1. UNIVERSITÀ DEGLI STUDI DI SALERNO
Bachelor Degree in Chemical Engineering
Course: Process Instrumentation and Control
(Strumentazione e Controllo dei Processi Chimici)
FEEDBACK AUTOMATIC CONTROL
PERFORMANCE CRITERIA AND TUNING OF PID CONTROLLERS
Rev. 2.4 – May 16, 2019

2. CONTROLLER DESIGN Questions
What type of feedback controller should be used to control a given process?
Does the controller have to be direct or reverse acting?
Which criterion should be used to evaluate the performance and to select the feedback controller when considering both the type of controller and the parameter values?
How can we optimize the controller parameters?
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

3. CONTROLLER DESIGN Answers
What type of feedback controller should be used to control a given process?
For the simpler and more common industrial controls (SISO or DISO system)
the continuous PID controller is chosen
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

4. Process Instrumentation and Control - Prof. M. Miccio
RULES OF THUMB
When it is possible to use a simple proportional controller
A simple proportional controller may be used when:
an acceptable offset value with a moderate Kc;
the proportional control does not provide offset because of the presence of an integral action in the process;
a P-only controller is used for the control of the pressure of gas and liquid.
A PI controller is used when a simple proportional controller cannot be adopted:
a PI controller should be used when a proportional controller cannot limit adequately to the offset;
a PI controller will be used for the control of level and pressure of gas. It is very often used for the control of flowrate. Its dynamic response is quite quick and the dynamic response of the closed-loop system is satisfactory despite the slowdown caused by the integral action.
A PID controller is used to increase the velocity of the closed-loop response:
a PI controller eliminates the offset but reduces the velocity of the closed-loop response. For a multicapacitive process, for which the response is very slow, the introduction of a PI controller slows down further the response. In this case, the addiction of the derivative action stabilizes this effect allowing the use with a wide range of the gain and with a more proper response without excessive oscillations.
The derivative action is recommended for the temperature and composition control.
see:
§ Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall, 1984
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

5. CONTROLLER DESIGN Answers
Does the controller have to be direct or reverse acting?
See the process gain
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

6. Process Instrumentation and Control - Prof. M. Miccio
What is Process Action ?
Process MV PV
Process action is how the process variable changes with respect to a change in the controller output (or manipulated variable). Process action is either direct acting or reverse acting.
The action of a process is defined by the sign of the process gain.
A process with a positive gain is said to be direct acting.
A process with a negative gain is said to be reverse acting.
adapted from:
D. Cooper (2208), "Practical Process Control ", PDF textbook
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

7. Process and Controller Action
The action of a process is important because it will determine the action of the controller:
A direct acting process requires a reverse acting controller.
Kc and KP >0
Conversely, a reverse acting process requires a direct acting controller.
Kc and KP <0
adapted from:
D. Cooper (2208), "Practical Process Control ", PDF textbook
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

8. CONTROLLER DESIGN Answers
Which criterion should be used to evaluate the performance and to select the feedback controller when considering both the type of controller and the parameter values?
Define an appropriate performance criterion and quantify the result using a P or PI or PID controller with a set of values: Kc, tl, tD
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

9. SIMPLE PERFORMANCE CRITERIA (CLOSED–LOOP SYSTEMS)
The simplest perfomance criteria are based on some desirable characteristic features of a closed-loop system giving an underdamped response.
The main criteria refer to:
OVERSHOOT
DECAY RATIO (e.g. C/A = ¼)
FREQUENCY OF OSCILLATION OF THE TRANSIENT RESPONSE
RISE TIME
SETTLING TIME
see:
Par in Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall, 1984
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Process Instrumentation and Control - Prof. M. Miccio

10. Process Instrumentation and Control - Prof. M. Miccio
GENERAL PERFORMANCE CRITERIA BASED ON MINIMUM ERROR e(t) (CLOSED–LOOP SYSTEMS)
Each integral points out a different aspect of the closed-loop response:
ISE and ITSE penalize higher errors more, giving rise to more prompt but more oscillating answers.
ITAE and ITSE give more importance to errors in the final part than the initial part of the dynamic response, giving rise to a higher error in the initial part.
 the inf. extreme t = 0 identifies the time instant in which the variation is applied on the input variable.
see:
Ch. 7 in Magnani, Ferretti e Rocco (2007)
Par in Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall, 1984
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

11. Process Instrumentation and Control - Prof. M. Miccio
CLOSED-LOOP RESPONSE comparison between different general performance criteria
see:
par Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

12. CONTROLLER DESIGN Answers
How can we optimize the controller parameters?
Use the tuning methods:
OPEN LOOP TUNING
Self-Regulating Systems
Non Self-Regulating Systems
CLOSED LOOP TUNING
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

13. OPEN LOOP TUNING for Self Regulating Systems

14. OPEN LOOP TUNING
see:
§ Stephanopoulos
Cohen e Coon (1953) proposed the Process Reaction Curve method for the open loop process:
CO(t) t
Make a step-wise variation of amplitude A in the input variable
Record the dynamic response ym (t) until the stationary state B is asymptotized.
Adapt a FOPDT model to the ym (t) response and determine its parameters:
Calculate the optimal parameters of the PID controller from the parameters of the FOPDT model.
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

15. Process Instrumentation and Control - Prof. M. Miccio
BLOCK DIAGRAM (in the time domain) manual mode of the controller  Open Loop operation
Final
control
element
PROCESS
SENSOR
PID Controller
ySP(t)
ε(t)
o(t)
m(t)
d(t)
ym(t)
y(t) + -
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

16. First Order Plus Dead Time (FOPDT) MODEL
Complex or unknown
process
f(t)
y(t)
First order process
Dead time
f(t)
y(t)
y(t-td)
L[y(t-td)]
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

17. COHEN and COON FORMULAS
The performance criteria of the controller consist of obtaining a closed-loop response with:
decay ratio = ¼, minimum offset, minimum ISE
 Really good for first-order processes
K≡Kp
≡p
PB=100/Kc
see:
§ Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

18. 1st ZIEGLER–NICHOLS METHOD
Tuning table
NOTE:
in Magnani, Ferretti e Rocco (2007), respect to Stephanopoulos (1984):
t  td
T  t
NOTE: the table was obtained by a simulation on a really first-order plus dead time system changing the ratio /T in order to have underdamped dynamic response with  = 0.21
 It can be used only for controllability ratio:
see:
Ch. 7 in Magnani, Ferretti e Rocco (2007)
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

19. Internal Model Control (IMC) FORMULAS
θP≡td
LOOP-PRO software uses IMC formulas
adapted from:
D. Cooper (2208), "Practical Process Control ", PDF textbook
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

20. OPEN LOOP TUNING for Non-Self Regulating Systems

21. Process Instrumentation and Control - Prof. M. Miccio
BLOCK DIAGRAM (in the time domain) manual mode of the controller  Open Loop operation
Final
control
element
PROCESS
SENSOR
PID Controller
ySP(t)
ε(t)
o(t)
m(t)
d(t)
ym(t)
y(t) + -
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

22. FOPDT model integrating
In this case we cannot use the common procedure for the FOPDT model because the dynamic response does not reach a new steady state value.
 Adopt a FOPDT model integrating
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

23. PROCESS REACTION CURVE for Non-Self Regulating Processes
The dynamic response to a step input change is a straight line (either increasing or decreasing).
The slope of the response line is Kp*.
The time interval before the answer starts is just td.
Example:
dynamic response to a step input change for a pumped tank
tYstart
tUstep
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

24. Internal Model Control (IMC) FORMULAS for Non-Self Regulating Processes
Standard Tuning:
Conservative Tuning:
p  td
LOOP-PRO software uses IMC relations
adapted from:
D. Cooper (2008), "Practical Process Control ", PDF textbook
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

25. CLOSED LOOP TUNING

26. BLOCK DIAGRAM FOR THE FEEDBACK CONTROL
CONTROLLER
FINAL CONTROL ELEMENT
PROCESS
MEASURING DEVICE
ySP(t)
ε(t)
o(t)
m(t)
d(t)
ym(t)
y(t) + -
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

27. 2nd ZIEGLER – NICHOLS METHOD
ySP t
P controller
FINAL CONTROL ELEMENT
PROCESS
MEASURING DEVICE
SET POINT
ε(t)
o(t)
MANIP. VAR.
LOAD
CONTR. VAR.
MEASURED VAR. Kc
CLOSED LOOP METHODS are popular for two reasons:
it is sufficient to determine only a parameter (the natural oscillation period T)
many works are reported in literature, in particular for the electric application
Note:
the process is brought to the limit of stability (marginal stability). What risks can it entail?
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

28. 2nd ZIEGLER – NICHOLS METHOD
The method acts on the proportional controller with a fixed P.B.
The integral and derivative actions are deactivated.
The procedure starts from a steady state of the process.
A step input change is forced on the set-point and the dynamic response y(t) is monitored.
The P.B is reduced until a stable cycle (constant amplitude oscillation of y(t)) is reached (with the final controlling element not close to saturation)
The specific value Ku of Kc is recorded, for which the stable oscillation (with the closed-loop) of y(t) occurs
The distance between two consecutive peaks is measured (natural period of oscillation t0 or Pu or T)
The natural frequency of oscillation is f0=1/t0
The crossover frequency is ωco =2π/t0
by trial and error
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

29. Process Instrumentation and Control - Prof. M. Miccio
CLOSED-LOOP METHODS
ySP t
y(t)
SET POINT ySP 
Subsequently to a step input change of the set-point, the dynamic response of the closed loop reaches a continuous oscillating condition
Kc=Ku
Kc<Ku
Kc>Ku
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio

30. 2nd ZIEGLER–NICHOLS METHOD Tuning table
Only 2 parameters ―>
They were obtained by assuming a closed-loop underdamped response  = 0.25
 Validity range: 2 < KuKp < 20
NOTE:
the actual plant is brought to the stability limit. What are the risks?
see:
§ Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall
see:
Ch. 7 in Magnani, Ferretti e Rocco (2007)
11/10/2019
Process Instrumentation and Control - Prof. M. Miccio