James B. Rawlings Research Group
Murali R. Rajamani
B. Chem. Engg., University of MumbaiInstitute of Chemical Technology, 2002 Ph.D., University of WisconsinMadison, 2007
rajamani[AT]bevo[DOT]che[DOT]wisc[DOT]edu


Model Predictive Control (MPC) is one of the most widely used
control techniques in the chemical industry. As its name suggests,
MPC uses a model to predict the inputs that will give optimal
control. MPC casts the control
problem in the form of an optimization, which makes it convenient to
handle constraints and nonlinear models explicitly. The three
components of MPC are the regulator/controller, the estimator and the
target calculator. A simple block representation of MPC is shown in
Figure 1.
Figure 1. Model Predictive Controlblock diagram



It is usually convenient to start with a discrete time state space
model of the following form (may be a minimal realization of a
transfer function):
in which, , , and are known; , and
respectively represent the states, inputs and outputs; and and
are the state and output noises.
The estimator part of the MPC uses the past outputs and inputs to calculate
the optimal estimate of
the current state of the plant. The regulator on the other hand
predicts the optimal inputs over a future horizon. The operator must
choose the parameters for the regulator ( and
) and the estimator ( and ). The tuning parameters for
the regulator are straightforward to choose.
The parameters for the estimator on the other hand are not intuitive
and require the knowledge of the disturbances entering the plant.
Usually only closed loop data is available from the plant, in which case an
autocovariance least squares (ALS) technique can be used to find the
optimal parameters for the estimator.
Example of industrial application
The technique was applied to data from a gasphase reactor at
Eastman chemical company to update the estimator. The process is
represented in Figure 2.
Figure 2. Eastman gas phase reactor control



By calculating the new parameters for the estimator from data, the
error in the predicition of the states is reduced, which can be seen
in Figures 3 and
4.
Figure 3.
Composition prediction error frequencyoriginal and updated estimator.



Figure 4.
Temperature prediction error frequencyoriginal and updated estimator.



Example of laboratory scale CSTR
Figure 5. Laboratory setup to verify technique



Figure 5 shows a setup of a laboratory CSTR
where acetic anhydride mixes with water to give acetic acid. This CSTR
follows a non linear model due to the temperature effects. The above
technique was also used to find the optimal parameters for the
estimator when uncharacterised disturbances entered the plant. An
example of the improved performance with the updated filter gain is
shown in Figure 6 for
the CSTR.
Figure 6. Output while rejecting a
deterministic output disturbance.



The goal of our research is to extend the technique to nonlinear models so
that parameters for the Extended Kalman Filter (EKF) and the Moving Horizon
Estimator (MHE) can be estimated.
Validation of the technique will be done using the laboratory
CSTR.
 1

Murali R. Rajamani.
Databased Techniques to Improve State
Estimation in Model Predictive
Control.
PhD thesis, University of WisconsinMadison, October 2007.
 2

Murali R. Rajamani and James B. Rawlings.
Estimation of the disturbance structure from data using semidefinite
programming and optimal weighting.
Technical Report 200702, TWMCC, Department of Chemical and
Biological Engineering, University of WisconsinMadison (Available at
http://jbrwww.che.wisc.edu/techreports.html), June 2007.
 3

James B. Rawlings and Murali R. Rajamani.
A hybrid approach for state estimation: Combining moving horizon
estimation and particle filtering.
In Sandia CSRI Workshop, LargeScale Inverse Problems and
Quantification of Uncertainty, Santa Fe, New Mexico, September 2007.
 4

Murali R. Rajamani, James B. Rawlings, and Tyler A. Soderstrom.
Application of a new databased covariance estimation technique to a
nonlinear industrial blending drum.
Submitted for publication in IEEE Transactions on Control
Systems Technology, September, 2007.
 5

Murali R. Rajamani, James B. Rawlings, and S. Joe Qin.
Achieving state estimation equivalence for misassigned disturbances
in offsetfree model predictive control.
Submitted for publication in AIChE Journal, August, 2007.
 6

Murali R. Rajamani and James B. Rawlings.
Estimation of the disturbance structure from data using semidefinite
programming and optimal weighting.
Accepted for publication in Automatica, January, 2008.
 7

Wu Zhuang, Murali R. Rajamani, James B. Rawlings, and Jakob Stoustrup.
Application of autocovariance leastsquares method for model
predictive control of hybrid ventilation in livestock stable.
In Proceedings of the American Control Conference, New York,
USA, July 1113 2007.
 8

Murali R. Rajamani and James B. Rawlings.
Improved state estimation using a combination of moving horizon
estimator and particle filters.
In Proceedings of the American Control Conference, New York,
USA, July 1113 2007.
 9

Wu Zhuang, Murali R. Rajamani, James B. Rawlings, and Jakob Stoustrup.
Model predictive control of thermal comfort and indoor air quality in
livestock stable.
In Proceedings of the European Control Conference, Kos, Greece,
25 July 2007.
 10

Murali R. Rajamani and James B. Rawlings.
Estimation of noise covariances and disturbance structure from data
using least squares with optimal weighting.
In AIChE Annual Meeting, San Francisco, California, November
2006.
 11

Murali R. Rajamani, James B. Rawlings, and S. Joe Qin.
Equivalence of MPC disturbance models identified from data.
In Proceedings of Chemical Process Control 7, Lake Louise,
Alberta, Canada, January 2006.
 12

Brian J. Odelson, Murali R. Rajamani, and James B. Rawlings.
A new autocovariance leastsquares method for
estimating noise covariances.
Automatica, 42(2):303308, February 2006.
University of Wisconsin
Department of Chemical Engineering
Madison WI 53706