MAXIMUM DYNAMIC ERRORS OF LEGENDRE FILTERS IN CONTROL AND CONTROL SYSTEMS
Abstract
In control and monitoring systems, low-pass filters and band-pass filters are most often used.
To limit the spectrum of signals from sensors, analog, discrete-analog and digital filters are widely used,
the amplitude-frequency characteristics of which are approximated by various mathematical functions,
incl. Legendre polynomials. The use of Legendre filters in the circuit of an automatic control system leads
to a change in its dynamic characteristics. The nature of this influence depends on the order of the filter
transfer function, as well as on the type of approximation that are chosen when designing the control and
monitoring system. The information delay in such filters causes the appearance of a dynamic component
of their error, which affects the overall error of the control and monitoring system, which reduces the
permissible speed of its operation. The article provides an analytical assessment of the dependence of the
magnitude of the dynamic error for low-pass and bandpass Legendre filters. This allows you to quickly
solve the direct and inverse problems of error distribution of the control and monitoring system and justify
the speed of its operation. The article analyzes the Legendre bandpass filter circuits of the first, second
and third orders, and then the results obtained are generalized to the Legendre bandpass filter of an arbitrary
order. It is shown that for low-pass filters the values of maximum dynamic errors can be obtained
with high accuracy. For Legendre bandpass filters, the errors in approximation of the mathematical dependence
of the maximum dynamic errors on the filter parameters are determined in units of percent, but
in some cases they can reach 20%.
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