The design of systems for automatic control of the position of massive objects

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 log-gain/log-frequency 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 power-amplifying 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 non-thermionic amplifier stages. By introducing explicitly the relationship which exists between power amplification and the associated time-constants 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 machine-amplifier 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 ?phase-utilization 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 power-amplifying element and for the design of the most satisfactory elements. The specification, and its implications in terms of the required log-gain/log-frequency 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 machine-amplifier elements to provide the power amplification is discussed and the concept of phase utilization is developed, making use of the fact that the time-constants 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