Position control of temperature of electric resistance furnace

The problem of determining the frequency and amplitude of temperature fluctuations of the heating furnace by resistance at positional regulation with the help of unipolar ideal relay and relay with loop characteristic is considered. The aim is to optimize the operation of the two furnaces in the power supply system so that the furnaces are not switched on simultaneously in the temperature stabilization mode. In the literature, as a rule, simplified examples of tracking systems with the use of an ideal relay are considered, various methods of accurate and approximate methods for determining the frequency and amplitude of symmetric oscillations are given, however, with asymmetric oscillations, taking into account the displacement, the most acceptable is the algebraic method using the harmonic linearization method, with the dependence of the frequency and amplitude of the oscillations on the relay characteristic loop parameter in order to assign this parameter at an acceptable temperature deviation. The coefficients of the harmonic linearization of a relay with a loop characteristic with allowance for bias are complex expressions involving the amount of displacement. To simplify the calculations, the limiting variant is adopted, when the magnitude of the amplitude of the oscillations is equal to the sum of the displacement and half the width of the relay loop.