ChE / MET 433
19 Mar 12
1
ChE / MET 433
19 Mar 12
Ziegler-Nichols (ZN I)
(QDR or QAD Tuning)
(Ultimate Gain)
Ls 
GL  ??
GP  ??
Rs  +
E s 
M (s )
Gc
GP
GL
+
+
C s 
2
Feedback Controller Tuning:
(General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc
• easy, simple, do on existing process
• multiple solutions
2) Time integral performance criteria
• ISE
integral square error
• IAE
integral absolute value error
• ITAE
integral time weighted average error
3) Semi-empirical rules
• FOPDT (ZN II)
• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
3
Ziegler Nichols I (Ultimate Gain Method)
Procedure, done closed loop (on-line):
• P-Only (switch off integral & derivative modes)
• Controller in Auto mode (closed loop)
• Adjust Kc
o “bump” process with small setpoint change
o Find Kc where loop response is undamped
4
Dynamic Changes as Kc is Increased for a
FOPDT Process
Time
Time
Time
K CU  ultimate gain
Time
Time
Time
Ziegler Nichols I (Ultimate Gain Method)
Procedure, done closed loop (on-line):
• P-Only (switch off integral & derivative modes
• Controller in Auto mode (closed loop)
• Adjust Kc
o “bump” process with small setpoint change
o Find Kc where loop response is undamped
• Record Kc (call it Kcu – the ultimate gain)
TU
• Measure Tu (the ultimate period)
• Use Table 7-1.1 to get tuning constants
• Adjust controller settings to calculated values
• Test to see if need to make fine adjustments
6
Quarter-decay-ratio response (sometimes called QAD)
7
Ziegler Nichols I (Ultimate Gain Method)
Response to disturbance should be close to QDR (QAD)
Advantages:
• Don’t need to know mathematical models
• Easy to use
• Use on any process you can get to oscillate
Disadvantages:
• Must force loop / process to oscillate (operating close to unstable)
• Tuning constants not unique, except for P-only
8
Quarter Decay Ratio (QAD)
Advantages:
• Good for load disturbances
• Prevents large initial deviations w/o too much oscillations
• Gives good “Ball Park” values; leading to fast responses for
most processes
Disadvantages:
• For SP changes, may
overshoot too much
• Parameters for PI, PID, not
unique
• May be too aggressive for
cases where K or to change.
9
PS Exercise: Tuning Two Tanks in Series
Loop Pro Trainer (process simulator):
• Launch Loop Pro Trainer
• Select Case Studies
• Select Gravity Drained Tanks
• Press the pause button
• Adjust controller output to 50%
• Press run (continue) button and let run till achieve steady state
• Click the rescale button to re center the plot
• Adjust controller output to achieve a level in tank 2 of 2 meters
• Click the controller button and turn to PID control (P-Only)
• You may have to turn the Integral part off; and Kc = 4 %/m
•
Press run button and adjust the disturbance up and down 0.5 l/min
• Then adjust the set point up and down 0.5 m
• Observe how the system behaves.
10
PS Exercise: Tuning Two Tanks in Series
Loop Pro Trainer (process simulator):
• Launch Loop Pro Trainer
• Select Case Studies
• Select Gravity Drained Tanks
• Now, double Kc and observe effect.
• Double it again…
• Try it at Kc = 2 %/m
11
PS Exercise: Tuning Two Tanks in Series
Loop Pro Trainer (process simulator):
• Now turn on the Integral term (tI should be 4.0 min) and do the
same adjustments, observing the behavior of the system.
• You may need to adjust the History to see the full change.
• Change tI and observe the effect.
• Make sure you are back to the original settings (SP = 2m, Level at
2 m, etc) when you start and end with the PI controller.
12
PS Exercise: Tuning Two Tanks in Series
Loop Pro Trainer (process simulator):
• Now turn on the Integral term (tI should be 4.0 min) and do the
same adjustments, observing the behavior of the system.
• You may need to adjust the History to see the full change.
• Change tI and observe the effect.
• Make sure you are back to the original settings (SP = 2m, Level at
2 m, etc) when you start and end with the PI controller.
Now let’s tune the controller.
• Use the Ziegler Nichols I method to find Kcu and Tu.
• Tune the controller for:
• P – only control
• And then for PI control.
13
Loop-Trainer
Kcu ~ 72, delta R = 4 –> 4.5
14
Kcu ~ 72, delta R = 4 –> 4.5…set Kc = 1/2Kcu = 36
15
ChE / MET 433
21 Mar 12
16
Feedback Controller Tuning:
(General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc
• easy, simple, do on existing process
• multiple solutions
2) Time integral performance criteria
• ISE
integral square error
• IAE
integral absolute value error
• ITAE
integral time weighted average error
3) Semi-empirical rules
• FOPDT (ZN II)
• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
17
PS Exercise: Tuning Two Tanks in Series
Different opinions:
1. Different correlations will give different constants in the controller
equations. D. Cooper suggests if one is uncertain, to start
conservative, i.e. with the smallest controller gain and the largest
integral (reset) time, thus, giving the least aggressive controller. Final
controller tuning may best be performed on-line by trial and error,
using experience and knowledge of the process, to obtain the desired
controller performance.
To changes in the setpoint or load disturbances:
• if the process response is sluggish; Kc is too small and/or tI is too
large.
• if the process response is too quick and perhaps oscillating is not
desired; Kc is too large and/or
tI is too small.
2. Ziegler-Nichols may be too aggressive for many ChE applications. Luyben
(Plantwide Dynamic Simulators in Chemical Processing and Control, Wiley,
2002) suggests for PI controller Kc = Ku / 3.2 and tI = 2.2 * Tu .
18
Step Change
Responses:
Kc
tI
19
c (t ) or %CO
m
Kc too large
Is Kc or tI
too high?
Lag
Properly tuned controller
cy(s t ) or PV
cm(t ) or %CO
Time
Lag
ycs(t ) or PV
c (t ) or %CO
m
Time
Lag
ycs(t ) or PV
tI too
large
Time
20
Feedback Controller Tuning:
(General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc
• easy, simple, do on existing process
• multiple solutions
2) Time integral performance criteria
• ISE
integral square error
• IAE
integral absolute value error
• ITAE
integral time weighted average error
3) Semi-empirical rules; FOPDT fit to Open Loop Step Test
• Ziegler-Nichols Open Loop (ZN II)
• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
21
Ziegler Nichols II (ZN II)
Fit response to FOPDT model
Ls 
GL  ??
GP  ??
Rs  +
E s 
M (s )
Gc
GP
GL
+
+
C s 
-
K e  to s
GP 
t s 1
KV , KT , K P all in K
22
Ziegler Nichols II (FOPDT fit)
Procedure, usually done open loop:
• Put controller in Manual mode
• Manually make step change in controller output
• Observe (record) data and fit to FOPDT model
K e  to s
fit 
t s 1
K  process SS gain
t  effective process time constant
to  effective process dead time
23
Open-Loop Step Test……..FOPDT
24
Open-Loop Step Test……..FOPDT: Loop Pro Method
K
K
K
25
Open-Loop Step Test……..FOPDT: Loop Pro Method
t
t
t
t
t
26
Open-Loop Step Test……..FOPDT: Loop Pro Method
to
to
to
0.3 min
27
Open-Loop Step Test……..FOPDT: Smith & Corripio
Method
cs
c(t )
m
K
cs
m
m(t )
28
Open-Loop Step Test……..FOPDT: Smith & Corripio Method
Estimation of t
& to
Fit 3 suggested for non-integrating processes:
@ 0.632cs
@ 0.283cs
cs
t
3
2
t2  t1 
to  t 2  t
t1
Fit 3: 7-2.16
p 239
t2
29
Open-Loop Step Test……..FOPDT: Smith & Corripio Method
Estimation of t
& to
Fit 1 suggested for integrating processes.
Fin
if Fin  A u (t )
Fin
What happens to h ??
h
Fout = constant
integrating process
h
non-integrating process
(self-regulating)
Fout  h
30
Ziegler Nichols II (FOPDT fit)
Procedure in open loop:
• Put controller in Manual mode
• Manually make step change in controller output
• Observe (record) data and fit to FOPDT model
K e  to s
fit 
t s 1
K  process SS gain
t  effective process time constant
to  effective process dead time
t 
0.1   o   0.5
t 
31
Cohen-Coon:
Procedure same as for ZN II (open loop step test):
•
The Ziegler-Nichols rules are more 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 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.
•
“Quarter-amplitude damping-type tuning also leaves the loop vulnerable to going
unstable if the process gain or dead time doubles in value.” Smuts suggests
reducing Kc by ½ to avoid problems later on.
* Jacques F. Smuts, Process Control for Practitioners,
Opticontrols, Inc (2011)
32
PS Exercise: Compare “Loop Pro” and “Fit 3” FOPDT Methods
33
PS Exercise: Use The Step Test (ZN II, or Open
Loop FOPDT Fit) to Tune The PI Controller
• Launch Loop Pro Trainer
• Select Case Studies
• Select Gravity Drained Tanks
• Press the pause button
• Adjust controller output to 51%
• Tune controller for operation around a tank level of 2 meters
34
ChE / MET 433
23 Mar 12
35
Feedback Controller Tuning:
(General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc
• easy, simple, do on existing process
• multiple solutions
2) Time integral performance criteria
• ISE
integral square error
• IAE
integral absolute value error
• ITAE
integral time weighted average error
3) Semi-empirical rules
• FOPDT (ZN II)
• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
36
Time Integral Performance Criteria
•disturbance/load change
Integrate error from old SP
c(t )
SP (old )
•setpoint change
c(t )
new SP
Integrate error from new SP
37
Time Integral Performance Criteria
Smith/Murrill developed unique tuning relationships
•IAE (Integral of the Absolute value of the Error)

IAE   e(t ) dt
Eqn: 7-2.17 p 245
0
•ITAE (Integral of the Time-weighted Absolute value of the Error)

ITAE   t e(t ) dt
0
•Determine type of input/forcing function (i.e. purpose of controller)
•maintain c(t) at setpoint (“Regulator” controller)
•c(t) track setpoint signal (“servo” control)
38
Time Integral Performance Criteria
39
Time Integral Performance Criteria
40
PS EX: Find PI Parameters for IAE Criteria
41
PS EX: Find PI Parameters for IAE Criteria
• Launch Loop Pro Trainer
• Select Case Studies
• Select Gravity Drained Tanks
• Put your PI tuning parameters into the
simulator controller and check tuning.
• Do the parameters need to be
adjusted?
42
In-Class EX: Loop Pro Demo Fitting
43
44
ChE / MET 433
26 Mar 12
45
Step Testing Thoughts
• Single step; can be analyzed by hand
• Pulse, doublet, pseudo-random binary sequence (PRBS) tests; require
computer tools for analysis
Data collected should meet these criteria:
• Process at steady state before data collected
• Signal to noise ratio should be 10 or greater
• Collected data should be done when no disturbances were present
• After fitting, the model appears to fit the data visually
46
Single step
Step Testing Thoughts
+ simple, graphical analysis can be done
- long time away from desired operating level (DLO; or SP)
- Data only on one side of DLO
Pulse (two step tests in rapid succession; 1 up and 1 back down)
+ only need to let measured process variable show a clear response
- long time away from desired operating level (DLO; or SP)
- Data only on one side of DLO
47
Doublet Test
Step Testing Thoughts
+ two pulse tests; one up; one down; ending at beginning level
+ obtain data on both sides of DLO
+ relatively quickly return to normal operation level
+ a preferred method of some in industry for open loop tests
- since done open loop; could be concern for certain systems
48
Step Testing Thoughts
PRBS Test (pseudo-random binary sequence )
+ theoretically PV shouldn’t vary far from DLO
- need a well defined, random test
- should have some idea of process gain, time constant, and deadtime
- might take longer than a doublet test
49
Step Testing Comparisons
PRBS
Doublet
50
PS EX: Find PI Parameters for IAE Criteria
51
Step Testing Thoughts
• Can do closed loop studies, and fit to FOPDT
• Controller aggressive enough for 10 times S to N response
• Data should begin and end at steady state
• No load disturbances should occur
• Do step, pulse, doublet changes to the set point.
• Fit data to FOPDT; check tuning parameters on the process
52
ChE / MET 433
28 Mar 12
53
Feedback Controller Tuning:
(General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc
• easy, simple, do on existing process
• multiple solutions
2) Time integral performance criteria
• ISE
integral square error
• IAE
integral absolute value error
• ITAE
integral time weighted average error
3) Semi-empirical rules
• FOPDT (ZN II)
• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
54
Auto-Tune Variation (ATV)*
Relay feed back test or ATV
+ Keeps process close to normal operation
+ More efficient for process with long time constant.
General method:
• determine reasonable h value to move FCE (3 – 10 % change)
• Input the change +h
• When PV starts to move, input change of –2h
• When PV cross the set point, input change of +2h
• When PV re-crosses the set point, input change of –2h
• Repeat until constant oscillations of PV are maintained (~3-4 cycles)
• Record amplitude (a) and period of oscillation (Pu)
c(t )
sp
m(t )
* Åström and Hägglund (1983);
* Luyben & Luyben (1997)
55
Auto-Tune Variation (ATV)
4h
Ku 
 a
K
ZN
c
 0.45 K u
K cTL  0.31Ku
t
ZN
I
 Pu / 1.2
t ITL  Pu / 0.45
• Calculate Ku from
ATV results.*
• ZN settings
• TL settings** (less
aggressive and recommended
for more sluggish processes)
* Riggs & Karim (2006)
** TL = Tyreus & Luben
56
Auto-Tune Variation (ATV)
Relay feed back test or ATV
+ Keeps process close to normal operation
+ More efficient for process with long time constant.
Mole Percent
2.3
2.2
Open Loop Test
2.1
ATV Test
2
1.9
0
20
40
Time (hours)
60
Riggs & Karim (2006)
57
PS EX: Find PI Parameters using the ATV Method
58
Auto-Tune or Self-Tuning Controllers
General loop auto-tuning:
• On demand or on-the-fly (continuous updating)
• Can be simple step test or pulse doublet
• Can be sophisticated self-tuning for difficult process
Example single point industrial controllers:
http://www.watlow.com/downloads/en/manuals/945e_a.pdf
59
Example single point industrial controllers:
60
61
Feedback Controller Tuning:
(General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc
• easy, simple, do on existing process
• multiple solutions
2) Time integral performance criteria
• ISE
integral square error
• IAE
integral absolute value error
• ITAE
integral time weighted average error
3) Semi-empirical rules
• FOPDT (ZN II)
• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
62
Trial and Error (field tuning)*
• Select the tuning criterion for the control loop.
• Apply filtering to the sensor reading
• Determine if the control system is fast or slow responding.
– For fast responding, field tune (trail-and-error)
– For slow responding, apply ATV-based tuning
• Turn off integral and derivative action.
• Make initial estimate of Kc based on process knowledge.
• Using setpoint changes, increase Kc until tuning criterion is
met
ys
c
a
b
Time
* J.B. Riggs, & M.N. Karim
Chemical and Bio-Process
Control, 3rd ed. (2006)
63
Trial and Error (field tuning)*
Decrease Kc by 10%.
Make initial estimate of tI (i.e., tI=5tp).
Reduce tI until offset is eliminated
Check that proper amount of Kc and tI are used.
c
b
ys
•
•
•
•
a
Time
* J.B. Riggs, & M.N. Karim
Chemical and Bio-Process
Control, 3rd ed. (2006)
64
Kc and
Kc
tI
levels good?
tI
65
Feedback Controller Tuning:
(General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc
• easy, simple, do on existing process
• multiple solutions
2) Time integral performance criteria
• ISE
integral square error
• IAE
integral absolute value error
• ITAE
integral time weighted average error
3) Semi-empirical rules
• FOPDT (ZN II)
• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
66
Rules of Thumb
*
* D.A. Coggan, ed., Fundamentals of
Industrial Control, 2nd ed., ISA, NC (2005)
67
Higher Order Process
68
Feedback Controller Tuning:
(General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc
• easy, simple, do on existing process
• multiple solutions
2) Time integral performance criteria
• ISE
integral square error
• IAE
integral absolute value error
• ITAE
integral time weighted average error
3) Semi-empirical rules
• FOPDT (ZN II)
• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
69
ChE / MET 433
70