Ramesh R. Rao

Isermann Department of Chemical EngineeringRensselaer Polytechnic Institute

Applications of Model Predictive Control

Glass Forehearth ControlDrug Infusion Control

Chemical Process Control Group at RPI

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

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.

Biomedical systems: regulation of hemodynamic variables of patients in critical care or surgery. Automated infusion of insulin for diabetics.

Optimization of chromatographic separations: off-line and run-to-run optimization of protein separations.

Batch reactor operability and safety, multirate nonlinear model predictive control.

Control of a Glass Cooling Forehearth

Motivation Downstream product quality dependent on

temperature Open-loop unstable process Requires tight regulation of temperature

Illustration source: (http://www.brainwave.com/industry/d3_furnace.html)

Glass Cooling Forehearth

123456 T0

T6

Tc1Tc3Tc5

T2T4

R

iipi

p

isssiccciipi

p

TTMMwhere

TTMCdt

dTVC

ifor

TTAUTTAUTTMCdt

dTVC

ifor

ii

60

1

1

6,4,2

5,3,1

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Steady-State Energy Balance

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

Eigen ValuesSS1 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

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.

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Estimation using EKF

EKF Equations

Model prediction

Kalman filter gain and covariance

Measurement correction

TwwwT1k1k|1k1k1k|k

w1k|1k

w

w1k|1k

w1k1k|1kt

w1k|k

1k|k

)(R

xA

)xC,u,x(F

x

xs

1k|kkkk|k

1vTk1k|kk

Tk1k|kk

)LI(

)R(L

)yy(Lx

x

x

xkkkw

1k|k

1k|k

wk|k

k|k

Interaction of Estimation and Control

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Setpoint tracking Parameter estimation

Viscosity parameter Unmeasured disturbance

fluctuations in flow rate M0

Bias in heating circuit [Tc1, Tc3, Tc5]

Bias in output measurements [T2, T4, T6] Control parameters:

sample time 10 minutes 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

Results

Summary of Glass Forehearth Control

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

Patients in critical care or surgery require regulation of vital states

Typical clinical practice manual regulation with drip IV programmable pumps (open loop)

State of the art clinical trials of closed loop control of mean

arterial pressure (MAP)

Control objective automated regulation of hemodynamic

variables with physician “in the loop” free-up physician to monitor difficult-to-

measure variables

Problem Overview

Multivariable, nonlinear system regulation of mean arterial pressure (MAP),

cardiac output (CO) using sodium nitroprusside (SNP), phenylephrine (PNP) and dopamine (DPM)

Inter- and intra-patient variability requires on-line adaptation to patient conditions

Interactions from anesthetics Presence of constraint specifications

inputs: drug dosage 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

Lack of models that encompass the wide variety of patient responses to drugs

Models from first principles fairly cumbersome requires online parameter

estimation/adaptation not viable for real-time applications

Empirical model fitting step response tests pseudo random binary sequence (PRBS) tests

Optimization

Prediction

r(k)

Reference Model Plant

1

2

m

Model Bank

-

-

-

+

+

u(k) y(k)

i(k)

y(k)^

y(k)

wi(k)

Weight Computation

Constrained MPC

X

X

X

+

+ +

+

yi(k)^

y(k+1:P)^

Multiple-Model Predictive Control (MMPC)

Model Bank Parameters

MAP (mmHg) Cardiac Output (ml/kg/min)Gain

(by g/kg/min)(Time Constant,Time Delay)

Pairs in MinutesGain

(by g/kg/min)(Time Constant, Time Delay)

Pairs in Minutes

SNP -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)

DPM 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)

PNP 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)

MENNEN

BAXTER

ANESTHESIA

ROTARY PUMPS

DRUGS

MAP

CO

Experimental Setup

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MAP Regulation (SISO)

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MAP and CO Regulation (MIMO)

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Weighted-Model Tracking

MAP and CO Regulation (MIMO)

Summary of Drug Infusion Control

Multiple-model predictive control approach weighted model bank provides a flexible and

bounded prediction model to handle inter- and intra-patient variability

handling constraints

Controller issues controller tuning 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

David M. Koenig, Corning Inc.

Animal Research Facility – Albany Medical Center

Vinay Prasad, Brian Aufderheide

AspenTech