Showing papers on "Control theory published in 1975"

Self-tuning controller

Abstract: A strategy for the design of self-tuning controllers of systems with constant but unknown parameters is presented. A cost function which incorporates system input, output and set-point variations is selected, and a control law for a known system is derived. This control law is shown to comprise a least-squares predictor of a function related to the cost function, and the control input is chosen to make the prediction zero. The parameters of the control law for the unknown system are estimated using a recursive-least-squares algorithm, and the optimal parameters are shown to be a fixed point of the algorithm. Whilst retaining their computational simplicity, the proposed method has several advantages over self-tuning-regulator strategies which attempt to minimise the output variance alone: weighting of control is allowed for; set-point variation may be optimally followed; there is no requirement to choose a system-related parameter to ensure convergence; and, for stable but nonminimum phase systems, there is no need to employ time-consuming methods, such as the solution of a Riccati equation. Several simulated examples are used to demonstrate the potential of the method.

Feedback control of two beam, two joint systems with distributed flexibility

Abstract: The control of the flexible motion in a plane of two pinned beams is addressed with application to remote manipulators. Three types of linear feedback control schemes are considered: joint angle and velocity feedback with (GRC) and without (IJC) cross joint feedback, and feedback of flexible state variables (FFC). Two models of the distributed flexibility are presented along with some results obtained from them. The relative merit of the three control schemes is discussed.

Multivariable tuning regulators: The feedforward and robust control of a general servomechanism problem

Abstract: A new notion of compensator identification, as opposed to the conventional plant identification problem, is introduced in this paper. It is assumed that it is desired to synthesize a robust feedforward-feedback controller for an unknown plant so that asymptotic tracking, in the presence of disturbances, occurs. The only assumptions made regarding the description of the plant model are that 1) the plant is linear and time-invariant and 2) the uncontrolled plant is stable. Note that it is assumed that the order of the plant model is unknown. It is assumed that the control inputs to the plant can be excited, that the outputs of the plant which are desired to be regulated can be measured, and that the class of disturbance inputs and reference inputs is known. In addition, it is also assumed in the feedforward controller case, that the disturbance inputs can be measured and be excited; this assumption is not required in the robust feedback controller case. Necessary and sufficient conditions which allow the robust feedforward-feedback compensator to be synthesized so that the controlled system is stable and so that asymptotic tracking, in the presence of both measurable and unmeasurable disturbances, occurs are obtained. An algorithm which allows the controllers to be synthesized is given. Some numerical examples are included to illustrate the results.

The robust decentralized control of a general servomechanism problem

Abstract: The decentralized robust control of a completely general servomechanism problem is considered in this paper. Necessary and sufficient conditions, together with a characterization of all decentralized robust controllers which enables asymptotic tracking to occur, independent of disturbances in the plant and perturbations in the plant parameters and gains of the system, is obtained. A new type of compensator called a decentralized servo-compensator which is quite distinct from an observer is introduced. It is shown that this compensator, which corresponds to an integral controller in classical control theory, must be used in any decentralized servomechanism problem to assure that the controlled system is stablizable and achieves robust control; in particular, it is shown that a decentralized robust controller of a general servomechanism problem consists of two devices (i) a decentralized servo-compensator and (ii) a decentralized stabilizing compensator. It is then shown that, under certain mild conditions, there almost always is a solution to the robust decentralized servomechanism problem for any composite system consisting of a number of subsystems interconnected in any arbitrary manner. This last observation has important implications for process control.

Application of Optimal Control Theory to Civil Engineering Structures

Abstract: Modern control theory has been successfully applied to control the motions of aerospace vehicles. An exploratory study is made herein to investigate the feasibility of applying such a theory to control the vibration of civil engineering structures under random loadings. It is assumed that random excitations to structures, such as wind loads and earthquakes, can be modeled by passing either a stationary Gaussian white noise or a nonstationary Gaussian shot noise through a filter. The performance index to be minimized consists of the covariances of both the structural responses and the control forces. Under these conditions, the optimal control law is a linear feedback control. The optimal control forces are obtained by solving a matrix Riccati equation. Applications of the optimal control to a multi-degree-of-freedom structure, under stationary wind loads and nonstationary earthquakes, are demonstrated. It is shown that significant reduction in covariances of the structural responses can be achieved by the use of an active control system.

Recent advances in gradient algorithms for optimal control problems

Abstract: This paper summarizes recent advances in the area of gradient algorithms for optimal control problems, with particular emphasis on the work performed by the staff of the Aero-Astronautics Group of Rice University. The following basic problem is considered: minimize a functionalI which depends on the statex(t), the controlu(t), and the parameter π. Here,I is a scalar,x ann-vector,u anm-vector, and π ap-vector. At the initial point, the state is prescribed. At the final point, the statex and the parameter π are required to satisfyq scalar relations. Along the interval of integration, the state, the control, and the parameter are required to satisfyn scalar differential equations. First, the sequential gradient-restoration algorithm and the combined gradient-restoration algorithm are presented. The descent properties of these algorithms are studied, and schemes to determine the optimum stepsize are discussed. Both of the above algorithms require the solution of a linear, two-point boundary-value problem at each iteration. Hence, a discussion of integration techniques is given. Next, a family of gradient-restoration algorithms is introduced. Not only does this family include the previous two algorithms as particular cases, but it allows one to generate several additional algorithms, namely, those with alternate restoration and optional restoration. Then, two modifications of the sequential gradient-restoration algorithm are presented in an effort to accelerate terminal convergence. In the first modification, the quadratic constraint imposed on the variations of the control is modified by the inclusion of a positive-definite weighting matrix (the matrix of the second derivatives of the Hamiltonian with respect to the control). The second modification is a conjugate-gradient extension of the sequential gradient-restoration algorithm. Next, the addition of a nondifferential constraint, to be satisfied everywhere along the interval of integration, is considered. In theory, this seems to be only a minor modification of the basic problem. In practice, the change is considerable in that it enlarges dramatically the number and variety of problems of optimal control which can be treated by gradient-restoration algorithms. Indeed, by suitable transformations, almost every known problem of optimal control theory can be brought into this scheme. This statement applies, for instance, to the following situations: (i) problems with control equality constraints, (ii) problems with state equality constraints, (iii) problems with equality constraints on the time rate of change of the state, (iv) problems with control inequality constraints, (v) problems with state inequality constraints, and (vi) problems with inequality constraints on the time rate of change of the state. Finally, the simultaneous presence of nondifferential constraints and multiple subarcs is considered. The possibility that the analytical form of the functions under consideration might change from one subarc to another is taken into account. The resulting formulation is particularly relevant to those problems of optimal control involving bounds on the control or the state or the time derivative of the state. For these problems, one might be unwilling to accept the simplistic view of a continuous extremal arc. Indeed, one might want to take the more realistic view of an extremal arc composed of several subarcs, some internal to the boundary being considered and some lying on the boundary. The paper ends with a section dealing with transformation techniques. This section illustrates several analytical devices by means of which a great number of problems of optimal control can be reduced to one of the formulations presented here. In particular, the following topics are treated: (i) time normalization, (ii) free initial state, (iii) bounded control, and (iv) bounded state.

Constant pressure pump

Abstract: A controller maintains a constant desired fluid pressure in a fluid load driven by a variable flow fluid pump with a variable speed motor. A set point signal representing desired pressure and a signal from a pressure transducer representing actual pressure are applied to an error amplifier. The resulting error signal is applied through a variable gain stage to the motor control. The variable gain stage includes first and second variable gain amplifiers the first of which has a gain which is controlled inversely to pressure. The second variable gain amplifier has a gain which is controlled in proportion to flow. In this manner, the gain of the controller changes in inverse proportion to the restriction of the fluid load. This makes the performance of the controller independent of changes in the fluid load by keeping the total loop gain constant.

On observers for systems with unknown and inaccessible inputs

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).

Signal analyzer system

Abstract: A signal analyzer system is disclosed which includes an arithmetic processor containing a plurality of pipeline processor elements in parallel array with each element connected to a respective working store, with all of the elements being under microprogram control of an arithmetic element controller. A storage controller included in the system is connected to the arithmetic processor, to a system input and to a system ouput. A bulk storage included in the system is connected to the storage controller. The storage controller controls data transfers into and out of the system and between the bulk storage and arithmetic processor. A control processor included in the system is connected to the arithmetic processor and the storage controller by means of a data bus for centrally controlling the operation of the plurality of pipeline processor elements by transmitting micro control words over the bus.

Cheap control of the time-invariant regulator

Abstract: The asymptotic solution of the linear quadratic state regulator problem is obtained as the cost of the control tends to zero. Matrix Riccati gains are obtained via singular perturbations theory and are used to asymptotically calculate the optimal control and the corresponding trajectories. Several cases are distinguished and applications are discussed.

Feedback stabilization of a class of distributed systems and construction of a state estimator

Abstract: In this paper, we study feedback stabilization of a class of distributed systems governed by partial differential equations of parabolic type and its application to constructing a state estimator for asymptotic state identification. It is proved that, when a controller (an observation) can be arbitrarily constructed, observability (controllability) of the system is necessary and sufficient for stabilizing the system so that it has an arbitrarily large damping constant. As an application of this result, it is shown that a state estimator can be constructed, the output of which approaches asymptotically the real state of the system with an arbitrary convergence rate.

Proportional temperature controller

Abstract: A temperature controller for use with an electrical heater for precisely maintaining the temperature within a system at a selected set point, and employing an improved bridge circuit. A temperature sensitive resistor forms one of the two variable arms of the bridge circuit. The resistor varies in value as a function of temperature exhibiting a temperature coefficient of resistance which is not constant but which varies, decreasing with increasing temperature. The other variable arm, the setting arm, is in the form of a network, including a linear setting resistor and a pair of fixed resistors arranged in a series-shunt circuit. The setting resistor is linearly calibrated in terms of temperature, the series-shunt arrangement providing a composite resistance-set point temperature characteristic which closely corresponds to that of the sensing arm. The temperature controller further includes an operational amplifier which provides an output signal dependent upon the degree of bridge imbalance and a zero voltage switch responsive to the operational amplifier for providing trigger pulses to a triac coupled in the load circuit of the heater. A ramp generator is preferably included as a supplemental input to the zero voltage switch thereby to produce a control system in which the heat released is proportional to the degree the bridge is unbalanced.

Static controller for power factor correction and adaptive filtering

Abstract: A polyphase cycloconverter operating in regenerative mode is connected between a voltage distribution system and a single phase high frequency resonant tank and controlled to produce essentially no real power flow to the resonant tank and a variable amount of leading (or lagging) reactive power. The static reactive power controller has fast response and can function as an electronically variable capacitor for power factor regulation, VAR control and adaptive filtering.

Optimal constant controllers for stochastic linear systems

Abstract: The design of a fixed, linear, dynamic controller for a linear system subjected to random disturbances and additive measurement noise is examined. The objective is to achieve satisfactory performance with controllers of order significantly lower than that of a Kalman filter or Luenberger observer. Matrices which define the controller are chosen to minimize the steady-state average of a quadratic function of the control and state variables. Necessary conditions which the gains must satisfy in order to minimize this criterion are developed.

Control system for an air conditioner

Abstract: A control system for an air conditioner having detectors for detecting at least the radiation temperature in a room or controlled space, a device for setting a desired room air parameter in response to the detected radiation temperature, and a controller for controlling the air conditioner in accordance with the desired room air parameter.

River pollution control

Abstract: In this paper, a preliminary study is made of the dynamic optimization problem for a river with many polluters using a recently developed model of a section of the river Cam near Cambridge in England. Because of the high dimensionality of the system it is computationally prohibitive to obtain optimal solutions. However, the system has a fairly simple structure which could be utilized to alleviate the computational burden. A simple hierarchical structure is proposed for the river pollution control and the strategy is demonstrated on a digital simulation. For the practical implementation of the strategy, it is necessary, however, to have available the state vector of the system. In practice, only certain corrupted measurements of the outputs are available. It is therefore necessary to construct a state estimator. Like the optimal controller, the optimal estimator also requires prohibitive amounts of computation. However, a hierarchical strategy similar to the control strategy could be used to allev...

Power controller with a modular power output

Abstract: A power controller having a plurality of power output modules which can be added or removed as desired to change the power output rating. The electrical output of the individual power modules are removably attached to an output combining structure. The electrical connections to the output combining structure also provide mechanical support for the power output modules. The servo controller is constructed so that as additional power modules are added, each provides a predetermined proportion of the output power. That is, each module will add in a linear fashion to the total output capability of the amplifier. Load sharing among the modules is provided. An etched copper resistor having a positive resistance versus temperature characteristic is provided to aid load sharing among the output semiconductors. A feedback signal is derived from the power output modules to protect the servo controller. The protection of the power controller is one function of the feedback signal, in that, it limits the maximum current derivable from the controller under normal conditions. The primary function of the current feedback signal is to provide an error signal which when combined with the input command causes the current output to be properly metered to a load. The feedback signal can be obtained from only one of the output modules since load sharing is provided or can be obtained in several or all of the power output modules as desired. Temperature sensing of a representative module is provided for system protection.

Electrically propelled vehicle

Abstract: A propulsion system for an electrical vehicle including a linear proportional controller operable in a plurality of modes for operating a dc drive motor via power derived from a propulsion battery Low speed operation is achieved in an armature control mode wherein the controller is interposed between the propulsion battery and the motor armature while the motor field is coupled directly across the battery High speeds are attained in a field control mode wherein the controller is interposed between the battery and motor field while the armature is coupled directly across the propulsion battery, thereby eliminating controller losses from the high current armature circuit Switching between modes is achieved in a manner which minimizes stress on the switching elements The controller is also adapted to operate in a charger mode wherein unregulated dc power is fed to the controller which functions to regulate the charge provided to the battery Overall efficiency is increased by use of a dual chopper as a power modulator element The circuit further includes protection means for controlling or preventing operation under conditions wherein circuit elements might be damaged

Parameter adaptive control of multivariable systems

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.

Hardwired marker for time folded tst switch with distributed control logic and automatic path finding, set up and release

Abstract: A marker circuit communicating with a stored program controller and switch stages, implementing pathfinding, connect, and disconnect operations while using address, status, and data buses to control the switch through exchange of connect information from the stored program controller and disconnect information from the switch control stores.

Electronic digital process controller having simulated analog control functions

Abstract: An electronic process controller comprises a digital computer programmed to digitally simulate the functions of each of a plurality of conventional analog and discrete control blocks and a process operator's panel for selecting and arranging these simulated blocks into a simulated control circuit configuration. The operator's panel provides means for direct operator selection of: (1) the input signal to be processed by the computer; (2) the arrangement of simulated blocks for processing the input signal in order to derive an output process control signal; and (3) the output control device to which the output signal is directed. This controller permits assembly and modification of simulated analog process control configurations in a manner analogous to the assembly of conventional hard wire control circuits without the expense of wiring, breaking, and rewiring of hard wire interconnections. At the same time, it permits the operator to use a computer for providing analog control functions without knowledge of a specialized programming language.

Programmable interface controller for numerical machine systems

Abstract: A programmable interface controller capable of assuming specific sequential control functions is disclosed. The disclosed controller is a slave device under the direct control of the numerical control computer and is effectively transparent to numerical control machine system. Upon a first command the interface controller receives and stores data from the numerical control computer. The stored data is processed in accordance with an internal program and the results of the processing temporarily stored therein. Upon a second command, the results of the processing are returned to the numerical control computer from where they are distributed via the systems bi-directional bus to the machine as well as to operating routines elsewhere in the numerical control system. The programmable interface controller performs Boolean and logic arithmetic on the data received from the numerical control computer and is capable of assuming the control functions of prior art magnetics as well as other sequential control functions normally performed by the numerical control computer.

Method and apparatus for preventing pump cavitation

Abstract: The speed of an engine driven pump is sensed and compared with the desired maximum operating speed to detect overspeed. The discharge of the pump is controlled by a variable flow rate controller. When an overspeed condition exists, a command signal is sent to the discharge controller to reduce flow by a discrete decrement. The control signal is blocked after activating the controller for a preselected time interval. During the blocking interval the engine speed is maintained substantially at the operating speed by cyclical reduction of the power input thereto.