Linear Servo Theory

SIMPLE servo system is one which controls an output quantity The design of linear feedback amplifiers has been developed to a high degree in terms of frequency response; that is, in terms of circuit response to sinusoidal signals.1 The servo system is a special type of feedback amplifier, and usually can be made fairly linear. Thus, it is logical to analyze and design the servo circuit on a frequency response basis. Also, 1 See "Network Analysis and Feedback Amplifier Design," by H. VV. Bode, D. Van Nostrand Co., 1945. 616 LINEAR SERVO THEORY 617 servo systems usually are combinations of electrical, mechanical, thermal, or hydraulic circuits. In order to describe the behavior of these various circuits in homogeneous terms, it is desirable to recognize the analogous relationships established by similarity of the underlying differential equa* tions. Before proceeding to a discussion of frequency analysis, a typical analogy between electrical and mechanical systems will be described. 2.1 Electrical-Mechanical Analogy Confining the discussion to rotating mechanical systems, the analogy which will be chosen here puts voltage equivalent to torque, and current to rotational speed. This choice leads to the array of equivalents shown in Fig. 1; inductance, capacity, and resistance corresponding to inertia, compliance, and mechanical resistance, respectively. Charge is equivalent to angular displacement, and both kinetic and potential energy are selfanalogous. The ratio of voltage to current, or torque to speed has the dimensions of resistance.