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Control Modes System Response

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Submitted By sonkab
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HNC in Electrical and Electronic Engineering

Control Systems & Automation

Control Modes and System Response

Contents

Introduction 3
Brief 3
Tasks 4
Task 1 4
Task 2 9
Task 3 12
Task 4 15
Appendix 24

Introduction

In practical applications of controlling systems, engineers need to understand the basic modes of control, the response that these modes of control produce in terms of control accuracy and response time, and how to successfully adjust the parameters of a controller to give optimal response for input load changes.

1 Brief

This assessment relates to outcome 4 ‘ Describe process control terminology, describe control action and examine several controller tuning techniques.’

Tasks

1 Task 1

1. Using a computer based controller, explain the theory associated with proportional only control, carry out tests using a proportional only controller and draw conclusions about the controllers output response as detailed in the attached experiment sheet (worksheet 1).

Proportional only control – Worksheet 1

Objective:

The aim of this simulation is to: • Discover the relationship between the value of gain (K) and the magnitude of offset in a P only controller. • Discover the relationship between the value of gain (K) and the stability of control for a P only controller.

Procedure:

First find the ‘PID Control Simulator’ folder in the Control Systems & Automation folder on the ‘Blackboard’ website for HNC Electrical & Electronic Engineering.

Open the file newpid.zip.

This is a three term controller that will show the control system output and controller input for a simulated control system. A brief instruction manual for this program can be found in the file PIDhelp.doc. Read this before starting!

Switch the control mode to ‘PID’ with the value of Gain (Kc) set to 0.00. The output should stabalise at about +1. Now ‘Pause’ the display and set the value of Gain (Kc) to 0.01. Click ‘Resume’ and allow the output (Y) to stabilise. Record its value in the table below (should be a value of about 0.9). Record the value of set point of the control system (SP) then, for each value of Kc, compute the value of offset and record in the table

Now ‘Pause’ the display and set the value of controller gain (Kc) to the next value in the table (0.1). Click ‘Resume’ and allow the output (Y) to stabilise. Record its value in the table below (should be a value of about 0.9) and compute the offset. Also estimate and record in the table the time taken for the output to settle to a constant value (use the ‘Pause’ button to freeze the display as appropriate).

Repeat the process for the values of Kc indicated to complete the table of results below.

Using Microsoft Excel, draw graphs of gain (Kc) versus offset and gain (Kc) versus settling time. (Hint: Copy the data in the table using edit/copy. Paste into an open but blank Excel spreadsheet using ‘edit/paste special’ and picking ‘unicode text’ before clicking ‘OK’.)

|Gain (Kc) |Output (Y) |Set Point (SP) |Offset (Y-SP) |Settling Time |
|0.01 |0.91 |0 |0.909 | |
|0.1 |0.507 |0 |0.507 |87 |
|0.2 |0.33 |0 |0.33 |77 |
|0.3 |0.252 |0 |0.252 |68 |
|0.4 |0.255 |0 |0.255 |57 |
|0.5 |0.198 |0 |0.198 |40 |

Graph Showing Gain ‘Kc’ versus Output ‘Y’

Graph Showing Gain ‘Kc’ versus Offset ‘Y-SP’

Graph Showing Gain ‘Kc’ versus Settling Time

Q. What conclusions can you draw about the effect of increasing gain on the value of offset in a proportional only control system?

A. As the proportional gain in a P only control system is increased the error between the set point and the system output seems to decrease.

Q. What conclusions can you draw about the effect of increasing gain on the response settling time in a proportional only control system?

A. As the proportional gain in a P only control system is increased there is a decrease in the time needed for the system output to achieve a constant value.

Q. Now return to the PID simulator program and set Kc to 1.0. Observe the response of the output. The advantage of increasing the proportional gain Kc with regard to the offset is:

A. The system responds quicker.

Q. But if Kc is set too high what happens to the stability of the control system?

A. If Kc (proportional gain) is set too high the control system output oscillates and becomes unstable.

Task 2

Using a computer based controller, explain the theory associated with integral control, carry out tests using a proportional and integral controller and draw conclusions about the controllers output response as detailed in the attached experiment sheet (worksheet 2).

Proportional and Integral control – Worksheet 2

Objective:

The aim of this simulation is to: • Examine the effect of integral action, and changing the value of integral action time (tI), on the speed of response and magnitude of offset in a P+I controller. • Discover the relationship between the value of integral action time (tI) and the stability of control for a P+I controller.

Procedure:

First find the ‘PID Control Simulator’ folder in the Control Systems & Automation folder on the ‘Blackboard’ website for HNC Electrical & Electronic Engineering.

Open the file newpid.zip.

This is a three term controller that will show the control system output and controller input for a simulated control system. A brief instruction manual for this program can be found in the file PIDhelp.doc. Read this before starting!

• Switch the control mode to ‘PID’ and set the value of Gain (Kc) to 0.1, then allow the output (Y) to stabilise (should be a value of about 0.5).

• Click the ‘PAUSE’ button, click the ‘Switch On’ button above ‘Reset Time tI’ and change the value of tI to 100.0 (if it is not already this value). Now click ‘RESUME’ and record the start time of the output changing. Observe the time taken for the offset to reduce to its constant value. Record the finish time.

• Record in the table below the eventual value of offset for the integral action time (tI) = 100. Record the time taken for the output response to settle.

• Now ‘Switch Off’ the integral action and allow the output (Y) to settle (about 0.5). The system is now back in P-only mode.

• Click the ‘PAUSE’ button, click the ‘Switch On’ button above ‘Reset Time tI’ and change the value of tI to 30.0. Now click ‘RESUME’ and record the start time of the output changing. Observe the time taken for the offset to reduce to its constant value. Record the finish time.

• Record in the table below the eventual value of offset for the integral action time (tI) = 30. Also record the time taken for the output response to settle.

• Now ‘Switch Off’ the integral action and allow the output (Y) to settle (about 0.5). The system is now back in P-only mode.

• Click the ‘PAUSE’ button, click the ‘Switch On’ button above ‘Reset Time tI’ and change the value of tI to 5.0. Now click ‘RESUME’ and record the start time of the output changing. Observe the time taken for the offset to reduce to its constant value. Record the finish time.

• Record in the table below the eventual value of offset for the integral action time (tI) = 5. Also record the time taken for the output response to settle.

Q. What conclusions can you draw about the effect of integral action on the value of offset in a P+I control system?

A. Using a P+I Controller all integral time will reduce the offset to zero.

Q. What conclusions can you draw about the effect of decreasing integral action time (tI) on the response settling time and stability in a P+I control system?

A. In a P+I control system after an input change the time needed for the system to settle will be reduced as the integral time decreases.

If the integral time is decreased too much the system response will become unstable.

Task 3

Using a computer based controller, explain the theory associated with derivative control, carry out tests using a proportional and derivative controller and draw conclusions about the controllers output response as detailed in the attached experiment sheet (worksheet 3).

Proportional and Derivative control – Worksheet 3

Objective:

The aim of this simulation is to: • Examine the effect of derivative action, and changing the value of derivative action time (tD), on the speed of response and magnitude of offset in a P+D controller. • Discover the relationship between the value of derivative action time (tD) and the stability of control for a P+D controller.

Procedure:

First find the ‘PID Control Simulator’ folder in the Control Systems & Automation folder on the ‘Blackboard’ website for HNC Electrical & Electronic Engineering.

Open the file newpid.zip.

This is a three term controller that will show the control system output and controller input for a simulated control system. A brief instruction manual for this program can be found in the file PIDhelp.doc. Read this before starting!

• Switch the control mode to ‘PID’. Ensure SP=0 and set the value of Gain (Kc) to 0.1, then allow the output (Y) to stabilise. Note the offset value (should be about 0.5).

• Click the ‘PAUSE’ button, click the ‘Switch On’ button above ‘Reset Time tD’ and change the value of tD to 0.1. Use the slider at the right hand side of the output display to step down the set point to about minus 0.9. Now click ‘RESUME’. Record, in the table below, the time that elapses before the response is stable (in the region of 100 time units) and the value of offset once the response is stable.

• Now ‘Switch Off’ the derivative action, reset the set point to zero and allow the output (Y) to settle (about 0.5). The system is now back in P-only mode.

• Click the ‘PAUSE’ button, click the ‘Switch On’ button above ‘Reset Time tD’ and change the value of tD to 10.0. Use the slider at the right hand side of the output display to step down the set point to about minus 0.9. Now click ‘RESUME’. Record, in the table below, the time that elapses before the response is stable and the value of offset once the response is stable.

• Now ‘Switch Off’ the derivative action, reset the set point to zero and allow the output (Y) to settle (about 0.5). The system is now back in P-only mode.

• Click the ‘PAUSE’ button, click the ‘Switch On’ button above ‘Reset Time tD’ and change the value of tD to 1000.0. Use the slider at the right hand side of the output display to step down the set point to about minus 0.9. Now click ‘RESUME’. Record, in the table below, the effect on response and stability.

|Derivative action time |Eventual Offset Value |Settling Time of |
|(tD) | |response |
|0.1 |0.954 |100 |
|10 |0.952 |55 |
|1000 |0.952 |Not stable 793+ |

Q. What conclusions can you draw about the effect of derivative action on the value of offset in a proportional only control system?

A. In a P only Control System the offset is not affected by derivative control.

Q. What conclusions can you draw about the effect of increasing derivative action time (tD) on the response settling time and stability in a P+D control system?

A. In a P+D Control System after input changes the time needed for the system to settle decreases as derivative action time increases.

If derivative action time is increased too much the system becomes unstable.

Task 4

Explain the purpose of controller tuning and describe two methods that can be used to tune a PID controller (worksheet 4).

Purpose of controller tuning -
To regulate the output of a system to a user specified setpoint by controlling one or more or the system inputs or control variables.
This is done by determining the error in the system output as well as the derivative and integral of the error. Information is fed into an equation which determines the controller output and system input necessary to return the system output to the setpoint.
The objective of PID tuning is to determine the Proportional, Integral and derivative scaling coefficients in the control equation. This will provide the optimal control scheme.
The control scheme should be robust and responsive with minimal actuator activity.

Control Systems & Automation
Closed Loop (Ziegler-Nichols Ultimate Cycle) Tuning Method Worksheet 4

Objective:

The aim of this simulation is to tune a PID controller using the Ziegler-Nichols Ultimate Cycle method.

Procedure:

. Open the file PIDSim.html in Internet Explorer. First, note whether the required proportional control gain is positive or negative. To do so, step the input u up (increased) a little, under manual control, to see if the resulting steady state value of the process output has also moved up (increased). If so, then the steady-state process gain is positive and the required Proportional control gain, Kc, has to be positive as well.

. Turn the controller to P-only mode, i.e. turn both the Integral and Derivative modes off.

. Turn the controller gain, Kc, up slowly (more positive if Kc was decided to be so in step 1, otherwise more negative if Kc was found to be negative in step 1) and observe the output response. Note that this requires changing Kc in step increments and waiting for a steady state in the output, before another change in Kc is implemented.

. When a value of Kc results in a sustained periodic oscillation in the output (or close to it), mark this critical value of Kc as Ku, the ultimate gain. Measure the period of the oscillation, Pu, referred to as the ultimate period – you may want to print the output response to do this. ( Hint: for the control system simulated in the PID simulator, Ku should be around 0.7 and 0.8 )

. Using the values of the ultimate gain, Ku, and the ultimate period, Pu, Ziegler and Nichols prescribes the following values for Kc, tI and tD, depending on which type of controller is desired:

Ziegler-Nichols Tuning Chart:

| |Kc |τI |τD |
|P control |Ku/2 | | |
|PI control |Ku/2.2 |Pu/1.2 | |
|PID control |Ku/1.7 |Pu/2 |Pu/8 |

. Calculate below the required values of Kc, tI and tD for the simulated control system to give a quarter wave response. ‘PAUSE’ the simulation and enter your calculated values. ‘RESUME’ the simulation and introduce a step change in set point of about 0.5. Observe the response and use the ‘Print Screen’ key to print out the response using Word or a similar program. Confirm that this is about a quarter wave damped response.

Kc = 0.454

tI = 17

tD = 4.25
As an alternative to the table above, another set of tuning values have been determined by Tyreus and Luyben for PI and PID, often called the TLC tuning rules. These values tend to reduce oscillatory effects and improves robustness.

. Repeat the tuning exercise as in paragraph 6 using the TLC equations below to calculate controller parameters. Repeat the step change in set point and print out the response.

Tyreus-Luyben Tuning Chart:

| |Kc |τI |τD |
|PI control |Ku/3.2 |2.2 Pu | |
|PID control |Ku/2.2 |2.2 Pu |Pu/6.3 |

.
. Compare the two tuned control systems responses obtained using Ziegler and Nichols Ultimate Cycle and Tyreus-Luyben Chart methods in terms of response time and system stability. What are the pros and cons of each method of tuning?

Two methods of tuning a controller –

Ziegler-Nichols and Tyreus Luyben
Both involve a similar tuning procedure, to experimentally determine Ku ultimate gain and Pu ultimate period. • System operated in proportional control only • Started with low value Kc • Disturbance introduced at input • Increase Kc incrementally until sustained and stable oscillation observed in output • Ku is smallest value of Kc which achieves oscillation • Pu is the period of oscillation at Ku • Correlation tables then used to determine values Kc, Ti and Td

In 1942 Ziegler and Nichols, both employees of Taylor Instruments, described simple mathematical procedures for tuning PID controllers. These procedures are now accepted as standard in control systems practice. The techniques make assumptions on the system model, but do not require that these models be specifically known. Ziegler-Nichols formulae for specifying the controllers are based on plant step responses.

Tyreus Luyben
Ziegler-Nichols tuning constants are aggressive and oscilate. This results in a controller not very robust to model imprecises. If minor oscillations and robustness is required then the Tyreus Luyben tuning constants may be used.

Cohen-Coon
The Cohen-Coon tuning rules are suited to a wider variety of processes than the Ziegler-Nichols tuning rules. The Ziegler-Nichols rules are very sensitive to the ratio of dead time to time constant, and work well only on processes where the dead time is between 1/4 and 2/3 the length of the time constant.
The Cohen-Coon tuning rules work well on processes where the dead time is between 1/10 and 4 times the time constant.

Cohen-Coon is also one of the few sets of tuning rules that has rules for PD controllers – should you ever need this.

• Impulse is generated in one of system outputs which is to be controlled • System output monitored as a function of time • Several values calculated using this data - the original steady state output the new steady state output the time at which output = 50% the time at which output = 63.2% • Curve fitting or Linear interpolation between data points

Advantages
Used for systems with time delay.
Quicker closed loop response time.
Disadvantages and Limitations
Unstable closed loop systems.
Can only be used for first order models including large process delays.
Offline method.
Approximations for the Kc, τi, and τd values might not be entirely accurate for different systems.

1

5

6

Ziegler-Nichols Screenshots
[pic]

[pic]
[pic]

Tyreus Luyben Screenshots

[pic]
[pic]
[pic]

[pic]

8 Appendix

9

Worksheet 1 – Proportional only control

Worksheet 2 – Proportional and Integral control

Worksheet 3 – Proportional and Derivative control

Worksheet 4 – Closed Loop ( Ziegler-Nichols Ultimate Cycle) Tuning Method
-----------------------
|Integral action time (tI) |Eventual Offset Value |Settling Time |
|100 |0.002 |1130 |
|30 |0.001 |272 |
|5 |oscillates |unstable |

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