ISR research accomplishments
Feedback Optimization of Process and Manufacturing Systems Operation in the Presence of Modeling Error
Research team
Evanghelos Zafiriou (ChE/ISR), S. Adivikolanu, J.-H. Cheng, G. Gattu, H.-W. Chiou, R. Sreenivasan
Accomplishment
Development of a paradigm that
makes the actual system operation an integral part of its optimization,
to achieve robustness with respect to modeling error
Does not require model parameter adaptation, which cannot remove all model error for most complex systems due to structural model error and insufficient data
Main concept. Standard approach in handling Modeling Error (model-plant mismatch): Use model in operation optimization, Apply “optimal” operating policy and collect measurement (feedback) information, Use data to update model and repeat.
New approach uses analogy between repeated system operation and iterations in numerical optimization. Incorporates measurement information directly in computing an optimization gradient so that it is not based only on the (uncertain) model. Is inherently robust to modeling error and does not require model adaptation between repeated system operation. Can be applied with any optimization technique that utilizes gradients in finding a search direction. Can be used with algebraic or differential equation models, dynamic, static or steady state models.
Examples
1. Economic Optimization of Steady State Process Operations. Otto-Williams CSTR. Very large structural error in the chemistry is emulated to test robustness. Previous attempts in the literature determined this error to be too much to be handled by parameter adaptation.
(left) True optimum
reached from all corners of optimization space, without any model
adaptation.
(left) The combination
of measurements and the imperfect model result in search directions
that may not be the best, but are directions of improvement.
Profit surfaces as function
of optimization variables.
(left) For “true”
process equations
(left) For model equations
2. Run-to-Run
Optimization of Plasma Etching Reactor
Test on Commercial Tool (AMD, Austin). Nonlinear RSM model with four inputs (recipe variables) and two outputs (etch rate and uniformity). Model error present; became worse after long interruption for maintenance and cleaning following the third wafer run. No model adaptation. Outputs reach target values in spite of difference with values predicted by model. Objective function (weighted sum of deviations from target for outputs) improved in every run.
(left) Recipe variable
changes
3. Run-to-Run
Control of Drifts in Semiconductor Manufacturing
Internal Model Control formulation. Extends EWMA algorithm to handle drifts. Provides a framework for robustness analysis with respect to model error. Applies to systems with multiple inputs and outputs. Experimentally tested on a Tungsten CVD reactor in collaboration with Prof. G. W. Rubloff’s group.
(left) Curves providing
bounds for guaranteed performance, robustness, noise handling
can be used to tune the RtR controller a priori
Allows optimization of systems
with significant model uncertainty. Applicable to a wide range of
systems and types of models. Applied to:
-- Economic optimization of steady state process operations
-- Run-to-Run control of semiconductor manufacturing systems
-- On-line modification of optimal operating policies for batch
polymerization reactors
For more information
Zafiriou et al., Electrochem. Soc. Proc.,Vol. 95-4, pp. 18-31, 1995
Adivikolanu, PhD Thesis, 1999; Adivikolanu and Zafiriou, IEEE Trans. on Electronics Packaging Manufacturing, Vol. 23, January 2000
