Abstract
Analytical methods of analysis for linear feedback control systems are extended to include distributed lag in its most generalized form (terminating impedance having both resistive and reactive components). Methods are developed for examining analytically the effect of the distributed lag element with general impedance termination on the performance of a linear feedback control system in regard to frequency response, root locus, and time response to a specified input. In the analytical development a generalized approach is used resulting in mathematics and corresponding computer programs that are readily usable for a wide variety of distributed lag systems containing any type and combination of input, cascaded element, and termination impedance. The only restriction of the methods developed is that each element or variable within the system is linear and can be described by a Laplace transform. In the development of the root locus equations the transformation w = [square root]s is used to simplify the mathematics describing the root loci. The method is extended by projecting the root loci back into the s plane within the area of interest for convenience in interpretation of these loci in regard to stability and transient response. For calculating the time response an explicit inversion technique is employed that makes use of the shifted Legendre polynomials and a Gaussian quadrature formula to approximate the indefinite integral. The technique features a method of time scaling that permits calculation of the time response within any desired interval of time. Using the analytical methods developed, typical first and second order distributed lag systems are analyzed for various combinations and values of system parameters. The calculated values of the first order distributed lag system obtained by use of the digital computer are compared with those measured in a laboratory simulation using a distributed lag model in conjunction with the analog computer.
Ivy, Edward Weber (1965). An analysis of distributed lag in feedback control systems with general impedance termination. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -176422.