1. Tuning PID Controller Institute of Industrial Control,
Zhejiang University, Hangzhou, P. R. China
2013/03/27

2. Last Lecture Selection of Valve Action Action of Feedback Controllers
Performance Criterion of Process Control Systems
Understand Typical Controllers (P, PI and PID)

3. Single-loop PID Control System
Problem: For an unknown extended controlled process, how to design and tune our PID controller ?

4. Proportional-Integral-Derivative (PID) Controller
Ideal PID Controller
Td is the derivative time.
Industrial PID Controller (design and realization ?)
The derivative gain Ad = 10.

5. Problem Discussion
Explain the function of PID controller for a stable controlled process.
Analyze the effect of PID parameter changes on control performances
How can we realize the industrial PID controller in Simulink ?
PID tuning example (See ../PIDControl /PIDLoop.mdl )

6. ( discuss the initial condition setting)
Problem 2-1
For the level controlled process, h2 is selected as its controlled variable, and Qin is the main input of the process. Suppose the sectional area of two tanks are A1 and A2. The rates of outlet flow are assumed to satisfy the following equations:
Please obtain the process characteristics by dynamic equations, and build the corresponding SimuLink model.
( discuss the initial condition setting)

7. ( load the file temp.mat )
Problem 2-2
For a heater with electricity, the step response data of outlet temperature can be shown as follows. Please determine its characteristic parameters K, T,τ if the span of temperature transmitter is 0 to 50 ℃.
t, min 3 6 9 12 15 18 21 24 27
U, % 60 40
T, ℃
38.7
38.3
38.8
39.0
38.4
37.0
35.3
33.6 30 33 36 39 42 45 48 51 54 57
32.2
31.0
30.2
29.5
29.0
28.6
28.3
28.0
27.9
27.8
( load the file temp.mat )

8. Contents Selection of PID Controller Types （PID控制器类型选择）
Tuning of PID Controller Parameters （控制器参数整定）
Flow Control （流量控制）
Level Control （液位控制）
Reset Windup and Its Prevention （积分饱和与防止）
Summary

9. Type Selection of PID Controllers
*1: For some slow processes with long time constants, the derivative action is suggested to use. However, if there exists strong measurement noises, a first-order or average filter should be added.
Controlled Variable
Controller Type
Temperature / Composition
PID*1
Flow / Pressure /Liquid-Level PI
Liquid-Level P
Please analyze the rule of type selection ?

10. PID Tuning Concept

11. Offline Tuning Based on Process Parameters: K, T,τ
Step 1: switch the controller to manual mode, change the output of controller in step form, and record input/output data of controller.
Step 2: obtain process characteristics: K, T,τ, from the step response data.
Step 3: set the PID parameters Kc, Ti , Td, and switch the controller to automatic mode.
Step 4: increase or decrease the gain Kc until obtaining the satisfactory response.

12. Simulation of Offline Tuning step 1: Step Testing
See ../PIDControl/PIDLoop.mdl

13. Step 2: Obtain Process Para.

14. Step 3: Obtain Initial PID Para. (Ziegler-Nichols Method)
Controller Kc Ti Td P PI
PID
Note: the above method was developed for

15. Step 3: Obtain Initial PID Para. (Lambda Tuning Method)
Controller Kc Ti Td P PI T
PID
τ/2
Initial Value
Note: the above method is not limited by the value of

16. Simulation Example #1 K = 1.75 T = 6.5,τ= 3.3 min For PI Controller,
Z-N tuning: Kc = 1.0, Ti = 11 min
Lambda tuning: Kc = 0.56, Ti = 6.5 min

17. Simulation Example #2 K = 1.75 T = 6.5,τ= 6.3 min For PI Controller,
Z-N tuning: Kc = 0.53, Ti = 20.8 min
Lambda tuning: Kc = 0.30, Ti = 6.5 min

18. Procedure of Online Tuning: Ziegler-Nichols Technique
Step 1: with the controller online (in automatic mode), remove all the reset (Ti = maximum) and derivative (Td = 0) modes. Start with a small Kc value.
Step 2: make a small set point or load change and observe the response of CV.
Step 3: if the response is not continuously oscillatory, increase Kc, or decrease PB, repeat step 2.
Step 4: Repeat step 3 until a continuous oscillatory response is obtained.

19. Example of Online Tuning
See ../PIDControl/PIDLoop.mdl

20. Online Tuning: Ziegler-Nichols Technique
The gain that gives these continuous oscillations is the ultimate gain (临界增益), Kcu. The period of the oscillations is called the ultimate period (临界周期), Tu. the ultimate gain and the ultimate period are the characteristics of the process being tuned. The following formulas are then applied:
Controller Kc Ti Td P
0.5Kcu PI
0.45Kcu
Tu /1.2
PID
0.65Kcu
Tu /2
Tu /8

21. Online Tuning Result
See ../PIDControl/PIDLoop.mdl

22. Limitation of Online Tuning

23. Auto-tuning Based on Relay Feedback (基于继电反馈的参数自整定)
Here we suppose the process gain > 0

24. Relay Feedback Example
The controlled process can be described as
The amplitude of relay controller is d = ±2.0

25. Response of Relay Feedback
Oscillation period TU & amplitude AY（振荡周期与幅度）?
See the detailed results:
../ PIDLoopAutoTuning.mdl

26. The Ultimate Gain (临界增益) Kcu Calculation
经FT变换可知，控制输出的一次谐波幅度为
而对应的控制器临界增益为

27. Online Z-N Tuning Parameters
Controller Kc Ti Td P
0.5Kcu PI
0.45Kcu
Tu /1.2
PID
0.65Kcu
Tu /2
Tu /8
If we use a PID controller, then we select the following parameters ……

28. Closed-loop Response of PID Feedback System
Above auto-tuning method can be applied to other controlled processes ?

29. Characteristics of Flow Loops
Fast dynamic response
Zero dead time, which results in an infinite controller gain in every tuning equation
Large measurement noise
To decrease the change of control valve, a PI controller is common used with very small proportional action and a large integral action to approximate an integral controller. (Why?)

30. Tuning Example of Flow Loops
See ../PIDControl/FlowLoop.mdl
Please compare the proportional gain with the integral gain

31. Examples of Level Loops

32. Characteristics of Level Loops
Very often levels are integrating processes
There are two types of possible control objectives when the input flow varies:
(1) Tight Level Control;
(2) Average Level Control
(“液位均匀控制”)

33. Tight Level Control
The objective is to control the level tightly at set point, and the output flow can be allowed to vary without limitation
If a level process happens to be self-regulated, and it is possible to obtain K, T andτ, the above tuning techniques can be used directly
If a level process is integrating, a PI controller is common used with large proportional action and a very small integral action

34. Average Level Control
The objective is to smooth the output flow from the tank, which feeds the downstream unit, the level in the tank must be allowed to “float” between a high and a low level
A P controller is common used in Average Level Control with a small proportional gain
Tuning: the gain should be set to be as small as possible, as long as the level changes between a high and a low level for the expected flow deviation from the average flow.

35. Example of Level Control
See ../PIDControl/ LevelLoop.mdl

36. Analysis of Average Level Control Systems
Dynamic equation of the controlled process:
where A is the area of the tank.
Suppose

37. Analysis of Average Level Control Systems (cont.)
For a proportional controller, Gc = －Kc,
Please analyze the above models.

38. Examples of Average Level Control Systems
Please see ../PIDControl/ AverageLevelLoop.mdl

39. Simulation Results of P-type Average Level Control

40. Please see the following simulation example
Reset Windup Problem
Please see the following simulation example
…/PIDControl/PidLoopwithLimit.mdl

41. Simulation Result with Reset Windup in a Single-Loop System
Discussion:
Which difference exists between reset windup and the open or closed status of the control valve completely ?

42. The Principle of Preventing Reset Windup
Principle: remove the reset or integral action if the control output is beyond the normal operation range.

43. Anti-reset Windup Example

44. Industrial PID Controller

45. Summary Selection of PID Controller Types
Tuning of PID Controller Parameters
Tuning of PID Controller for Flow Loops
Tight / Average Level Control
Reset Windup and Its Prevention

46. Problem Discussion
For an unknown stable temperature control system, can you determine PID parameters in Offline and Online tuning methods ?
Please realize the industrial PID controller in Simulink ?
For the fast flow control loop, show me your tuning principle and explain why.
For the AVERAGE level control loop, show me your tuning principle and explain why.
Explain the existing reason of reset windup and show me your prevention schemes

47. Exercise 3.1
A controlled process is shown in the Problem 2-1 (p.34) in Automated Continuous Process Control.
calculate its characteristics parameters K, T and τ;
decide on the action of the valve and the controller;
tune your PID controller.

48. Exercise 3.2
假设Relay(继电器法)镇定PID参数时，控制器输出如上图所示，信号周期为Tu, 振幅为d=2。证明经傅立叶变换，控制输出的一次谐波幅度为