DT009 Year 3
Control and Automation
Minor
Revision Worksheet
Questions
1. Explain
the terms open loop and closed loop as applied to a control system. Illustrate your answer by reference to a
particular example of each system and sketch its relevant block diagram.
2. What is meant by the term proportional gain?
Explain proportional offset and describe how it is affected by changing the proportional gain.
What is the danger in making the proportional gain too large?
3. What is meant by the term integral control and why is it often used in control systems?
4. Describe the ultimate cycle and process reaction curve methods of tuning a PID control loop. Name one disadvantage of using the ultimate cycle method.
5. Explain each of the four steps which make up the programme scan cycle of a PLC.
6. (a) Write a ladder logic program to correctly implement Start/Stop control of a fixed speed motor by a PLC. What types of push buttons are normally used for Start and Stop and why are they used?
(b) Level control in a tank using two level switches (high and low) can be done using very similar code. Can you write it? The high level switch gives zero on high level and the low level switch gives zero on low level. For each of the level switches define whether it is normally open or closed.
7. (i) Write a fully commented program to configure a Mitsubishi FX-4AD analogue input card for the following situation:
The card is installed in the first slot next to the PLC
Channels 4, 3 and 2 are off (no field devices connected)
Channel 1 is connected to a 4 to 20 mA temperature transmitter
The number of averages for channel 1 is set to 100
The averaged value from channel 1 is read into address D0.
(ii) How can the effect of noise be reduced in the analogue input card configuration?
(iii) Why is an instrument cable typically a shielded, twisted pair?
(iv) Why is current preferred to voltage in the transmission of control signals?
8. The block diagram for a simple proportional control system is shown in Figure Q8a, where:
qi is an input signal which represents some desired state of the process
Kp is the gain of the proportional controller
K is the static gain of a process
t is the time constant of the process
qo represents the output from the process
Figure Q8a
Reduce the block diagram above to a single block which relates qo to qi and hence write down the overall transfer function for this system
Rearrange the result for the transfer function to show that the overall system is first order and use this to define the static gain and time constant of the overall system.
9. Figure Q8, below, shows the block diagram for a simple proportional control system where:
G represents a mathematical model of some process which must be controlled
qo represents the output from the process
qi is an input signal which represents some desired state of the process
Kp is the gain of the proportional controller
b represents the behaviour of some measuring system
Explain the operation of the system, illustrating your answer with a suitable example.
Reduce the block diagram above to a single block which relates qo to qi and hence show that a proportional control system can never force the process output to exactly match the input.
Given that the steady state gain of the process (G) in the above is 0.8, b is 2 and Kp is 10, calculate the magnitude of qo when qi is a steady value of 10.
Is there any danger in making Kp larger and larger in an effort to achieve zero steady state error
10. The figure below shows the block diagram for a control system that has a proportional controller acting on a first order process with unity feedback.
(i) Resolve the above into one block and show the transfer function of the overall system. Rearrange to show that the system is first order type and state the static gain and time constant of the over all system.
(ii) Given a static gain of 5 for the process, determine the proportional gain required to make the time constant of the system equal to 1/10th the time constant of the process. In this case, what is the steady state error?
11. The movement of mercury, and hence the temperature displayed, by a mercury-in-glass thermometer when it is immersed in a bath of water is described by the following first-order differential equation:
where t is the time constant
qout is the displayed temperature
qin is the water bath temperature
(i) Use a
(ii) What is the frequency domain equation for the output from the system if a step change in the input of magnitude a is applied?
(iii) Use an inverse Laplace transform to give the equation for the output from the system in the time domain based on a step change in the input of magnitude a.
(iv) A mercury-in-glass thermometer with a time constant of 5 s is allowed to reach steady state in a beaker of ice and water before it is quickly placed into a beaker of boiling water. Write down the equation that describes how the temperature displayed on the thermometer changes with time and from this determine the temperature displayed after three time constants.
12. The contents of a batch reactor are heated by passing steam through a jacket surrounding the reactor. The relationship between the reactor temperature, TR, and the temperature of the steam supplied to the jacket, TJ, is described by the first-order differential equation
where t is the time constant
TR is the temperature of the reactor contents
TJ is the jacket temperature
(i) Use
(ii) What is the frequency domain equation for the output from the system if a step change in the input of magnitude a is applied?
(iii) Apply the inverse
(iv) A jacketed reactor with a time constant of 5 s is allowed to reach a steady state temperature of 0°C before the steam valve is opened allowing steam at a temperature of 100°C to enter the jacket. Write an equation describing the variation of temperature of the reactor contents with time and from this determine the reactor temperature after three time constants.
13. The temperature of a batch reactor is controlled by a Programmable Logic Controller (PLC). The reactor is heated by an electric element situated at the base of the reactor. An RTD based temperature measurement system is used to monitor the temperature of the water in the reactor. The RTD is connected to the PLC via a signal conditioning circuit. An On-Off control algorithm is used in the PLC to switch the output to the electric heater.
(i) Draw a block diagram indicating all the components and variables in the system.
(ii) Explain why On-Off control is suitable for this application.
(iii) What improvement could be made to the control algorithm to prolong the life of the electric heater?
(iv) Sketch the time response of the following system variables:
Power to the electric heater
Reactor temperature
Error
14. The contents of a batch reactor are heated by passing steam through a jacket surrounding the reactor. The relationship between the reactor temperature, TR, and the temperature of the steam supplied to the jacket, TJ, is described by the first-order differential equation
where t is the time constant
TR is the temperature of the reactor contents
TJ is the jacket temperature
(i) Use
(ii) What is the frequency domain equation for the output from the system if the input is ramped at a constant rate of 1ēC/second (ramp of unit slope)?
(iii) Apply the inverse
(iv) A jacketed reactor with a time constant of 40 seconds is allowed to reach a steady state temperature of 0°C before the temperature of the jacket is ramped at a constant rate of 1ēC/second. Write an equation describing the variation of temperature of the reactor contents with time and from this sketch how the reactor temperature changes with time.
What is the temperature of the reactor after 4 minutes of ramping the temperature?
15. Write the equation for a three term PID controller and briefly explain the function of each term.