Transcript Chapter 20 Model Predictive Control • Model Predictive Control (MPC) – regulatory controls that use an explicit dynamic model of the response of process variables.

Chapter 20
Model Predictive Control
• Model Predictive Control (MPC) –
regulatory controls that use an
explicit dynamic model of the
response of process variables to
changes in manipulated variables
to calculate control “moves”.
• Control moves are intended to
force the process variables to
follow a pre-specified trajectory
from the current operating point to
the target.
• Base control action on current
measurements and future
predictions.
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Figure: Two processes exhibiting unusual dynamic
behavior. (a) change in base level due to a step
change in feed rate to a distillation column. (b)
steam temperature change due to switching on soot
blower in a boiler.
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DMC – dynamic matrix control
became MPC – model
predictive control
• Optimal controller is based on
minimizing error from set point
• Basic version uses linear
model, but there are many
possible models
• Corrections for unmeasured
disturbances, model errors are
included
• Single step and multi-step
versions
• Treats multivariable control,
feedforward control
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When Should Predictive
Control be Used?
1. Processes are difficult to control
with standard PID algorithm –
long time constants, substantial
time delays, inverse response,
etc.
2. There is substantial dynamic
interaction among controls, i.e.,
more than one manipulated
variable has a significant effect on
an important process variable.
3. Constraints (limits) on process
variables and manipulated
variables are important for normal
control.
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Model Predictive Control
Originated in 1980s
• Techniques developed by industry:
1. Dynamic Matrix Control (DMC)
- Shell Development Co.,
Cutler and Ramaker (1980),
- Cutler later formed DMC, Inc.
- DMC acquired by Aspentech
in 1997.
2. Model Algorithmic Control (MAC)
• ADERSA/GERBIOS, Richalet
et al (1978)
• Over 4000 applications of MPC since
1980 (Qin and Badgwell, 1998 and
2003).
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Model Predictive Control
Based on Discrete-time
Models
•
•
Time-delay compensation
techniques predict process
output one time delay ahead.
Here we are concerned with
predictive control techniques
that predict the process
output over a longer time
horizon. (e.g., open-loop
response time).
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Figure 20.2 Basic concept for Model Predictive Control
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General Characteristics
• Targets (set points) selected
by real-time optimization
software based on current
operating and economic
conditions
• Minimize square of deviations
between predicted future
outputs and specific reference
trajectory to new targets
• Discrete step response model
• Framework handles multiple
input, multiple output (MIMO)
control problems.
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• Can include equality and
inequality constraints on
controlled and manipulated
variables
• Solves a quadratic
programming problem at each
sampling instant
• Disturbance is estimated by
comparing the actual
controlled variable with the
model prediction
• Usually implements the first
move out of M calculated
moves
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Discrete Step
Response Models
Consider a single input, single output
process:
u
Process
y
Where u and y are deviation
variables (i.e. deviations from
nominal steady-state values).
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Discrete Convolution
Models (continued)
Denote the sampled values as
y1, y2, y3, etc. and u1, u2, u3, etc.
The incremental change in u will
be denoted as
Duk = uk – uk-1
The response, y(t), to a unit step
change in u at t = 0 (i.e., Du0 = 1
is shown in Figure 7.14.
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Figure 7.14 Unit Step Response
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In Fig. 7.14,
Si 
hi 
step response coefficients
impulse response coefficients
Note: hi = Si – Si-1
y1 = y0 + S1Du0
y2 = y0 + S2Du0 (Du0 = 1 for unit step
.
.
change at t = 0)
.
.
.
.
yn = y0 + SnDu0
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Alternatively, suppose that a step
change of Du1 occurred at t = Dt.
Then,
y2 = y0 + S1Du1
y3 = y0 + S2Du1
.
.
.
.
.
.
yN = y0 + SN-1Du1
If step changes in u occur at both
t = 0 (Du0) and t = Dt (Du1).
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From the Principle of Superposition for linear systems:
y1 = y0 + S1Du0
y2 = y0 + S2Du0 + S1Du1
y3 = y0 + S3Du0 + S2Du1
.
.
.
.
.
.
yN = y0 + SNDu0 + SN-1Du1
Can extend also to MIMO Systems
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Figure 20.8. Individual step-response models for a
distillation column with three inputs and four outputs.
Each model represents the step response for 120
minutes. Reference: Hokanson and Gerstle (1992).
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Selection of Design
Parameters
Model predictive control techniques
include a number of design
parameters:
N:
model horizon
Dt: sampling period
P:
prediction horizon
M: control horizon (number of
control moves)
Q:
weighting matrix for predicted
errors (Q > 0)
R:
weighting matrix for control
moves (R > 0)
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Selection of Design
Parameters (continued)
1.
N and Dt
These parameters should be selected so
that N Dt > open-loop settling time.
Typical values of N:
30 < N < 120
2.
Prediction Horizon, P
• Increasing P results in less
aggressive control action
Set P = N + M
3.
Control Horizon, M
• Increasing M makes the controller
more aggressive and increases
computational effort, typically
5 < M < 20
4.
Weighting matrices Q and R
• Diagonal matrices with largest
elements corresponding to most
important variables
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