Proceedings of the IEE  Part C: Monographs
Volume 105, Issue 1S, 1958
Volumes & issues:
Volume 105, Issue 1S
1958

 Author(s): A. Tustin ; J.T. Allanson ; J.M. Layton ; R.J. Jakeways
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 1S, p. 1 –57
 DOI: 10.1049/pic.1958.0001
 Type: Article
 + Show details  Hide details

p.
1
–57
(57)
The particular class of automatic feedback control systems is considered in which the purpose is to move a massive body in agreement with the variations of an input quantity, usually the angular displacement of an input shaft, and in which the power required for the movement of the load is large, i.e. far beyond the possibility of provision directly from a thermionic amplifier. Additional power amplification must then be provided, for example by magnetic or rotary amplifiers. By confining attention to a restricted class of system it is possible to suggest procedures by which the simplest system that will ensure a specified performance may be designed with a minimum of trial and error. The requirements for satisfactory performance are reviewed, and it is shown how they may conflict. The design of such systems is constrained by the need for limitation of torques and speeds, by the possible occurrence of random disturbances, by the need for smooth operation at low speeds, and by many other considerations not taken into account in discussions of control systems in general. It is shown how these restrictions may usefully be regarded as restrictions on the loggain/logfrequency diagram. In arranging a design to meet these requirements the usual procedure of taking the elements of a basic control loop as given and designing a modifying network to secure stability is inappropriate. The timeconstants associated with the poweramplifying elements depend on the power and dominate the design. The conventional procedure is therefore supplemented by a different approach. By making certain minimal assumptions about the characteristics of a modifying network or phase advancer eventually to be designed, the possibility is considered of meeting the specification by suitable choice and arrangement of the nonthermionic amplifier stages. By introducing explicitly the relationship which exists between power amplification and the associated timeconstants it is found possible to express the condition for adequate damping, i.e. the satisfaction of Nyquist's criterion with adequate margin, in terms of the requisite power amplification and accuracy, together with simple functions which are characteristic for the various classes of machineamplifier element that may be used. These characteristic functions express the contribution made towards meeting the requirements in using up the limited amount of phase lag allowable. Such functions of phase angle have been called ‘phaseutilization functions’, and for given classes of dynamically similar element they may be calculated once and for all. These functions provide a basis for comparing the merits of different forms of poweramplifying element and for the design of the most satisfactory elements. The specification, and its implications in terms of the required loggain/logfrequency characteristic, is the topic of Section 1. It is then necessary to discuss in some detail the design of the motor and the generator that feeds it, which must be adequate to give the required movements to the load, these movements being defined statistically. This is done in Section 2, which leads to a definition of the power amplification required and a basis for ensuring that all elements have adequate rating. It also provides a prior estimate of the supplementary small angle of lag or lead associated with the motor armature circuit. In Section 3 the selection of machineamplifier elements to provide the power amplification is discussed and the concept of phase utilization is developed, making use of the fact that the timeconstants are related to the power amplification. Section 4 shows how modifying networks for insertion in the thermionic stages may be selected, when it has been ensured by the principles discussed in Sections 1 and 3 that the requirements can be met. Section 5 discusses the use of feedback on machines as a contribution to meeting the requirements. It is shown that the apparent benefits of some types of feedback may be offset by reduction of power amplification, and this leads to discussion of feedback by such means as transformers, which introduce a derivative term. A concluding Section (No. 6) discusses briefly how a physical construction may be achieved to conform with the timeconstants found to be desirable, the general nature of the limitations to the attainable performance and some possibilities of improvement.  Author(s): A. Tustin
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 1S, p. 58 –62
 DOI: 10.1049/pic.1958.0002
 Type: Article
 + Show details  Hide details

p.
58
–62
(5)
The essential theorems of dimensional analysis are reviewed and related to the familiar process of normalizing or ‘nondimensionizing’, by which the results of calculation or observation of relationships between varying quantities may be expressed so as to be applicable to many possible observations. In recording or cataloguing the behaviour of systems of given kinds having various combinations of values of parameters, it is desirable to express the behaviour in terms of the fewest possible composite parameters. It is shown that, for transfer functions, this is achieved by the usual process of normalizing applied to the transfer function when expressed in the form of a ratio of polynomials in p. In systems with feedback this number of parameters may be smaller than the number of the ratios of independent timeconstants of the equations. This implies that systems with feedback may have dynamically similar behaviour, even though their basic timeconstants are in different ratios. Consideration is given to systems involving nonlinear relationship. In such cases the choice of the products, having dimension zero, in terms of which results may most effectively be recorded is particularly important and may be less obvious. A procedure is outlined, using the concepts of sets of affine curves and representative values, by which the appropriate composite variables may be discovered.
The design of systems for automatic control of the position of massive objects
Similarity and dimensional relationships in control systems
Most viewed content for this Journal
Article
content/journals/pic
Journal
5
Most cited content for this Journal

Breakdown of solid dielectrics in divergent fields
 Author(s): J.H. Mason
 Type: Article

Perturbation theory of resonant cavities
 Author(s): R.A. Waldron
 Type: Article

The energyintegral criterion of transient stability limits of power systems
 Author(s): P.D. Aylett
 Type: Article

Double knifeedge diffraction in fieldstrength predictions
 Author(s): G. Millington ; R. Hewitt ; F.S. Immirzi
 Type: Article

The order of complexity of electrical networks
 Author(s): P.R. Bryant
 Type: Article