05-07-2013, 04:23 PM
Robust Nonlinear Model Predictive Control of Batch Processes
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ABSTRACT
NMPC explicitly addresses constraints and nonlinearities during the feedback control
of batch processes. This NMPC algorithm also explicitly takes parameter uncertainty
into account in the state estimation and state feedback controller designs. An extended
Kalman filter estimates the process noise co®ariance matrix from the parameter uncertainty
description and employs a sequential integration and correction strategy to reduce
biases in the state estimates due to parameter uncertainty. The shrinking horizon NMPC
algorithm minimizes a weighted sum of the nominal performance objecti®e, an estimate
of the ®ariance of the performance objecti®e, and an integral of the de®iation of the
control trajectory from the nominal optimal control trajectory. The robust performance
is quantified by estimates of the distribution of the performance index along the batch
run obtained by a series expansion about the control trajectory. The control and analysis
approaches are applied to a simulated batch crystallization process with a realistic uncertainty
description. The proposed robust NMPC algorithm impro®es the robust performance
by a factor of six compared to open loop optimal control, and a factor of two
compared to nominal NMPC. Monte Carlo simulations support the results obtained by
the distributional robustness analysis technique.
Introduction
Batch processes are widely applied in many sectors of the
chemical industries including pharmaceuticals, polymers, food
products, biotechnology, and electronic chemicals. Increased
competition has motivated the interest in mathematical modeling,
optimization, and advanced process control techniques
that enable the operation of flexible high-performance production
lines ŽLe Lann et al., 1999; Rippin, 1983.. Advanced
control techniques have the potential to improve performance.
Since the advent of dynamic matrix control ŽCutler
and Ramaker, 1980., model predictive control ŽMPC. has
been the most popular advanced control strategy.
Conclusions
A robust EKF-based NMPC algorithm for batch processes
is presented which incorporates parameter uncertainty into
both the EKF and NMPC algorithms. A series expansion of
the performance index is used to estimate the distribution of
the process output for the whole batch run. For a simulated
batch crystallization process, NMPC considerably improved
robust performance compared to open-loop optimal control.
Robust performance is significantly enhanced when parameter
uncertainty is taken into account in the objective function
of the NMPC. The conclusions obtained from the series-based
analysis approach are verified through Monte Carlo simulation.