Control systems and automation-design a system utilising

Question

Control Systems and Automation

Part -1:

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.

FIG. 2

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

FIG. 3

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

5.

FIG. 4

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, V_D, derived from a potentiometer, sets the desired oven temperature, T_D . 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.

FIG. 5

(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, k_o and k_t.

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

PARAMETER	VALUE
kt	10 μ V/°C
ko	6.9 °C/A
k1	6 A/V
k2	2400

TABLE A

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

Fig. 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.

Part -2:

Control Actions

1. A 5 to 20 bar reverse acting proportional pressure controller has an output of 4 to 20 mA. The set point is 11 bar. Determine:

(a) the measured value pressure which gives an output of 15 mA when the proportional band setting of the controller is 40%

(b) the proportional band setting which will give an output of 8 mA when the measured value is 14 bar and the desired value is 11 bar.

2. FIGURE 1(a) shows a flow control system whose output Q_o. is regulated by using a proportional controller to control Q₁. (Note that Q₂ is not controlled). The control system can be represented by the block diagram shown in FIGURE 1(b).

(a) Derive a relationship between Q_o and Q₂, B, C and D_v, where C is the gain of the controller.

(b) If Q₂ is 3000 m³ h^-1 when the bias B is 1000 m³ h^-1, the PB setting of the controller is 40% and the desired value of the controller is 4000 m³h^-1, determine the resultant value of Q_o.

(c) If Q₂ now changes to 2500 m³ h^-1, determine the new bias figure required to ensure that Q_o is maintained at its original flow rate value.

3. (a) With the aid of a sketch explain how proportional action is produced in a pneumatic controller whose output is 0.2 to 1.0 bar. Assume that the controller is direct acting.

(b) Show, mathematically, that the output is dependent on the difference between the measured and desired values.

(c) With the aid of a well annotated sketch describe the construction and operation of a P + I + D controller having a pneumatic output.

4. (a) FIGURE 2 shows an electronic 'black box' whose output is ten times the difference between its two input signals. Show how the 'black box' could be realised using just two operational amplifiers and five resistors. Give the relative values of the resistors.

FIG. 2

(b) With the aid of circuit diagrams show diagrammatically, and prove mathematically, how op-amps are utilized to produce:
(i) integral action
(ii) derivative action.

(c) Show how generation of the above actions are combined with proportional action generation to produce a three term electronic output controller.

5. The proportional control system of FIGURE 3(a) has an input, θ₁, of 10 units. The uncontrolled input, θ₂, has a value of 50 units, prior to a step change down to 40 units. The result of this disturbance upon the output, θ_o, is shown in FIGURE 3(3).

(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)

Fig 3(b)

6. FIGURE 4(a) shows a flow control system that is controlled by a P + I controller. The control objective is to maintain a constant flow rate, Q_o, for varying values of input flow rate, Q₂. The system can be represented by the block diagram shown in FIGURE 4(b).
Assume that the following initial conditions apply.

Dv  I Q2

= = =

2000 1000 1000

ε       =       0 C       =       0.2 Ki      =       0.8

Show that following a permanent step disturbance in Q₂ from 1000 m³ h^-1 to 1200 m³ h^-1, the resulting offset is eliminated.

You should continue your calculations until Q₀ is within 4 m³ h^-1 of its final value for two successive calculations.* Derive any formulae used.

7. (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

8. (a) FIGURE 7 shows the closed-loop response of a plant to a step input when the proportional only gain was set to 4. Use the 'Quarter Amplitude Response Method' to estimate the required settings of a P + I + D controller.

Time (seconds)

FIG. 7 Plant Response to Step Input

(b) If the same plant was 'tuned' using the 'Ultimate Cycle Method', estimate the P + I + D controller settings if a proportional only gain of 6 was required to produce steady oscillations.

Part -3:

Modelling of processes

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.

Fig. 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 how The cross-sectional area of the first tank is A_in m² and the second tank A_out m²

FIG. 2

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 = 10s.

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

https://newton.ex.ac.uk/teaching/CDHW/Feedback/OvSimForm-gen.html,

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.

Part -4:

Control Devices and Systems

1. A control valve is to be used to control water flow at a maximum rate of 120 US gallons per minute. If the maximum pressure drop across the valve is 100 psi, determine the valve size required for this particular application. The table below relates C_v and valve size.

Cv	Valve size (inches)
0.3	0.25
3	0.5
14	1
35	1.5
55	2
108	3
174	4
400	6
725	8

Table 1

2. FIGURE 1 shows the valve characteristics of three different types of valve trim.

FIG. 1

(i) Identify each of the three characteristics.
(ii) State, with reasons, a typical type of application for each of the three types of valve trim.

3. Write brief notes on the following topics:
(a) flashing in control valves
(b) cavitation in control valves
(c) control valve noise
(d) reasons for the use of valve positioners.

4. The level of liquid in an open tank (FIGURE 2) is to be controlled by regulating the flow of liquid into the vessel.
(a) Complete the drawing to show how the level can be controlled by linking the liquid inflow and liquid level controls in cascade.
(b) Draw a control block diagram of the cascaded system.
(c) Describe the response of the cascaded system to a change in the measured level of liquid.

Fig 2

5. FIGURE 3 shows the block diagram of the control of an electric heating system. The heater is driven from a voltage-controlled power supply, the voltage V₁ being derived from a potientiometer. The output temperature, θ_o, is subject to disturbances, θ_D, because of changes in the ambient temperature. It is proposed to apply 'disturbance feedback control' to the system by the inclusion of a transducer that measures the external temperature and feeds a signal back to the input via a proportional controller of gain H.
Determine the required value of H to eliminate the effect of the disturbance.

Fig 3

6. The purpose of the arrangement shown in FIGURE 4 is to mix the two liquid products A and B in a fixed mass ratio. Product A, which is itself a mixture, is a 'wild' flow, whilst product B, a pure compound, is controlled. As the mixture leaves the tank the transmitter ρTX measures its density.
(a) Complete the diagram to show how the arrangement could be controlled by the method of 'variable ratio control'.
(b) Identify which transmitter provides 'feedforward'.
(c) Describe how the control system responds to a disturbance caused by a variation in the density of product A.

Fig 4

7. FIGURE 5 shows a partially completed diagram of a flow control system. The flow controller is reverse acting and has a 0.2 to 1.0 bar pneumatic output signal which will supply both control valves V₁ and V₂.

The small range control valve, V₂, only needs to operate on the first 25% output change of the controller output signal. For larger flow rates the small range valve will remain fully open and control will be achieved by operation of the large range valve. Note the differing air failure action of the two valves.

Design a system utilising valve positioners which will meet the prestated specifications.