1. cascade control chapter 16 2. time-delay compensation 3...
TRANSCRIPT
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Enhanced Single-Loop Control Strategies
1. Cascade control2. Time-delay compensation3. Inferential control4. Selective and override control5. Nonlinear control6. Adaptive control
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Example: Cascade ControlC
hapt
er 1
6
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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. primaryinner vs. outer
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1
2
1
2
1
2
= hot oil temperature= fuel gas pressure= cold oil temperature (or cold oil flow rate)= supply pressure of gas fuel= measured value of hot oil temperature= measured value of fuel gas tem
m
m
YYDDYY
1 1
2 2
perature= set point for
= set point for sp
sp
Y Y
Y Y%
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1 21
2 2 2 2 1 2 2 1 1(16 5)
1P d
c v p m c c v p p m
G GD G G G G G G G G G GY
= −+ +
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Example 16.1Consider the block diagram in Fig. 16.4 with the following transfer functions:
( )( )1 2
1 22 1
5 4 11 4 1 2 1
11 0.05 0.23 1
v p p
m md d
G G Gs s s
G G G Gs
= = =+ + +
= = = =+
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Example 16.2Compare the set-point responses for a second-order process with a time delay (min) and without the delay. The transfer function is
Assume and time constants in minutes. Use the following PI controllers. For min, while for min the controller gain must be reduced to meet stability requirements
( ) ( )( )16 18( )
5 1 3 1
s
peG s
s s
θ−−=
+ +
1m vG G= =0,θ= 13.02 6.5cK andτ= = 2θ=
( )11.23, 7.0min .cK τ= =
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( ) ( )1 1 2 16 19spE E Y Y Y Y Y −= − = − − −% % %'
If the process model is perfect and the disturbance is zero, then 2Y Y=% and
( )1 16 20spE' Y Y −= − %
For this ideal case the controller responds to the error signal that would occur if not timewere present. Assuming there is no model error the inner loop has the effective transfer function
( ),G G=%
( ) ( )16 211 * 1
cs
c
GPGE G G e θ−
−= =+ −
'
Time Delay Compensation
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For no model error:
By contrast, for conventional feedback control
θ= * - sG = G G e%
( )1 1
1 1
θ
θ
θ
−
−
−
′ =+ −
′= =
′+ +
cc * s
c
* sc c
* s *sp c c
GG
G G e
G G e G GYY G G e G G
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( )* 16 231 *
sc
ssp c
G G eYY G G e
θ
θ
−
−= −+
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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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Inferential Control with Fast and Slow Measured Variables
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Selective Control Systems & Overrides
• For every controlled variable, it is very desirable that there be at least one manipulated variable.
• But for some applications,
NC > NMwhere:
NC = number of controlled variables
NM = number of manipulated variables
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• Solution: Use a selective control system or an override.Selective control is also referred as “Auctioneering”.
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• Low selector:
• High selector:
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• Median selector:
• The output, Z, is the median of an odd number of inputs
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• multiple measurements• one controller• one final control element
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Example: High Selector Control System
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2 measurements, 2 controllers, 1 final control element
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Overrides• 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).• Softer than ESD or SIS• Example:
- anti-reset wind-up- lower and upper heat input rate for distillation
column for ensuring liquid inventory or preventing flooding of the column
• Split-range control
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Nonlinear Control Strategies• Most physical processes are nonlinear to some degree. Some are very
nonlinear.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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Enhancements of Conventional Feedback Control
We will consider three enhancements of conventional feedback control:1. Nonlinear modifications of PID control2. Nonlinear transformations of input or output variables3. Controller parameter scheduling such as gain scheduling.
Nonlinear Modifications of PID Control:
0(1 ( ) ) (16-26)c cK K a|e t |= +Cha
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• Kc0 and a are constants, and e(t) is the error signal (e = ysp - y).
• Also called, error squared controller because controller output is proportional to |e(t)||e(t)|
• Example: level control in surge vessels.
• One Example: nonlinear controller gain
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Nonlinear Transformations of Variables
• 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)
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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 neutralizationCVs: pH and liquid level, hMVs: 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
1 (16-27)1
* DD
Dsp
xx logx−
=−
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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. 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.
(16-30)c c I I D DK wK , / w, / w,τ τ τ τ= = =
• Compare with the IMC controller settings for Model H in Table 12.1:
1 2( ) , , ,1 2 2
2
s
c I D
c
KeG s Ks K
θθτ θ τθτ τ τθτ τ θτ
− += = = + =
+ ++Model H :
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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 controlReason: Gain scheduling is much easier to implement and less trouble
prone.
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Block Diagram for Self-Tuning Control
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Bumpless Transfer
• When a control loop is turned on without bumpless transfer, the process can become unduly upset.
• With bumpless transfer, an internal setpoint is used for the controller and the internal setpoint is ramped at a slow rate from the initial conditions to the actual desired setpoint to order to provide a smooth startup of a control loop.
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Comparison of True and Internal Setpoints
Time
Internal Setpoint
True Setpoint
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Control Performance With and Without Bumpless Transfer
Time
w/o bumpless transfer
w/ bumpless transfer
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Split Range Flow Control• In certain applications, a single flow control
loop cannot provide accurate flow metering over the full range of operation.
• Split range flow control uses two flow controllers (one with a small control valve and one with a large control valve) in parallel.
• At low flow rates, the large valve is closed and the small valve provides accurate flow control.
• At large flow rates, both valve are open.
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Split Range Flow Controller
FT
FT
FC
FC
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Coordination of Control Valves for Split Range Flow Control
Total Flow Rate
Sign
al to
Con
trol
Val
ve
(%)
Larger ControlValve
Smaller ControlValve
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Example for Split Range Flow Control
AcidWastewater
NaOHSolution
Effluent
FTFT
FC
pHTpHC
RSP×
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Titration Curve for a Strong Acid-Strong Base System
02468
101214
0 0.002 0.004 0.006 0.008 0.01Base to Acid Ratio
pH
• Therefore, for accurate pH control for a wide range of flow rates for acid wastewater, a split range flow controller for the NaOH is required.
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Other Split-Range Flow Control Examples
• When the controlled flow rate has a turn down ratio greater than 9
• See value sizing examples in Chapter 2
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Split Range Temperature Control
TT
CoolingWater
Steam
Split-RangeTemperature
Controller
TT TC
RSP
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Split Range Temperature Control
0
20
40
60
80
100
Error from Setpoint for Jacket Temperature
Sign
al to
Con
trol
Val
ve
(%)
SteamCooling Water
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Overview
• All controllers that employ integral action should have anti-reset windup applied.
• Bumpless transfer provides a means for smooth startup of a control loop.
• When accurate metering of a flow over a very wide flow rate range is called for, use split range flow control.
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Bumpless Transfer
• When a control loop is turned on without bumpless transfer, the process can become unduly upset.
• With bumpless transfer, an internal setpoint is used for the controller and the internal setpoint is ramped at a slow rate from the initial conditions to the actual desired setpoint to order to provide a smooth startup of a control loop.
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Comparison of True and Internal Setpoints
Time
Internal Setpoint
True Setpoint
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Control Performance With and Without Bumpless Transfer
Time
w/o bumpless transfer
w/ bumpless transfer
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Split Range Flow Control• In certain applications, a single flow control
loop cannot provide accurate flow metering over the full range of operation.
• Split range flow control uses two flow controllers (one with a small control valve and one with a large control valve) in parallel.
• At low flow rates, the large valve is closed and the small valve provides accurate flow control.
• At large flow rates, both valve are open.
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Split Range Flow Controller
FT
FT
FC
FC
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Coordination of Control Valves for Split Range Flow Control
Total Flow Rate
Sign
al to
Con
trol
Val
ve
(%)
Larger ControlValve
Smaller ControlValve
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Example for Split Range Flow Control
AcidWastewater
NaOHSolution
Effluent
FTFT
FC
pHTpHC
RSP×
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Titration Curve for a Strong Acid-Strong Base System
02468
101214
0 0.002 0.004 0.006 0.008 0.01Base to Acid Ratio
pH
• Therefore, for accurate pH control for a wide range of flow rates for acid wastewater, a split range flow controller for the NaOH is required.
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Other Split-Range Flow Control Examples
• When the controlled flow rate has a turn down ratio greater than 9
• See value sizing examples in Chapter 2
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Split Range Temperature Control
TT
CoolingWater
Steam
Split-RangeTemperature
Controller
TT TC
RSP
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Split Range Temperature Control
0
20
40
60
80
100
Error from Setpoint for Jacket Temperature
Sign
al to
Con
trol
Val
ve
(%)
SteamCooling Water
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Overview
• All controllers that employ integral action should have anti-reset windup applied.
• Bumpless transfer provides a means for smooth startup of a control loop.
• When accurate metering of a flow over a very wide flow rate range is called for, use split range flow control.