TEMPERATURE CONTROL OF LIQUID TANK

Process model

The process model used in the simulator is based on energy balance:

(1) d(crVT₁)/dt = K_eu + cw(T_inn - T₁) + U(T_env - T₁)

where K_eu = P is the power delivered by the heating element. T₁ is the temperature in the tank assuming homogenous conditions. In practice there is a time delay between an excitation in the heating element and the response in the temperature sensor:

(2) T(t) = T₁(t-t)

We assume that this time delay is inversely proportional to the mass flow w:

(3) t = K_t/w

The parameter values are shown on the front panel of the simulator.

By taking the Laplsce transform of the model above we can get the following transfer function from the control signal to the temperature T:

(4) T(s)/u(s) = H(s) = [Ku/(Ts+1)]e^-ts

Thus a first order model with time delay. The parameters of H(s) are:

(5) Gain Ku = K_e/(cw+U)

(6) Time constant T_k = rV/(w+U/c)

(7) Time delay  t = K_t/w

In addition the simulator contains a 1. order transfer function representing a time constant in the heating element. (This submodel is not shown in the model above.)

[KYBSIM] [TechTeach]

Updated August 16, 2004. Developed by Finn Haugen. E-mail: finn@techteach.no.