504 AUTOMATIC TRACKING CIRCUITS 



where &ss = steady state error 

 Ri = input position 

 Ri = input rate 

 Ri = input acceleration 

 Kp = position error constant 

 Ky = velocity error constant 

 Ka — acceleration error constant. 



The values for Kp, K^, and Ka are readily derived for a given system-^ by 

 writing the expression 



R. 1 + M D(s) ^""''^ 



with powers of the complex frequency j" = jo^ in increasing order. A direct 

 division of D(j) into N(s) gives the desired constants. Variations in design 

 predicated upon higher derivatives than the second (acceleration) should 

 be avoided.^® 



Steady-state error as a function of time may be found using the input 

 position, velocity, and acceleration found above. The contemplated system 

 is satisfactory if the parameters (corner frequencies) have been selected 

 to cause the maximum error to equal the maximum allowable. 



The best system becomes the one that simultaneously meets the tracking 

 accuracy specifications and requires the minimum bandwidth. Such a 

 system is more readily realizable physically and excludes the maximum 

 amount of extraneous noise. 



Redesign. In the foregoing paragraphs a design procedure leading to 

 an initial trial design of a linear ^ervo system has been given. Before such 

 a system would be' recommended, the transient response, the possibilities 

 of improvement using nonlinear techniques, and the compatibility with 

 respect to the system environment should be studied. Methods of design 

 permitting prescribed steady-state and transient response have been 

 developed. Other developments indicate that the entire design may be 

 accomplished in the time domain. The foregoing notes refer to the older 

 steady-state design procedure. 



25A. S. Locke, Guidance, pp. 230-263. 

 26J. G. Truxal, op. cit., pp. 236-245. 



