No Slide Title
Download
Report
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
1
Chapter 16
Example: Cascade Control
2
3
Chapter 16
4
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
5
6
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
7
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
8
9
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 3.02and1 6.5 min, while for 2 min the controller
gain must be reduced to meet stability requirements Kc 1.23,1 7.0min .
10
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
11
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
12
13
Chapter 16
14
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
15
Chapter 16
Inferential Control with Fast and Slow
Measured Variables
16
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.
17
Chapter 16
• Low selector:
• High selector:
• Median selector:
• The output, Z, is the median of an odd number of inputs
18
Chapter 16
Example: High Selector Control System
• multiple measurements
• one controller
• one final control element
19
Chapter 16
2 measurements, 2 controllers,
1 final control element
20
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?
21
22
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.
23
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.
24
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
25
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.
26
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
27
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.
28
Chapter 16
Block Diagram for Self-Tuning Control
29