Chapter 16
Enhanced Single-Loop Control Strategies
Chapter 16
Chapter 16
Cascade Control (multi-loop)
Chapter 16
•
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 setpoint 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
Chapter 16
Gp1Gd 2
Y1

D2 1  Gc 2GvGp 2Gm 2  Gc1Gc 2GvGp 2Gp1Gm1
(Eq.16-5)
Chapter 16
Chapter 16
Chapter 16
Time Delay Compensation
•
Model-based feedback controller that improves
closed-loop performance when time delays are present
•
Effect of added time delay on PI controller performance
for a second order process (t1 = 3, t2 = 5) shown below
Chapter 16
Chapter 16
No model error:
GC 
G  G*e s  G*e s
GC

1  GC G* 1  e s

GC G*e  s
GC G
Y


*
Ysp 1  GC G
1  GC G *
GC G
Y

Ysp 1  GC G
(16  22)
(sensitive to model errors > +/- 20%)
Chapter 16
Direct Synthesis Approach (Smith Predictor)
Chapter 16
GC GP
Y

 Q( s)e s
Ysp 1  GC GP
Assume time delay between set-point change and controlled
variable (same as process time delay,  ).
If
then
G P  P(s)es
GC 
C
1
R  1 
1  C G P P  Pes
R
Q
From Block Diagram,
Equating...
GC 
Q
GC 
P(1  Q)
1
1
 P  P es
GC
Chapter 16
SELECTIVE CONTROL SYSTEMS (Overrides)
For every controlled variable, there must be at least one manipulated
variable.
Chapter 16
In some applications
# of controlled
variables
•Low selector:
•High selector:
NC  N M
# of manipulated
variables
Chapter 16
Figure 16.13 Control of a reactor hot spot temperature by using a high selector.
multiple measurements
one controller
one final control element
Chapter 16
Figure 16.15 A selective control system to handle a sand/water slurry.
Override using PI controllers - “old way” (vs. digital logic)
2 measurements, 2 controllers, 1 F.C.E.
Chapter 16
Split Range Control
2 Manipulated Vars.:
V1 and V2
While V1 opens, V2 should close
1 Controlled Var.:
Reactor pressure
Chapter 16
3
6
9
15
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
Chapter 16
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.
Examples of Gain Scheduling
• Example 1. Once through boiler
Chapter 16
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 ,
t I  t I / w, t D  t D / w,
• Example 2. Titration curve for a strong acid-strong base
neutralization.
(16-30)
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.
16-26
Chapter 16
Chapter 16
Figure 16.20 Membership functions for room temperature.
Chapter 16
Figure 16.23 Membership functions for the inputs of the PI fuzzy
controller (N is negative, P is positive, and Z is zero).
Chapter 16
Chapter 16
Chapter 16
Basic Design Information
Chapter 16
Final Control System – Distillation Train
Chapter 16
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