Design of Modern Control Systems
This book presents developments in analysis and design techniques for control systems. Included are exciting results for feedback systems using complex variable methods, the important concept of robustness in controller design and the increasingly important topic of decentralised control for large scale systems. The book also illustrates the great activity and rapid progress which has taken place in the subject over the past few years.
Inspec keywords: boilers; robust control; pole assignment; feedback; statespace methods; Nyquist stability; optimal control; control system synthesis; mathematical programming; nuclear power stations; control system analysis; distributed parameter systems; nonlinear control systems; multivariable systems; decentralised control
Other keywords: variable control system design robustness; feedback system analysis; DDC system design; pole assignment; optimal control; characteristic locus method; robust controller; complex variable method; nuclear boiler control; mathematical programming; feedback system design; inverse Nyquist array design; statespace theory; distributed parameter system control; multivariable design optimisation; decentralised control; nonlinear control system
Subjects: Nuclear power stations and plants; Multivariable control systems; Optimal control; Distributed parameter control systems; Optimisation techniques; Control system analysis and synthesis methods; Stability in control theory; Control of nuclear systems; Nonlinear control systems
 Book DOI: 10.1049/PBCE020E
 Chapter DOI: 10.1049/PBCE020E
 ISBN: 9780906048740
 eISBN: 9781849193344
 Page count: 344
 Format: PDF

Front Matter
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1 Statespace theory
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A brief review is given of the use of statespace methods in the study of linear timeinvariant systems. Topics covered include modal decomposition, controllability and observability, standard forms, calculation of transfer function matrices, construction of statespace realizations and system inversion.

2 Complex variable methods in feedback systems analysis and design
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Generalized Nyquist and generalized RootLocus diagrams are algebraic curves derived from the spectral analysis of appropriate matrixvalued functions of a complex variable. Their key properties can be comprehensively analysed in terms of a statespace model of the feedback loop which is being studied Such an analysis is essentially geometrical in nature and is concerned with the way in which certain subspaces, defined via the various operators involved, sit with respect to one another, and with ways of assigning complex frequencies to these subspaces. The current status of work on the' design of feedback systems using these results is briefly discussed, and possible future developments are noted.

3 Robustness in variable control systems design
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In this chapter, techniques are described for assessing the relative stability of a multivariable control system design. An interesting and important feature in multivariable feedback systems is that they have different stability margins at different points in their configuration. According to the generalized Nyquist stability criterion the feedback system is stable if, and only if, the number of anticlockwise encirclements of the critical point 1 by the characteristic gain loci, is equal to the number of openloop unstable poles.

4 A design study using the characteristic locus method
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A 3input multivariable control system is developed for the regulation of the product concentration and temperature of a 2bed exothermic catalytic reactor. Two of the inputs are the flow rate and temperature of a quench stream injected between the beds; the third input is the feed temperature. Through the use of the characteristic locus method of control system analysis, a cascade of dynamic compensators is developed by which interaction among variables is suppressed and the effects of feed concentration disturbances are con trolled. In this development, an analysis is made of the potential improvements in performance accruing from the use of internal bed temperature measurements. The system also has the feature of resetting the quench flow rate to its nominal value upon sustained system disturbance.

5 The inverse Nyquist array design method
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The general problem of the design of multivariable control systems is considered and the stability of multivariable feedback systems is examined. The concept of 'diagonal dominance' is introduced, and Rosenbrock's Inverse Nyquist Array Design Method is developed. Methods of achieving diagonal dominance are discussed and illustrated in terms of practical problems.

6 Analysis and design of a nuclear boiler control scheme
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The steam raising plant of a British designed nuclear power station for which the installed control scheme has given rise to performance and stability problems is considered. The lecture is based on studies carried out for the plant which illustrate the way in which multivariable frequency response methods can be used to analyse and identify the source of control problems and further enable alternative control schemes, having improved performance, to be designed.

7 Optimal control
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An overview of dynamic optimization is presented which commences with a statement of the important conditions from classical theory including the Weierstrass Efunction and the second variation. The classical results are then reformulated in modern optimal control notation which leads immediately to a statement of Pontryagin's Minimum Principle. Necessary conditions for optimality of singular trajectories are deduced from the theory of the second variation. A description of Dynamic Programming is followed by a study of the HamiltonJacobi approach for the linear system/quadratic cost problem together with the associated matrix Riccati equation.

8 Control system design via mathematical programming
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Control design requires the choice both of structure of the controller and parameters for a given structure; the first task is guided by system theory; the latter is aided by mathematical programming. For a given control structure design objectives can often be specified as satisfying a set of inequalities or minimizing a function subject to these in equalities. It is shown that many objectives can be expressed as infinite dimensional constraints (φ(z,α) ≤ 0 for all α ∈ A). Algorithms for the resultant semiinfinite programming problems are briefly outlined.

9 Optimisation in multivariable design
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Three new basic algorithms to achieve diagonal dominance will be described in this chapter: (i) to choose optimum per mutation of input or output variables of the plant; (ii) the optimal choice of scaling factors, and (iii) to find a real precompensator to optimise dominance measure of the compensated plant.

10 Pole assignment
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In this chapter, pole assignment is discussed. The problem of pole assignment using state feedback or output feedback is examined. An algorithm for the design of full rank minimum degree outputfeedback compensators is presented and results in a unification of previously obtained results. Pole assignment is simply concerned with moving the poles (or eigenvalues) of a given timeinvariant linear system to a specified set of locations in the splane (subject to complex pairing) by means of state or output feedback. The statefeedback approach is well established, however the outputfeedback case is still being explored as a research area.

11 Nonlinear systems
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Some methods for analysing the behaviour of nonlinear dynamical systems are discussed. Attention is concentrated on the use of describing functions for predicting limit cycles and Lyapunov's method for investigating stability. A brief treatment of absolute stability criteria and their use is also given.

12 Some DDC system design procedures
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As a result of the enormous impact of microprocessors, electronic engineers, with sometimes only a cursory back ground in control theory, are being involved in direct digitalcontrol (D.D.C.) system design. There appears to be a real need for an easily understood and simply imple mented comprehensive design technique for singleinput d.d.c. systems. The proposed design technique provides, first of all, a simple calculation that ensures that the data sampling rate is consistent with the control system's accuracy specification or the fatigue life of its actuators. Pulsed transferfunction design for a plant controller is based on two simple rules and a few standard frequency response curves, which are easily computed once and for all time. Structural resonances are eliminated by digital notch filters, the polezero locations of which are directly re lated to the frequency and bandwidth of an oscillatory mode; this is exactly as with analogue networks. In addition a computationally simple formula gives an upper bound on the amplitude of the control error (deviation) component due to multiplicative rounding effects in the digital computer; this thereby enables the selection of a suitable machine wordlength or machine. A distinct advantage of the proposed design technique is that its implementation does not necess arily involve a complex computeraideddesign facility.

13 Robust controller design
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An overview of some recent results in the controller de sign of multivariable linear timeinvariant systems, in which uncertainty/perturbation in plant behaviour occurs is made. In particular, the servomechanism problem is considered for various cases varying from the extreme case when the plant is known and fixed, to the opposite extreme when the plant is completely unknown and is allowed to be perturbed. In addition, the chapter includes the case of time lag systems, decentralized systems and the control of systems subject to sensor/actuator failure. The emphasis throughout is to characterize structural results for the servomechanism problem, e.g. to determine the existence of a solution to the problem and to determine the controller structure required to solve the problem under different conditions. The chapter concludes with a proposed design method for obtaining realistic robust controller design.

14 Control of distributed parameter systems
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Much of control theory is concerned with systems which are modelled by ordinary differential equations, socalled lumped parameter systems. In this chapter it is shown how the concepts of controllability, observability, optimal control and estimation may be investigated for system models based upon partial differential equations, socalled distributed parameter systems. Such a system with a single input and a single output is used to illustrate the theory presented.

15 Decentralised control
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In this chapter we give a brief overview of some of the recent results in decentralised control. Both the stochastic decentralised control as well as the deterministic decentralised control literature are reviewed. Some of the decentralised design techniques are also outlined.

Back Matter
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