Assignment

1. (a) Models can be classified into three categories, depending upon how they are developed.
(i) Name these three categories of model.
(ii) Give an advantage and disadvantage of each category.

(b) Explain what is meant by:

(i) a steady- state model
(ii) a dynamic model.

(c) State which type of model is most commonly produced and explain why.

2. A steady state distillation process is shown diagrammatically as FIGURE 1.

Assuming no heat losses to the atmosphere:

(i) Write four balanced equations for this system.

(ii) Identify where any constitutive equations may be required for the modelling processes.

3. (a) FIGURE 2 shows two cylindrical tanks interconnected with a pipe which has a valve that creates a constant resistance to flow of R_f when fully open. The height of liquid (of density ρ) in the first tank is h_in and the second tank h_out. The cross-sectional area of the first tank is A_in m² and the second tank A_out m².

The flow rate of liquid through the valve is given by

Q = (1/R_f) (p_in - p_out)

where Q = flow rate in m³ s^-1

p_in- pressure due to height of liquid in first tank (Pa)
p_out- pressure due to height of liquid in second tank (Pa)

Produce a mathematical model of the process to determine the change in height of fluid in the second tank when the valve is open.

(b) Determine the time constant for the system.

4. A process can be represented by the first order equation

4{dy(t)/dt} + y(t) = 3u(t)

Assume the initial state is steady (y = 0 at t = -0).

(a) Determine the transfer function of this process in the s domain.

(b) If the input is a ramp change in u(t) = 4t, determine the value of y(t) when t = 10 s.

5. Using a simulator of your own choice, or the one used during the lessons at the website;

Note the initial values used by the simulator and the output produced.

For BOTH ON-OFF and PID control,

(a) sketch (or print copies) of the effect of changing the following parameters from their existing value (resetting them to the original after every change has been recorded):

(i) Increasing the proportional control by a factor of 10.

(ii) Decreasing proportional control by a factor of 10.

(iii) Increasing the integral control by a factor of 10.

(iv) Decreasing integral control by a factor of 10.

(v) Increasing the derivative control by a factor of 10.

(vi) Decreasing derivative control by a factor of 10.

(vii) Increasing the hysteresis by a factor of 10.

(viii) Decreasing hysteresis by a factor of 10.

(ix) Increasing the system lag by a factor of 10.

(x) Decreasing system lag by a factor of 10.

(b) Explain your results.