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Minimization of Mean-Square Error and Quadratic Integral Estimate of Servo Systems’ Transients with the Help of the First and the Second Derivatives of Random Master Control

Keywords:

G.N. Arsenyev, Ye.V. Maslyonkin


The presence or absence of contradiction between the conditions of minimization of the mean-square error and the quadratic integral estimate depends not only on a system (its transfer function), but also on the character of random master control. For the case under consideration, when the non-stationary master control (its speed variation considered as a stationary random process) is fed to the input of a servo system, whose 2nd order of integration is achieved due to feeding of the first and the second derivatives of master control, the contradiction between the conditions of minimization of the mean-square error and the quadratic integral estimate is absent. Thus, in the case being considered the contradiction between the conditions of minimization of the mean-square error and the quadratic integral estimate is absent as both the mean-square error and the quadratic integral estimate decrease simultaneously with feeding into the system of the first and the second derivatives of master control. In conclusion the following summary may be done: 1. The feeding into the system of the first and the second derivatives of master control essentially reduces the mean-square error in comparison with both the system based on the principle of deviation control with the integration of the 1st order, and the combined system, into which the first derivative of master control is fed through the broken connection. 2. The optimum values of the time constant and of the first and the second derivatives of master control, at which the minimum mean-square error of a system is achieved, are equal to values and obtained from the condition of integration order increase from the first up to the second. 3. With the help of the second derivative of master control it is possible to reduce not only the mean-square error, but also the quadratic integral estimate in comparison with deviation control system and combined system, whose second order of integration is achieved with the help of the first derivative of master control. 4. Due to the fact, that the feeding of the first and the second derivative of master control into the system allows to reduce the mean-square error and the quadratic integral estimate on the same (significant) section of variation , the contradiction between the conditions of minimization of the mean-square error and the quadratic integral esti-mate disappears.
References:
June 24, 2020
May 29, 2020

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