Transcript No Slide Title

Chapter 16
Enhanced Single-Loop Control Strategies
1. Cascade control
2. Time-delay compensation
3. Inferential control
4. Selective and override control
5. Nonlinear control
6. Adaptive control
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Chapter 16
Example: Cascade Control
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Chapter 16
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Chapter 16
Chapter 16
Cascade Control
• Distinguishing features:
1. Two FB controllers but only a single control
valve (or other final control element).
2. Output signal of the "master" controller is the
set-point for “slave" controller.
3. Two FB control loops are "nested" with the
"slave" (or "secondary") control loop inside
the "master" (or "primary") control loop.
• Terminology:
slave vs. master
secondary vs. primary
inner vs. outer
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Chapter 16
Y1
Chapter 16
D2

G P1Gd 2
1  G c 2 G v G p 2 Gm 2  G c1 G c 2 G v G p 2 G p1 Gm1
(16  5)
Y1 = hot oil temperature
Y2 = fuel gas pressure
D1 = cold oil temperature (or cold oil flow rate)
D2 = supply pressure of gas fuel
Ym1 = measured value of hot oil temperature
Ym 2 = measured value of fuel gas temperature
Ysp1 = set point for Y1
Ysp 2 = set point for Y2
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Example 16.1
Consider the block diagram in Fig. 16.4 with the following
transfer functions:
Chapter 16
Gv 
5
s 1
Gd 2  1
G p1 
4
 4s 1 2s 1
Gm1  0.05
Gm2  0.2
G p2  1
Gd1 
1
3s  1
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Chapter 16
Example 16.2
Compare the set-point responses for a second-order process with a time delay
(min) and without the delay. The transfer function is
Chapter 16
e s
G p ( s) 
 5s  1 3s  1
16  18 
Assume Gm  Gv  1 and time constants in minutes. Use the following PI
controllers. For   0, Kc  3.02and1  6.5 min, while for   2 min the controller
gain must be reduced to meet stability requirements  Kc  1.23,1  7.0min  .
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Chapter 16

E'  E  Y1  Ysp  Y1  Y  Y2

16  19 
If the process model is perfect and the disturbance is zero, then Y2  Y and
16  20 
E'  Ysp  Y1
For this ideal case the controller responds to the error signal that would occur if not time
were present. Assuming there is not model error G  G , the inner loop has the effective
transfer function
Gc
P
G'  
16  21
E 1  G G * 1  e s
c




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Chapter 16
For no model error:
Gc 
G = G  G* e- s
Gc

1  Gc G* 1  e  s

Gc G* e  s
Gc G
Y


Ysp 1  Gc G* e  s 1  Gc G*
By contrast, for conventional feedback control
GcG*e  s
Y

Ysp 1  GcG*e  s
16  23
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Chapter 16
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Chapter 16
Inferential Control
Chapter 16
• Problem: Controlled variable cannot be measured or has
large sampling period.
• Possible solutions:
1. Control a related variable (e.g., temperature instead
of composition).
2. Inferential control: Control is based on an estimate
of the controlled variable.
• The estimate is based on available measurements.
–
Examples: empirical relation, Kalman filter
• Modern term: soft sensor
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Chapter 16
Inferential Control with Fast and Slow
Measured Variables
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Selective Control Systems & Overrides
Chapter 16
• For every controlled variable, it is very desirable that
there be at least one manipulated variable.
• But for some applications,
NC > NM
where:
NC = number of controlled variables
NM = number of manipulated variables
• Solution: Use a selective control system or an override.
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Chapter 16
• Low selector:
• High selector:
• Median selector:
• The output, Z, is the median of an odd number of inputs
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Chapter 16
Example: High Selector Control System
• multiple measurements
• one controller
• one final control element
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Chapter 16
2 measurements, 2 controllers,
1 final control element
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Overrides
Chapter 16
• An override is a special case of a selective control
system
• One of the inputs is a numerical value, a limit.
• Used when it is desirable to limit the value of a
signal (e.g., a controller output).
• Override alternative for the sand/water slurry
example?
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Chapter 16
Nonlinear Control Strategies
• Most physical processes are nonlinear to some degree. Some are very
nonlinear.
Chapter 16
Examples: pH, high purity distillation columns, chemical reactions
with large heats of reaction.
• However, linear control strategies (e.g., PID) can be effective if:
1. The nonlinearities are rather mild.
or,
2. A highly nonlinear process usually operates over a narrow range of
conditions.
• For very nonlinear strategies, a nonlinear control strategy can provide
significantly better control.
• Two general classes of nonlinear control:
1. Enhancements of conventional, linear, feedback control
2. Model-based control strategies
Reference: Henson & Seborg (Ed.), 1997 book.
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Chapter 16
Enhancements of Conventional Feedback Control
We will consider three enhancements of conventional feedback control:
1. Nonlinear modifications of PID control
2. Nonlinear transformations of input or output variables
3. Controller parameter scheduling such as gain scheduling.
Nonlinear Modifications of PID Control:
• One Example: nonlinear controller gain
Kc  Kc0 (1  a | e(t ) | )
(16-26)
• Kc0 and a are constants, and e(t) is the error signal (e = ysp - y).
• Also called, error squared controller.
Question: Why not use u  e2 (t ) instead of u  | e(t ) | e(t )?
• Example: level control in surge vessels.
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Nonlinear Transformations of Variables
Chapter 16
• Objective: Make the closed-loop system as linear as possible. (Why?)
• Typical approach: transform an input or an output.
Example: logarithmic transformation of a product composition in a high
purity distillation column. (cf. McCabe-Thiele diagram)
x*D  log
1  xD
1  xDsp
(16-27)
where x*D denotes the transformed distillate composition.
• Related approach: Define u or y to be combinations of several
variables, based on physical considerations.
Example: Continuous pH neutralization
CVs: pH and liquid level, h
MVs: acid and base flow rates, qA and qB
• Conventional approach: single-loop controllers for pH and h.
• Better approach: control pH by adjusting the ratio, qA / qB, and
control h by adjusting their sum. Thus,
u1 = qA / qB and
u2 = qA / qB
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Gain Scheduling
Chapter 16
• Objective: Make the closed-loop system as linear as possible.
• Basic Idea: Adjust the controller gain based on current measurements of
a “scheduling variable”, e.g., u, y, or some other variable.
• Note: Requires knowledge about how the process gain changes with this
measured variable.
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Examples of Gain Scheduling
Chapter 16
• Example 1. Titration curve for a strong acid-strong base neutralization.
• Example 2. Once through boiler
The open-loop step response are shown in Fig. 16.18 for two
different feedwater flow rates.
Fig. 16.18 Open-loop responses.
• Proposed control strategy: Vary controller setting with w, the fraction of
full-scale (100%) flow.
Kc  wKc ,  I   I / w,  D   D / w,
(16-30)
• Compare with the IMC controller settings for Model H in Table 12.1:
Model H : G ( s) 
 s
Ke
,
s  1
Kc 
1
K
 
c 

2,

I   

2
,
D 

2  
2
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Adaptive Control
Chapter 16
• A general control strategy for control problems where the process or
operating conditions can change significantly and unpredictably.
Example: Catalyst decay, equipment fouling
• Many different types of adaptive control strategies have been proposed.
• Self-Tuning Control (STC):
– A very well-known strategy and probably the most widely used adaptive
control strategy.
– Basic idea: STC is a model-based approach. As process conditions change,
update the model parameters by using least squares estimation and recent u &
y data.
• Note: For predictable or measurable changes, use gain scheduling
instead of adaptive control
Reason: Gain scheduling is much easier to implement and less trouble
prone.
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Chapter 16
Block Diagram for Self-Tuning Control
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