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1. This assignment forms part of the formal assessment for this module. If you fail to reach the required standard for the assignment then you will be allowed to resubmit but a resubmission will only be eligible for a Pass grade, not a Merit or Distinction.

You should therefore not submit the assignment until you are reasonably sure that you have completed it successfully. Seek your tutor's advice if unsure.

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1. Choose a simple single control loop used on a process you are familiar with (it could be domestic or industrial).

(a) Explain why the control is necessary.

(b) Write a description of the control system.

(c) Produce an algorithm of the control system.

(d) Draw a block diagram of the control system.

(e) State the type(s) of signal used in the process.

(f) State whether the control is open or closed loop, feed forward or feedback.

(g) State and describe the sensor used for measuring the process variable to be controlled.

2. The curve in FIGURE 1 shows the response of a bare thermocouple which has been subjected to a step change in temperature from 50°C to 10°C. Assuming that the bare thermocouple behaves as a single transfer lag system, determine the mathematical relationship between the temperature (T) and time (t) [i.e. determine the equation relating T to t].

3. FIGURE 2 shows the behaviour of a control system which has been switched from manual to automatic mode. Comment on the conditions existing in the control loop which would have given rise to the response shown.

System output

4. FIGURE 3 shows an open loop system containing a distance velocity lag and a single transfer lag.

If the system input x_i is subjected to a step disturbance from 2 units to 12 units, plot the response of x₀ on a base of time. Determine graphically, and verify mathematically, the time taken for the output to change by 4 units.

5.

Derive the closed loop transfer functions for the system shown in FIGURE 4 and show that for large values of G the value of V_o/V_i approaches unity.

6. FIGURE 5 shows an electrically heated oven and its associated control circuitry. The current, I, to the oven's heating element is fed from a voltage-controlled power amplifier such that I = εK₁. A voltage, VD, derived from a potentiometer, sets the desired oven temperature, TD. The oven temperature is measured using a thermocouple that, for simplicity, is assumed to generate a constant emf of 10 μV per degree Celsius. The effect of the ambient temperature is ignored.

(i) Represent the arrangement by a conventional control-system block diagram. Identify the following elements in the block diagram:

input; error detector (comparator); controller; controlled element; detecting element and feedback loop.

(ii) Derive an expression for the transfer function of the system, in terms of the system parameters k1, k2, kO and kt.

(iii) Using the data given in TABLE A, calculate the oven temperature when the potentiometer is at its mid-point.

TABLE A

7. (a) Derive an expression for the closed loop transfer function θ_o/θ_i for control system shown in FIGURE 6.

(b) Show that the value of θ_o/θ_i is 0.8 when the following values of the various control loop elements are adopted:

K₁ = 10
K₂ = 2
K₃ = 5
K₄ = 0.4
K₅ = 0.9