502 AUTOMATIC TRACKING CIRCUITS 



9-12 SERVO SYSTEM TRANSFER FUNCTION 



RELATIONSHIP TO INPUT TIME FUNCTION FOR A 

 RANGE TRACKING SYSTEM^i 



Target and interceptor flight-path analysis provides a time-function 

 specification for automatic range and angle tracking radar servo-system in- 

 puts. Whereas the tactical problem is entirely a time-domain phenomenon, 

 servo-system design procedures depend upon both time- and frequency- 

 domain quantities. The salient points in the practical realization of an 

 appropriate servo-system transfer characteristic in the preliminary design 

 stage are outlined in the following paragraphs. 



In radar systems, the received signal contains the desired information 

 together with uncorrected noise components. To proceed with the servo- 

 system design on a rational basis, the nature of the undesired noise should 

 be determined. The noise spectral density, its mean value relative to the 

 desired information, and the maximum excursions should be known. 



Tactical Problem Inputs. The initial considerations common to 

 automatic tracking servo-system preliminary design studies include: 



1. From the space geometry involved, derive analytical expressions for 

 the input position as a function of time. Take derivatives to find the 

 velocity and acceleration. 



2. Study the tactical situation and choose as typical problems those that 

 appear to place the most stringent demands upon the servo system under 

 study, i.e., the highest values of input velocity and acceleration. 



3. Select one set of parameter values to define the design problem. 

 Prepare accurate graphs of position, velocity, and acceleration as functions 

 of time. 



4. Make a critical appraisal of the desired performance to establish the 

 maximum allowable tracking error. 



Transformation to Frequency Domain. The intelligence to be 

 tracked is given by the input time function; however, the equivalent 

 frequency-domain transformation is desired. "Initial conditions" at the 

 start and end of the tracking period affect the resulting frequency-domain 

 equivalent. For some- geometries a direct analytic transformation may be 

 made, but in general a graphical procedure is needed. 



Any arbitrary function of time may be transformed to the frequency 

 domain by Guillemin's"'"^ impulse method, in which the integrand of the 



2iDiscussions with members of the Radar Division, U.S. Naval Research Laboratory — 

 especially with J. P. Dougherty and S. F. George — materially aided the author in rounding 

 out some of the concepts presented. 



22E. A. Guiilemin, "Computational Techniques which Simplify the Correlations Between 

 Steady-State and Transient Response of Filters and Other Networks," Proc. Nat. Electronics 

 Conf. 1953, 9, 513-532 (1954). 



2»J. G. Truxal, Automatic Feedback Control System Synthesis, pp. 379-382, New York: 

 McGraw-Hill Book Co., Inc.. 1955. 



