Showing papers on "Control theory published in 1968"

An Introduction to Optimal Control Theory

Abstract: : The report presents an introduction to some of the concepts and results currently popular in optimal control theory. The introduction is intended for someone acquainted with ordinary differential equations and real variables, but with no prior knowledge of control theory. The material covered includes the problems of controllability, controllability using special (e.g., bang-bang) controls, the geometry of linear time optimal processes, general existence of optimal controls, and the Pontryagin maximum principle. (Author)

A theory of modal control

Abstract: Although considerable progress has been made in various aspects of control theory, there still appears to be no adequate theory for the control of large-scale linear time-invariant multivariable systems. If the engineering specifications required of the controlled system can be effectively summarized in a quadratic performance measure, then linear optimal control theory, in principle, provides a linear feedback controller which would perform the required task. Even under these circumstances the computational problems may be insurmountable. In an effort to circumvent these difficulties Rosenbrock suggested the use of modal control as a design aid. Modal control may be defined as control which changes the modes (i.e., the eigenvalues of the system matrix) to achieve the desired control objectives. This paper presents a complete and rigorous theory of modal control as well as recursive algorithms which permit modal control to be realized.

Minimax controller design

Abstract: Given a system with uncertain parameters, a performance index, and a controller structure, it is sometimes appropriate to determine the controller parameters by minimaximizing the performance index. In many of the cases where such a controller is too pessimistic it is appropriate to minimaximize a performance sensitivity. Some properties of these two types of controllers are presented. Since the minimax problems that arise do not in general have a saddle point, they must be solved by an iterative or search procedure. A new algorithm for solving algebraic minimax problems with or without a saddle point is presented and proved to converge. The rate of convergence is discussed. The algorithm is applied to the design of a controller for a string of three vehicles.

A theory for driver steering control of motor vehicles

Abstract: THE VIEWPOINT AND PRINCIPLES OF GUIDANCE AND CONTROL THEORY PROVIDE THE BASIS FOR STRUCTURING AN ANALYTICAL MODEL THAT DESCRIBES THE DRIVER'S STEERING CONTROL OF MOTOR VEHICLES. THE MODEL HAS AS ITS ELEMENTS THE VEHICLE EQUATIONS OF MOTION, EXPERIMENTALLY DERIVED MODELS FOR THE HUMAN OPERATOR'S DYNAMIC RESPONSE CHARACTERISTICS, AND DESCRIPTIONS OF THE ROADWAY ENVIRONMENT. A VARIETY OF SINGLE-LOOP AND MULTILOOP FEEDBACK SYSTEMS ARE SYNTHESIZED AND EXAMINED TO SELECT THREE GOOD BUT SIMPLE AND LIKE ALTERNATIVE SYSTEM CONFIGURATIONS: TIME-ADVANCED LATERAL DEVIATION, WHICH HAS A PRIMARY OUTER-LOOP FEEDBACK OF LATERAL POSITION IN THE LANE WITH LEAD EQUALIZATION PROVIDED BY PERCEPTUAL PREVIEW ALONG THE FUTURE TRACK OF THE VEHICLE, PATH ANGLE PLUS INERTIAL LATERAL DEVIATION, WHICH CONTAINS A PATH ANGLE INNER LOOP AND A LATERAL POSITION OUTER LOOP, AND HEADING ANGLE PLUS INERTIAL LATERAL DEVIATION, WHICH HAS BOTH HEADING ANGLE AND LATERAL POSITION FEEDBACK LOOPS. THE RESULTANT MODELS GIVE THE HIGHWAY ENGINEER AN ANALYTICAL TOOL THAT CAN BE USED TO DETERMINE THE ROLE OF EACH SYSTEM ELEMENT (DRIVER, VEHICLE, ETC.), TO DEFINE THE INTERACTION BETWEEN ELEMENTS, AND TO ASSESS THE EFFECT OF CHANGING SYSTEM PARAMETERS AT THE PRELIMINARY DESIGN STAGE. /AUTHOR/

Optimal nonlinear control of systems with pure delay

Abstract: When the plant contains a pure delay and the control signal is subject to a saturation constraint, the optimal controller and optimal performance can often be calculated, provided the corresponding results in the delay-free case are known Several examples of the technique are given in the present paper Some sub-optimal controllers are also discussed

New approaches to human-pilot/vehicle dynamic analysis

Abstract: : New models for human pilot dynamics and new methods for pilot/vehicle dynamic analysis are investigated. The status of existing quasi-linear models is reviewed and deficiencies are noted as a basis for pinpointing areas needing the most effort. The pilot modeling topics explored include: low frequency lead generation using either velocity sensing at the periphery (eye) or difference computations accomplished at a more central level; mode-switching models for nonstationary or discrete inputs to the pilot/vehicle system; physiological aspects of pilot dynamics in tracking tasks; Successive Organization of Perception (SOP) theory for levels of pilot cognition higher than compensatory. For pilot/vehicle analysis, analytical approaches from control theory which appear to have promise are studied, including: time-optimal computing feedforward elements useful in the mode switching models for response to nonstationary inputs; optimal control theory using the crossover model in the performance criterion to estimate pilot response characteristics in compensatory tasks; inverse optimal control theory using known experimental results and quasi-linear pilot response models in an effort to define the pilot's adjustment rules in terms of performance indices; optimal control theory to provide a simple test for optimality (to an elementary quadratic criterion) using only average performance measure data.

Feedback control which preserves optimality for systems with unknown parameters

Abstract: A method is described for constructing a feedback control law which remains optimal for a class of systems with unknown parameters whose values may lie in given regions. The control depends only on the input and output, and there is no explicit dependence on the unknown parameters. In contrast to the usual adaptive strategy, there is no identification or adjustment period. The optimal controls generated in a Taylor series form, but truncation of the series results in a feedback control which is close to optimal for a range of parameter values. An n th-order truncation of the control results in a (2n+1)th-order approximation of the optimally adaptive performance index.

Multilevel Optimization Techniques with Application to Trajectory Decomposition

Abstract: Publisher Summary This chapter discusses some basic principles of decomposition and multilevel optimization as applied to static and dynamic systems, and uses these principles in an entirely new application—the decomposition and multilevel optimization of trajectories. The chapter discusses the concepts of decomposition and second level controllers by examining static systems. A very simple example is used to show the advantages and limitations of the techniques. A new second level controller is derived using the Newton-Raphson algorithm for finding the roots of equations. This controller seemingly can not only be applied to a larger class of problems, but also gives the advantage of calculating the step size for the second level controller algorithm. A new Newton-Raphson controller is derived for dynamic systems, analogous to that for the static systems. Decomposition of a system means to manipulate the system equations in such a manner that they can be uncoupled into smaller subsystems that can be independently optimized.

Applications of the closed-loop stepping motor

Abstract: This paper describes a bang-bang controller which, with a particular novel scheme of discrete-state variable instrumentation, operates the stepping motor as a digital servo. The near time-optimal servomechanism is designed on a second-order basis, and the rather coarse staircase approximation of the switching curve yields good results. All control circuits have been implemented with integrated circuit components. The entire package has been product tested in the field.

Krebs, ein instabiler Regelkreis

Abstract: A uniform block diagram has been designed describing the normal cell increase as well as that of goodnatured and malignant tumours. It was shown that the various cancer diseases have their origin in changements of the structure data of the controller.

The Surge Model of the Well-Trained Human Operator in Simple Manual Control

Abstract: A new model of the human operator, termed the surge model, is developed. It is dual mode, containing a linearized constant coefficient model and an optimum second-order controller model. The equations describing its performance are written in the time domain. When the absolute values of the system error and of the first error derivative are less than certain specified bounds, the linear constant coefficient model is employed; and when the absolute values of the system error and of the first error derivative exceed these bounds, the optimum second-order controller model is employed. The surge model accurately predicts actual human operator performance in situations where the present widely used constant coefficient models yield unrealistic results, namely, when the signal being tracked contains discontinuous as well as continuous components, of either a random or a predictable nature. An Applied Dynamics 256 analog computer and a Control Data 3600 digital computer were employed, respectively, to simulate a real-time tracking problem and to solve the surge model equations characterizing the tracking task. Results presented in graphical form clearly indicate the superiority of the surge model in simulating tracking situations where discontinuities may occur.

50 Microdegree Temperature Controller

Abstract: A temperature controller has been developed using a platinum resistance thermometer in a bridge with inductively‐coupled ratio arms. It is capable of maintaining water bath temperatures constant to within ±25 microdegrees Celsius for 24 h in an environment varying as much as ±1.5°C at any temperature from 18 to 28°C. The sensitivity of the controller approaches the theoretical limitation imposed by Johnson noise. The design makes possible control dials which are direct reading in °C.

Redundant, self-checking, self-organizing control system

Abstract: A self-organizing control system having a plurality of selforganizing controllers acting in parallel to provide actuation signals for plant control. The controllers are constantly monitored to locate faulty controllers. When one controller does not compare with the others, it is initially coerced to operate correctly and, after a predetermined period, if correct operation is not provided, the faulty controller is removed from the system. In one embodiment, an odd number of controllers is always in the system to provide control on a majority basis. Therefore, the removal of a faulty controller will require the removal of an operating controller as well.

Automatically tuned process controller

Abstract: A process control system is compensated for nonlinearities in the control loop by means of a variable gain feedback element in the controller. The gain of the feedback element is adjusted by the output signal from a function generator, the input of which is the measured variable. The function generator is calibrated to compensate for the nonlinearity of the control loop.

The Application of Techniques of Artificial Intelligence to Control System Design

Abstract: Publisher Summary This chapter discusses the applicationof techniquesofartificialintelligence tocontrolsystemdesign Aself-organizingsystemisone whichchangesitsbasic structureas a functionofitsexperienceand/or environment The general aim of a self-organizing system is to evolve toward some desired output state or mode of behavior, in spite of some degree of ignorance of process, inputs, or controls As its structure changes as a function of experience, the self-organizing system can be said to “learn” A controller that is also a self-organizing system is called a “self-organizing controller” Such a controller contains three basic subsystems: (1) sensors, (2) learning network, and (3) a goal circuit The sensors—accelerometers, rate gyros, and horizon scanners—observe the local environment and provide descriptive data to the learning network and the goal circuit The learning network consists of decision elements that operate on data input from the sensors and that render a desirable output response

Automatic chemical analyzer and controller

Abstract: A method and apparatus for the automatic monitoring, analyzing and controlling of the etch rate and chemical concentration of a chemical-milling solution responsive to pH values at first and second equivalence points for both caustic soda and inhibitor.

Ratio controller for gases

Abstract: 1,250,395. Respiratory appliances. VERIFLO CORP. 23 Jan., 1969 [18 March, 1968], No. 3872/69. Heading AST. [Also in Divisions B1, F2 and G3] In an apparatus for mixing gases (e.g. oxygen and air) in any rate and supplying the mixture according to instantaneous demand, the gases enter at substantially equal pressures through conduits 100, 103 and 110, 112 to a ratio setter 23 (see also Fig. 8, not shown, and Division G3) comprising respective needle valves 82, 81 geared together to operate in complementary senses whereby any ratio of the gases may be obtained. The gases then pass by conduits 105, 114 to respective flow controllers 20, 21 (see also Figs. 2-5, not shown and Division F2) having valve controlled outlets 48, 58 and thence to the mixture outlet conduit 115. The flow controller outlet valves are actuated by diaphragm assemblies in dependence on the pressures in chambers 34, 54, which are in turn dependent on pneumatic control and signals from the pressure controller 22 (see also Figs. 5 and 6, not shown, and Division). This has a venturiform pressure gas inlet 77, 78 whereby a reduced pressure is created in passage 67, 80 and transmitted by conduit 118 to the chambers 34, 54 in the flow controllers, causing the outlet valves thereof to close. If there is a demand in the outlet conduit 115, the pressure therein and in the conduit 117 and chamber 74 of the pressure controller will fall, the valve 79 will dose and the venturi effect will cease, so that pressure in the conduit 118 and chambers 34, 54 will rise, causing the outlet valves of the flow controllers to open. The pressure in the outlet conduit may be raised by adjustment of the compression of the spring 76 in the pressure controller.

Input/output controller with linked data control words

Abstract: IN ORDER TO INCREASE THE THROUGHPUT OF AN INPUT/OUTPUT CONTROLLER WITHIN A MODULATOR DATA PROCESSING SYSTEM, APPARATUS IS PROVIDED WITHIN THE INPUT/OUTPUT CONTROLLER FOR TRANSFERRING INFORMATION ACROSS AN INTERFACE TO A MEMORY AT AN INCREASED RATE WITHIN THE CONSTRAINTS IMPOSED BY THE INTERFACE. INFORMATION IS TRANSFERRED IN ACCORDANCE WITH DATA CONTROL WORDS. MEANS ARE PROVIDED WHEREBY A FIRST DATA CONTROL WORD IS USED UNTIL ITS WORD COUNT FIELD IS EXHAUSTED AND IN ANTICIPATION OF THIS, ANOTHER DATA CONTROL WORD MAY BE FETCHED IN ORDER THAT INFORMATION TRANSFER MAY CONTINUE.

Development and application of a terminal spacing system.

Abstract: : This report describes the results of laboratory and field tests of a NAFEC-developed computer system which provided aircraft rate control and spacing assistance to the air traffic controllers in a terminal area. A general purpose digital computer was used to provide heading, speed and turn information, in symbolic and numeric form, on an ASR-4 radar display used by the final approach controller. Additionally, an input/output device at the flight data location indicated which aircraft should depart which outer fix at a given time, in order to establish and maintain a consistent 'first-come, first-served' traffic flow in the final spacing area (metering). Initial testing was conducted at NAFEC. The system was subsequently relocated to the J. F. Kennedy Terminal Radar Control (TRACON) for further evaluation in an operational environment. In a comparison with the manual control system, use of the final spacing function of the computer system resulted in more consistent and accurate landing intervals which would proportionately increase the arrival rate. Other expected benefits could not be properly assessed during the field appraisal due to operational, environmental and other constraints resulting from the heavy J. F. Kennedy traffic. (Author)

Data processor having operator family controllers

Abstract: A DATA PROCESSOR HAS A NUMBER OF DIFFERENT PHYSICALLY SEPARATE OPERATOR FAMILY CONTROLLER, EACH FOR FORMING CONTROL SIGNALS PREDETERMINED BY AN OPERATOR PROVIDED THERETO. A COMMON FUNCTIONAL RESOURCES APPARATUS MA- NIPULATES DATA RESPONSIVE TO CONTROL SIGNALS FROM ANY ONE OF THE FAMILY CONTROLLERS. A PROGRAM CONTROLLER PROVIDES OPERATORS TO THE FAMILY CONTROLLERS FOR EXECUTION.

An optimal control method for predicting control characteristics and display requirements of manned-vehicle systems.

Abstract: : An analytic procedure for determining information display requirements and human control and instrument monitoring characteristics for complex multivariable vehicular control systems is developed. The method is based upon the assumption that the human controller will act in a near optimal manner. Optimal control theory and its associated state-space representation is used as the basis for the analytic procedure. A model for the human controller is developed in which the controller's inherent limitations are approximated by a time delay. The model includes a predictor for compensating for this time delay, a controller for producing the control inputs to the vehicle and a cost functional that is to be minimimized. The controller is assumed to be optimal. Several suboptimal predictors are investigated. Only quadratic cost functionals are considered. The analytic procedure assumes that the human operator's control characteristics can be represented by a set of gains operating on the delayed state variables of the system. These gains are predicted from the gains of optimal controller and from the characteristics of the predictor. It is further postulated that the information display requirements and instrument monitoring behavior can be determined from the sensitivity of the cost to changes in gain of the controller. (Author)