LINEARIZED MATHEMATICAL MODEL OF DYNAMIC PROPERTIES OF DIRECT-FLOW ELECTRODE WATER HEATER BY ELECTRIC CURRENT AND VOLTAGE
The research goal is linearized mathematical modeling of the dynamic properties of a direct-flow electrode water heater by the electric current and voltage for subsequent synthesis of the regulator and the formulation of the laws of the microcontroller regulation. The solution of the initial model is complicated by the existence of two nonlinear conditions: the first one is the square dependence of electrode water heater output capacity on the voltage and the current, and the second nonlinearity is the hyperbolic dependence of the electrical resistance of water on the output parameter, temperature. A known solution method of that problem is the linearization of non-linear dependences. The obtaining a linearized model of a direct-flow electrode water heater is discussed. In particular, as a result of Taylor expansion of the known square dependences of electrode water heater output capacity on the voltage and current, the linearized equations of the heater's output capacity as a function of voltage and current are derived. The method of piecewise linear approximation of the R = f (T) function with the prescribed error ε = const at each i interval of approximation is used as a method of linearization of the hyperbolic dependence of electrical resistance of water on the output parameter, temperature. The flowchart of iterative computation of the linearized transfer functions of the temperature of heated water in terms of the voltage and current is developed.