Control system performance measures: Past, present, and future

Abstract

accepting or rejecting a system design on the basis of this number. In a mathematical sense, this number is a metric, since it gives the "distance" between two functions. The actual process of selecting which metric is to be used to "measure the distance" between a desired output time-function and an approximation to the desired function is, of course, the major difficulty. It is here that a certain amount of personal opinion is found. Surely the choice should be governed by usefulness, in that the particular metric which is selected must be a convenient one to use, as well as one which yields practical results.Because real command signals, disturbances, and even system parameter values have random characteristics, it might be expected that choice of metrics or performance measures might be based upon statistical descriptions of these input functions. In the past, however, such a basis for metric choice seems often to have been more intuitive than explicit, and considerations of mathematical or computer equipment have often hidden a recognition of the underlying statistical problem.The written history of performance measures dates back to 1942, the earliest date of any published material found by the authors. The classified nature of the development of servomechanism theory during World War II con tributed to the delay in publication. For example, an early paper to appear in this country on the subject is the one written by Hall [1] in 1943, which had the classification, "restricted."Although it was not stated in an explicit mathematical form of a metric, the first proposal of a measure of the error of a control system is the "deviation area" concept of Obradovic [2]. His paper appeared in a German publication in 1942. According to Obradovic, the starting point for obtaining the deviation area is to "write the differential equation that describes the system, for example, Summary-An increased amount of emphasis on the mathematical formulation of control system performance can be found in recent literature on automatic control. There are two areas of control system theory in which the application of performance measures is of interest: 1) the evaluation of control system designs in general, and 2) the design of adaptive control systems. In the former case, the performance measure is becoming an increasingly important aid to the control system designer. In the latter case, the performance measure takes on even greater significance, since adaptive systems include, by definition, a performance measure as an essential function which permits correction of system dynamic response during actual operation. Furthermore, the over-all evaluation of the adaptive loop itself presents new problems in the choice and use of performance criteria.In the past, emphasis has been placed on various types of integrals, such as integral of error-squared and integral of the product of time and absolute error (ITAE); present emphasis is being placed on forms of integrals of a more general type; the trend for future emphasis appears to be in...

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