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.

3

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].

FIG. 1

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

FIG. 3

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

5

.

4. 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 = K1. 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 V per degree Celsius. The effect of the ambient temperature is ignored.

Power

12 V supply

Oven

FIG. 5

6

(a) 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.

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

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

PARAMETER VALUE

kt 10 V/°C

kO 6.9 °C/A

k1 6 A/V

k2 2400

TABLE A

5

5. The proportional control system of FIGURE 3(a) has an input, 1, of 10 units. The uncontrolled input, 2, has a value of 50 units, prior to a step change down to 40 units. The result of this disturbance upon the output, o, is shown in FIGURE 3(b).

(a) Calculate the change in offset in the output produced by the step change.

(b) Draw a modified block diagram to show how the offset could be minimised by the inclusion of another control action. Also, show by means of a sketch how the modification might be expected to affect the output response.

(c) Show, by drawing a modified block diagram, how the magnitude of the disturbance could be minimised by the inclusion of a third type of control action.

Fig 3 (a)

Time (minutes)

Fig 3 (b)

6. (a) FIGURE 5 shows the input and output waveforms for a proportional plus integral controller. State: (i) the controller’s proportional gain

(ii) the controller’s integral action time

Fig 5

(b) FIGURE 6 shows a proportional plus derivative controller that has a proportional band of 20% and a derivative action time of 0.1 minutes. Construct the shape of the output waveform for the triangular input waveform shown, if the input rises and falls at the rate of 4 units per minute.

Fig 6