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Control Theory and Applications, IEE Proceedings D

Issue 6 • Date November 1982

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Displaying Results 1 - 15 of 15
  • Sensitivity and robustness in control systems theory and design

    Page(s): 213 - 214
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    Freely Available from IEEE
  • Quantitative feedback theory

    Page(s): 215 - 226
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (1398 KB)  

    In quantitative feedback theory, plant parameter and disturbance uncertainty are the reasons for using feedback. They are defined by means of a set Q = {P} of plant operators and a set D = {D} of disturbances. The desired system performance is defined by sets of acceptable outputs Au in response to an input u, to be achieved for all P¿¿ Q. If any design freedom remains in the achievement of the design specifications, it is used to minimise the effect of sensor noise at the plant input. Rigorous, exact quantitative synthesis theories have been established to a fair extent for highly uncertain linear, nonlinear and time-varying single-input single-output, single-loop and some multiple-loop structures; also for multiple-input multiple-output plants with output feedback and with internal variable feedback, both linear and nonlinear. There have been many design examples vindicating the theory. Frequency-response methods have been found to be especially useful and transparent, enabling the designer to see the trade-off between conflicting design factors. The key tool in dealing with uncertain nonlinear and multiple-input multiple-output plants is their conversion into equivalent uncertain linear time-invariant single-input single-output plants. Schauder's fixed-point theorem justifies the equivalence. Modern control theory, in particular singular-value theory, is examined and judged to be comparatively inadequate for dealing with plant parameter uncertainties. View full abstract»

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  • Sensitivity reduction in ship-manoeuvring performance via nonlinear compensation

    Page(s): 227 - 232
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    During a manoeuvre it is frequently found that a ship's yaw dynamics vary widely. To obtain a consistent response to the helm, it is therefore advisable to provide an autopilot to cope with plant uncertainties. Using the method of Horowitz, a high-loop-gain linear system may be designed which achieves an acceptable spread of transient responses. Unfortunately, there is a penalty to be paid in the form of excessive rudder activity when course keeping. It is therefore desirable to find a way of reducing the loop-gain requirement by attempting to remove some of the plant ignorance. The paper therefore proposes to reduce the plant uncertainty by using an inverse nonlinear compensator derived from a simple linear time-invariant model of the ship. It is then possible to control the resultant modified (and of reduced ignorance) plant with a much smaller loop gain. The paper shows that the design results in consistent manoeuvring performance coupled with much reduced rudder activity during course keeping. The complete compensator is readily realisable in DDC. View full abstract»

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  • Principal gains and phases: insensitive robustness measures for assessing the closed-loop stability property

    Page(s): 233 - 241
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    In the paper, the use of principal gains and phases in assessing the robustness of the closed-loop stability property is examined. An improved version of the recently developed principal gain-phase method is presented, and conditions are derived under which the technique is insensitive to small perturbations. View full abstract»

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  • Analysis of feedback systems with structured uncertainties

    Page(s): 242 - 250
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    The paper introduces a general approach for analysing linear systems with structured uncertainty based on a new generalised spectral theory for matrices. The results of the paper naturally extend techniques based on singular values and eliminate their most serious difficulties. View full abstract»

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  • Stability margins of diagonally perturbed multivariable feedback systems

    Page(s): 251 - 256
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    For diagonally perturbed linear time-invariant multivariable feedback systems, the problem of finding an improved characterisation of the stability margin is examined. A readily computable lower bound for diagonally perturbed systems is developed using Perron-Frobenius non-negative matrix results. The present theory improves upon the existing singular-value stability-margin theory, providing a simple constructive method for determining previously unspecified norm weighting parameters (i.e. scaling factors) so as to minimise the conservativeness of stability-margin bounds. View full abstract»

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  • Frequency-response design of robust optimal controllers

    Page(s): 257 - 262
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    A simple guide to specifying the bandwidth of an optimal control feedback system (as measured by the unity-loop-gain crossover frequency) is developed. A brief description is given of how the guide helps in the design of robust optimally controlled systems. The only information necessary to use the guide is an open-loop gain plot for the plant, thus providing the designer with a powerful design tool, independent of the method used for solving the optimisation problem. View full abstract»

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  • Optimal control of linear uncertain multivariable stochastic systems

    Page(s): 263 - 270
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    A technique is described for the design of linear multivariable systems in which the plant parameters are constant but unknown. These parameters are represented by random variables with known mean values and variances. A Wiener type of z-domain solution is derived to the resulting generalised linear quadratic optimal control problem. These results are also interpreted in the time domain, and the equivalent Kalman filtering solution is derived. To enable the controller to be applied in self-tuning control systems, the plant is represented in discrete polynomial form and a simple diophantine equation solution is also obtained. View full abstract»

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  • State-inequalities approach to control systems with uncertainty

    Page(s): 271 - 275
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    Discrete-time systems with uncertainty are considered. The system description is given in terms of a basic state-space model, which is then extended by the use of inequalities. This approach enables the assessment of performance deterioration due to uncertainty and leads to a design of control system with a given degree of risk. Possible applications of the results to the case of discrete-stage systems are discussed. View full abstract»

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  • Multivariable stability-margin optimisation with decoupling and output regulation

    Page(s): 276 - 282
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    A procedure is developed for maximising frequency-weighted stability-margin singular values for a multivariable linear time-invariant feedback control system subject to design constraints requiring decoupling and asymptotic tracking in the presence of unstable command and disturbance signals and closed-loop stability. The results are derived using Sarason's H¿¿ optimal interpolation results, together with a new multivariable realisability lemma. View full abstract»

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  • Robust control strategy for a linear time-invariant multivariable sampled-data servomechanism problem

    Page(s): 283 - 292
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    A robust control strategy for a linear sampled-data control system such that the error is asymptotically zero not only at, but also between, the sampling instances, in spite of both continuous and discrete disturbances, is proposed. The tracking and the disturbances are assumed to satisfy a linear autonomous differential-difference equation. The control strategy consists of an analogue servocompensator driving the process, a digital servocompensator driven by the tracking error and driving the analogue servocompensator, and a digital stabilising compensator regulating an overall augmented discrete system formed by the discretised process and both the digital and analogue servocompensators. The analogue servocompensator contains the modes of the reference and the disturbance signals; the digital servocompensator contains the modes of the discrete reference and discretised disturbance signals. The tracking error is shown to be asymptotically zero at all times. Also, the control input to the analogue servocompensator is zero in the steady state. If the exogenous signal mode is at the origin, the analogue servocompensator need not contain a simple mode at the origin. However, in this case the control input to the analogue servocompensator is a constant signal in the steady state. View full abstract»

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  • Design of robust digital set-point tracking controllers for linear multivariable plants with time-delayed inputs

    Page(s): 293 - 297
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    It is shown that, for a large class of linear multivariable plants with multiple time-delayed inputs, robust digital set-point tracking controllers can be readily designed. The general design methodolgy is based upon the asymptotic analysis of the closed-loop characteristic roots of digitally controlled plants for large sampling periods, and is illustrated by designing a robust digital set-point tracking controller for a boiler furnace with four inputs and four outputs. View full abstract»

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  • Robust stability of Smith predictor controllers for time-delay systems

    Page(s): 298 - 304
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    The paper considers Smith predictor control structures for multivariable process plant with separable delays on the output and analyses the robustness of the control scheme with respect to mismatch between the real plant and its model and simultaneous changes in plant dynamics. The cases of additive and feedback mismatch are considered separately and represented in the form of easily checked graphical stability criteria in the frequency domain. View full abstract»

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  • Robustness properties of model-reference adaptive control systems

    Page(s): 305 - 309
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    Model-reference adaptive schemes are usually designed on the assumption that the structure of the plant transfer function is known, only the parameter values being uncertain. In the paper, the stability properties of such systems are studied when the plant can only be approximately represented by a model of the type assumed, i.e. when its transfer function does not belong to the class for which exact matching with the reference model can be achieved. View full abstract»

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  • Robust decentralised control using output feedback

    Page(s): 310 - 314
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    A decentralised control scheme is proposed for stabilisation of large-scale systems using dynamic controllers with local output feedback. The scheme is robust with respect to uncertainties in parameters and nonlinearities in the interactions among the subsystems. View full abstract»

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