Transcript No Slide Title - Rensselaer Polytechnic Institute

Applications of Model Predictive Control
Ramesh R. Rao
Isermann Department of Chemical Engineering
Rensselaer Polytechnic Institute
Glass Forehearth Control
Drug Infusion Control
Chemical Process Control Group at RPI
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Kevin Schott: Multiple model adaptive control
(MMAC)
Manoel de Carvalho: CVD reactor modeling and
control
Ramesh Rao: Drug infusion control, multiple model
predictive control (MMPC), gain scheduling
Vinay Prasad: batch operability/safety, multirate
estimation and control
Brian Aufderheide: Drug infusion and MMPC
Deepak Nagrath: optimization of chromatographic
separations, run-to-run control
Sandra Lynch: insulin infusion control
Vikas Saraf: Autotuning for unstable cascade
processes
Chemical Process Control Group at RPI
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Fundamental process control theory and
applications to practical problems, with a focus on
the effect of nonlinearity on control and the
interaction of process design and control.
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Biomedical systems: regulation of hemodynamic
variables of patients in critical care or surgery.
Automated infusion of insulin for diabetics.
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Optimization of chromatographic separations: offline and run-to-run optimization of protein
separations.
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Batch reactor operability and safety, multirate
nonlinear model predictive control.
Control of a Glass Cooling Forehearth
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Motivation
 Downstream product quality dependent on
temperature
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Open-loop unstable process
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Requires tight regulation of temperature
Illustration source: (http://www.brainwave.com/industry/d3_furnace.html)
Glass Cooling Forehearth
Tc5
6
T6
5
Tc3
4
Tc1
2
3
T4
1
T0
T2
for i  1,3,5

dTi
 C pV
 MC p Ti 1  Ti   U c Ac Tci  Ti
dt
for i  2,4,6
dTi
 C pV
 MC p Ti 1  Ti 
dt
where M  M 0   T6  TR 

 U s Asi Ts  Ti 
Steady-State Energy Balance
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Steady-States & Eigen Values
Zone Temp. oC
SS1
SS2
SS3
T1
581.8
979.6
1093.9
T2
581.8
979.6
1093.9
T3
501.8
850.5
1035.3
T4
501.8
850.5
1035.3
T5
763.1
837.2
1016.5
T6
763.1
837.2
1016.5
SS1
Eigen Values
SS2
SS3
1
-0.0119
-0.0673
-0.1732
2
-0.0104
0.0052
-0.0142
3
-0.0007
-0.0422 + 0.0257i
-0.1238 + 0.0609i
4
-0.0008
-0.0422 - 0.0257i
-0.1238 - 0.0609i
5
-0.0044 + 0.0074i
-0.0206 + 0.0263i
-0.0640 + 0.0612i
6
-0.0044 - 0.0074i
-0.0206 - 0.0263i
-0.0640 - 0.0612i
Control System Description
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Control of temperature in 3 zones of the forehearth
[T2, T4, T6] by manipulating [Tc1, Tc3, Tc5]
Need to operate at open-loop unstable steady state
operating point
Existence of model mismatch between plant and
model in addition to unmeasured disturbances and
measurement noise
EKF based nonlinear MPC is used for state
estimation and control
 explicit handling of constraints

inferential control
Estimation and Control Strategy
Extended Kalman filtering (EKF) is used to obtain current
estimates of model states.
Disturbances are modeled as integrated white noise states
augmented to the original model.
Nonlinear MPC algorithm uses EKF state estimates to
predict future values of states and controlled outputs, which
are then used to calculate the optimal manipulated variable
action.
Both the EKF and the nonlinear MPC algorithms are based
on successive linearization of nonlinear model.
Estimation using EKF
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EKF Equations
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Model prediction
 x k|k 1  Ft s ( x k 1|k 1 , u k 1 , Cw x kw1|k 1 )

x w   
w w
A
x
k 1|k 1
 k|k 1  

 k|k 1   k 1 k 1|k 1 Tk 1   w R w ( w )T
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Kalman filter gain and covariance
Lk   k|k 1 Tk ( k  k|k 1 Tk  R v ) 1
 k|k  (I  L k  k ) k|k 1
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Measurement correction
 x k|k   x k|k 1 
 x w    x w   L k ( y k  ŷ k )
 k|k   k|k 1 
Interaction of Estimation and Control
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Results
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Setpoint tracking
Parameter estimation
 Viscosity parameter 
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Unmeasured disturbance
 fluctuations in flow rate M0
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Bias in heating circuit [Tc1, Tc3, Tc5]
Bias in output measurements [T2, T4, T6]
Control parameters:
 sample time 10 minutes
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constraints on inputs 5 deg. C per 10 min
prediction horizon P = 20, control horizon N = 3,
output weights Q 1:1:5, input weights R 1:1:1,
Gaussian noise 0.1 deg. C
Summary of Glass Forehearth Control
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A first principles model was developed and
parameters were identified from plant data
EKF based NLMPC was developed and tested in
simulation studies
Setpoint tracking and regulatory control in the
presence of disturbances was achieved
Motivation For Drug Infusion Control
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Patients in critical care or surgery
 require regulation of vital states
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Typical clinical practice
 manual regulation with drip IV
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programmable pumps (open loop)
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State of the art
 clinical trials of closed loop control of mean
arterial pressure (MAP)
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Control objective
 automated regulation of hemodynamic variables
with physician “in the loop”
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free-up physician to monitor difficult-to-measure
variables
Problem Overview
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Multivariable, nonlinear system
 regulation of mean arterial pressure (MAP),
cardiac output (CO) using sodium nitroprusside
(SNP), phenylephrine (PNP) and dopamine (DPM)
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Inter- and intra-patient variability
 requires on-line adaptation to patient conditions
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Interactions from anesthetics
Presence of constraint specifications
 inputs: drug dosage
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outputs: setpoint specified as range, min or max
Use model predictive control (MPC) to handle
constraints explicitly
 model should encompass drug responses
Controller Design Challenges
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Lack of models that encompass the wide variety of
patient responses to drugs
Models from first principles
 fairly cumbersome
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requires online parameter estimation/adaptation
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not viable for real-time applications
Empirical model fitting
 step response tests
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pseudo random binary sequence (PRBS) tests
Multiple-Model Predictive Control (MMPC)
Constrained MPC
r(k)
Reference
Model
u(k)
y(k)
Optimization
Plant
Model
Bank
^y(k+1:P)
Prediction
+
1
-
^yi(k)
2
+
+
^y(k)
y(k)
m
-
+
+
X
+
X
X w (k)
i
Weight
Computation
i(k)
Model Bank Parameters
MAP (mmHg)
SNP
DPM
PNP
Cardiac Output (ml/kg/min)
Gain
(Time Constant,Time Delay)
Gain
(Time Constant, Time Delay)
(by g/kg/min)
Pairs in Minutes
(by g/kg/min)
Pairs in Minutes
-6 to -52
(1.2,0.5), (1.5,1.0), (2.0,1.5)
-1 to -9
(1.0,0.5), (2.0,1.0)
1 to 9
(5.0,2.0), (7.0,4.0)
5 to 57
(6.0,3.0), (7.0,5.0), (8.0,6.0)
2 to 13
(0.5,0.0), (1.0,0.5), (2.0,1.5)
-3 to -27
(1.0,1.0), (2.0,2.0)
Experimental Setup
BAXTER
ROTARY PUMPS
MENNEN
CO
MAP
DRUGS
ANESTHESIA
MAP Regulation (SISO)
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MAP and CO Regulation (MIMO)
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Weighted-Model Tracking
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MAP and CO Regulation (MIMO)
Summary of Drug Infusion Control
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Multiple-model predictive control approach
 weighted model bank provides a flexible and
bounded prediction model to handle inter- and
intra-patient variability
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Controller issues
 controller tuning
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handling constraints
choice of model banks (model types, number of
models)
Future work
 develop weighting scheme more conducive to
blending

more experiments
Acknowledgements

B. Wayne Bequette

The Whitaker Foundation, NSF, Merck, P&G
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David M. Koenig, Corning Inc.
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Animal Research Facility – Albany Medical Center
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Vinay Prasad, Brian Aufderheide
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AspenTech