Reference no: EM133001598

Question 1. Figure 2 shows an electrical circuit.

a) Showing all working, derive the following differential equation which describes the circuit;

RC dy(t)/dt + y(t) = RC.dx(t)/dt

b) Obtain the transfer function for the circuit,

c) Calculate the static or steady-state gain of the circuit

d) State whether the circuit is a; low-pass, high-pass, or band-pass filter

e) State whether the transfer function obtained in part b) is improper, proper or strictly proper

Question 2. A dynamic transfer function describing superheated steam temperature (CC) for mass of fuel (kg) input for the inner loop of thermal power plant when operating at 75% load is as follows;

G(s) = 1.657/(20s+1)²

Find the following;
a) system order/number of poles
b natural frequency
c) static gain
d) damping ratio

e) whether the system is underdamped, critically damped or overdamped - will there be any overshoot?

f) maximum phase shift for a system with a transfer function of this type/order (2 poles, no zeros) at very high frequencies

g) two first order transfer functions which could be cascaded and represent the same dynamics as the transfer function above

Question 3. The outlet substrate concentration Y (mol/L) of a stirred tank biorcaetor has dynamic response (Fig. 2) to a unit step change in feed substrate concentration X (rnolilL). Find the following;

a) static gain
b) time constant
c) transfer function model (Y(s)/i(s))
d) time domain function (y(t)=?)
e) If feed substrate concentration is suddenly increased to 2 mol/L at t=60s, what will the outlet substrate concentration be at t= 80s?