Enhanced Single-Loop Control StrategiesC
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Cascade Control (multi-loop)
• 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. mastersecondary vs. primary inner vs. outer
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1 21
2 2 2 2 1 2 2 1 11p d
c v p m c c v p p m
G GY
D G G G G G G G G G G
(Eq.16-5)
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Time Delay Compensation
• Model-based feedback controller that improvesclosed-loop performance when time delays are present
• Effect of added time delay on PI controller performancefor a second order process (1 = 3, 2 = 5) shown below
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No model error:
(sensitive to model errors > +/- 20%)
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*
*
* *
11 1
(16 22)1 1
C CC s
sp CC
sC C
sp C C
G G GYG
Y G GG G e
G G e G GY
Y G G G G
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Direct Synthesis Approach (Smith Predictor)
Assume time delay between set-point change and controlledvariable (same as process time delay, ).
If
then
From Block Diagram,
Equating...
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SELECTIVE CONTROL SYSTEMS (Overrides)
For every controlled variable, there must be at least one manipulatedvariable.
In some applications
# of controlledvariables
# of manipulatedvariables
•Low selector:
•High selector:
MC NN
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multiple measurementsone controllerone final control element
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Figure 16.13 Control of a reactor hot spot temperature by using a high selector.
Override using PI controllers - “old way” (vs. digital logic)
2 measurements, 2 controllers, 1 F.C.E.
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Figure 16.15 A selective control system to handle a sand/water slurry.
Split Range Control
2 Manipulated Vars.: V1 and V2
1 Controlled Var.:Reactor pressure
While V1 opens, V2 should close
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3 6 9 15
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Inferential Control
• 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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Gain Scheduling
• 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.
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• Note: Requires knowledge about how the process gain changes with this measured variable.
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Examples of Gain Scheduling
• Example 1. 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.
• Example 2. Titration curve for a strong acid-strong base neutralization.
(16-30)c c I I D DK wK , / w, / w,
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Adaptive Control
• 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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16-26
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Figure 16.20 Membership functions for room temperature.
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Figure 16.23 Membership functions for the inputs of the PI fuzzy controller (N is negative, P is positive, and Z is zero).
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Basic Design Information
Final Control System – Distillation TrainC
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