistically—for example, in terms of probability distribution or density functions—then stochastic or statistical design techniques will be used. However, if the a priori information required is unknown or incompletely known, in general an optimal design cannot be achieved. Two different approaches have been taken to solve this class of problems. One approach is to design a controller based only upon the amount of information available. In that case the unknown information is either ignored or is assumed to take on some known values chosen according to the designer’s best guess. The second approach is to design a controller which is capable of estimating the unknown information during its operation and of determining an optimal control action on the basis of the estimated information. In the first case a rather conservative design criterion (for example, the minimax criterion) is often used; the systems designed are in general inefficient and suboptimal. In the second case, if the estimated information gradually approaches the true information as time proceeds, then the controller thus designed will approach to the optimal controller.

Optimal linear control systems with incomplete state measurements

Abstract: Optimal control laws usually require the complete measurement of the plant state However, in practice one often has available only a small number of measurements A procedure is developed that leads to a dynamic feedback control law which is a function of any given set of measurements The resulting closed-loop system is optimal for all initial states of the system in the sense of minimizing a quadratic performance index The order of the controller depends upon the observability properties of the plant The development is extended to time-variable problems

Adaptive and manual control system for machine tool

Abstract: A control system for milling machines, and like metal-cutting machines, adapted to control the operation of the milling machines, at the option of an operator, in either a manual or an adaptive control mode. In the manual mode, a manual controller, comprising manually adjustable controls, is set to supply control signals having values determined by the settings to the milling machine drive system. In the adaptive control mode, an adaptive controller automatically generates control signals as a function of physical manifestations which exist at the work area when the milling cutter perform machining operations upon the workpiece. The physical manifestations are sensed and manifestation signals, which are a function of the physical manifestations sensed, are generated and supplied to a computer in the adaptive controller which compares the manifestation signals with constant signals having values establishing desired ranges of machine operation. If the manifestation signals have values which are within the range of values set by the constant signals, control signals are generated to increase machine productivity in accordance with a predetermined strategy. If the values of the manifestation signals are without the range of values set by the constant signals, restricting control signals are generated. The drive system receives the control signals and generates command signals in accordance with the values of the control signals received. The command signals are fed to the machine to regulate the relative rate of movement of the cutter and workpiece.

Time-shared numerical control system

Abstract: A data processing machine capable of providing numerical control of a plurality of numerically controlled multislide machine tools or other motion machinery on a time-sharing basis operable in response to request signals associated with the machine tools from sources located either internally or externally of their control systems, on an interleaved basis. The machine completes one sequence instruction or a single sequence of a multisequence instruction at a time for each machine tool controller, stops and seeks a request from the next tool controller in priority and then proceeds to service such next tool controller. Output data from the machine are directly connected to the inputs of the controllers from the logic of the machine without intervening buffering.

Control of a process variable by a computer and a controller which replaces the computer

Abstract: A method and apparatus for controlling a process variable wherein the variable is controlled primarily by a digital computer but where a part of the control function is performed by an analog controller. When the control is by the computer, an output signal is passed intermittently from the computer to a memory amplifier, the output signal of which is a control signal that may be used for correcting the process variable. When control is by the controller, the memory amplifier operates as a summing amplifier for negative feedback control.

Separation theorem for nonlinear measurements

Abstract: General solutions to the optimal stochastic control problem, or the combined estimation and control problem, are extremely difficult to compute since dynamic programming is required. However, if the system is linear, if the measurements are linear, and if the cost is quadratic, then the optimal stochastic controller is separated into 1) a filter to generate the conditional mean of the state, and 2) the optimum (linear) controller that results when all uncertainties are neglected. By altering the system configuration a new separation theorem is derived for arbitrary nonlinear measurements, discrete-time linear systems, and a quadratic cost. If a feedback loop is placed around the nonlinear measurement device (e.g., an analog-to-digital converter), then the stochastic control can be found without dynamic programming and is computed by cascading a nonlinear filter and the optimum (linear) controller. The primary advantage is the significant saving in computation. The performance of this new system configuration relative to the system without feedback depends on the nonlinearity, and it is not necessarily superior. A numerical example is presented.

Design of helicopter stabilization systems using optimal control theory.

Abstract: A technique is described for the design of multivariable controllers for helicopters, based on results obtained recently in optimal control theory For a specified quadratic performance index, the optimal feedback controller is obtained by solving a matrix Riccati equation A method of determining the performance index which yields a desired response is outlined in the paper The solution represents the fastest response that can be obtained for a specified amplitude of anticipated disturbance and a limited controller output An example is worked out in detail to indicate the effectiveness of the method

Speed control system for an automtoive vehicle

Abstract: This disclosure relates to a speed control system for an automotive vehicle operated by an internal combustion engine and includes a controller means or throttle coupled to the internal combustion engine for controlling the output power of the engine and the speed of the vehicle. Means are provided in the system for producing a first electrical signal corresponding to the actual speed of the vehicle and means are also provided for producing a second electrical signal corresponding to the position of the throttle or controller means. There are also means provided for producing a signal corresponding to a desired or set speed of the vehicle. Power actuating means in the form of a servomotor is coupled to the controller or throttle means for controlling the position of the throttle or controller means and a memory is provided for storing the signal corresponding to the set or desired speed of the vehicle. Means, preferably in the form of a differential amplifier, receive the first, second and third signals and combine them to produce an actuating error signal which is applied through circuit means to the power actuating means or servomotor to operate the controller means or throttle. The memory means for storing the signal corresponding to the desired speed ro set speed of the vehicle is connected or coupled to this circuit means for producing and storing a signal when the servomotor or power actuator begins to control the position of the controller means or throttle upon command by the vehicle operator.

Decision Processes in the Adaptive Behavior of Human Controllers

Abstract: A decision algorithm which simulates the rapid adaptive behavior of human controllers following sudden changes in plant dynamics is developed. The control of a VTOL aircraft in hover following failure of the stability augmentation system is used as a specific example. The decision algorithm is based on the assumption that the human controller recognizes certain pattern features in the error/error-rate phase plane. Experimental data, obtained from pilots facing four possible alternatives following the time of failure, are presented. The proposed decision algorithm is developed, and digital simulation results are discussed. A theoretical justification for the algorithm, based on statistical decision theory, is presented in the Appendix.

Sensitivity Analysis of Power Systems

Abstract: Modern control theory is being used more and more in regulator design of synchronous generator automatic regulating equipment. Making use of the well-established linearized equations of the synchronous machine and its control equipment, the characteristic equation of the system is developed from which the eigenvalues of the system are found. The sensitivities of these eigenvalues to the various parameters of the control system are calculated. This approach can provide a basis for optimal design of the system. A detailed sensitivity analysis is made of a particular system under various operating conditions, and results are tabulated, making it possible to obtain a clear idea about the effect of any parameter on the system performance and dynamic stability limit.

A simple temperature controller

Abstract: The design of a simple electronic temperature controller with a fast response time using a resistance bridge and readily available integrated amplifiers is described.

A Minimum Variance, Time Optimal, Control System Model of Human Lens Accommodation

Abstract: Experimental data relating ciliary nerve stimulation and lens motion are used to identify the open-loop plant dynamics of the lens accommodation system via a parameter identication variation of the Kalman filter equations. Using the resultant minimum variance plant model, experimental closed-loop responses of the human accommodative system are predicted by synthesizing the system closed-loop controller. The resultant control signals are shown to minimize the time required to change the refractive state of the eye. The plant dynamic model and the closed-loop model are further verified by comparing their frequency responses to experimental data. The optimal performance of the lens system is compared to analogous performance of another ocular control system, and a possible general theory of optimal control is discussed.

Use of power and energy concepts in the analysis of multivariable feedback controllers

Abstract: The general linear-feedback multivariable-regulator problem is considered in terms of the injection of power into the controlled system by the controller. The concepts of power, energy, power decomposition, active power and reactive power are studied in this context and shown to give a physical insight into the techniques of modal control and spin-space mapping. An analogy is established between the energy exchanges of a system and its controller, and the energy-interchange effects in quantum mechanics.

Control: past, present and future

Abstract: Automatic control developed historically as a necessary consequence of replacing human or animal power by wind and water power and later by steam power. Its beginnings were empirical, but an important contribution to the theory was made by Clerk Maxwell, and later the development of feedback amplifiers led to intensive theoretical work in the U.S.A. By 1945 a well-developed and highly successful theory was available, and wide applications have been made. In more recent times, theoretical effort has been concentrated on problems of guidance, using the calculus of variations. The incentive here was to solve aerospace problems, but there have been some applications to industrial problems. This theory seems to have a narrower range of applications than the earlier work. The development of the digital computer has placed in the hands of engineers a tool of unrivalled flexibility and power for the control of processes. By contrast, our theory is at present unable to exploit this power with full effect. The most promising field for control theory and application in the next five to ten years seems to be the application of computer control to all types of industry, and the development of the corresponding theory.

Liquid level controller

Abstract: An apparatus for controlling liquid levels for viscous liquids such as printing ink utilizing pneumatic probes and responsive liquid regulating means.

Applications of mathematical control theory to accounting and budgeting: ii. the continuous joint trading madel.

Abstract: : The paper applies the mathematical control theory to the accounting network flows, where the flow rates are constrained by linear inequalities. The optimal control policy is of the 'generalized bang-bang' variety which is obtained by solving at each instant in time a linear programming problem whose objective function parameters are determined by the 'switching function' which is derived from the Hamiltonian function. The interpretation of the adjoint variables of the control problem and the dual evaluators of the linear programming problem demonstrates an interesting interaction of the cross section phase of the problem, which is characterized by linear programming, and the dynamic phase of the problem, which is characterized by control theory. (Author)

Cigarette dense end measuring and controlling apparatus

Abstract: A dense end controller is provided for a cigarette machine having means for making a continuous cigarette rod having dense tobacco regions spaced along the length thereof and a cutter. A density gauge provides a first signal proportional to the density of the tobacco rod. A phase comparator, such as a synchronous detector, continuously compares the phase of the periodic variations in the first signal relative to the phase of pulses in a second signal from the cutter to provide a control signal directly proportional to any deviation of said dense tobacco regions from the ends of cut cigarettes.

Elevator control system

Abstract: AN ELEVATOR CONTROL SYSTEM INCLUDES A NEGATIVE FEEDBACK TYPE CONTROLLER APPLIED WITH BOTH A SIGNAL FOR COUNTERBALANCING AN UNBALANCED TORQUE APPLIED TO AN ELEVATOR DRIVE CIRCUIT AND STORED IN A MEMORY, AND A SPEED SIGNAL FOR AN ELEVATOR CAR. THE FORMER SIGNAL IS APPLIED TO THE CONTROLLER NOT ONLY BEFORE THE CAR STARTS BUT ALSO AFTER THE SPEED SIGNAL HAS BEEN APPLIED TO THE CONTROLLER. THUS THE CAR IS SMOOTHLY STARTED WITHOUT A DISCONTINUITY OF SIGNAL LEVEL BETWEEN BOTH SIGNALS APPLIED TO THE CONTROLER.