DOEbased Automatic Process Control with Consideration of Model Uncertainties

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DOE-based Automatic Process Control with
Consideration of Model Uncertainties
Jan Shi and Jing Zhong The University of
Michigan C. F. Jeff Wu Georgia Institute of
Technology
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Outline

• Introduction
• DOE-based Automatic Process Control with
  Consideration of Model Uncertainty
• Process model
• Control objective function
• Controller design strategies
• Simulation and case study
• Summary

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Problem Statement

• Process variation is mainly caused by the change
  of unavoidable noise factors.
• Process variation reduction is critical for
  process quality improvement.
• Offline Robust Parameter Design (RPD) used at the
  design stage
• To set an optimal constant level for controllable
  factors that can ensure noise factors have a
  minimal influence on process responses
• Based on the noise distribution but not requiring
  online observations of noise factors
• Online Automatic Process Control (APC) during
  production
• With the increasing usage of in-process sensing
  of noise factors, it will provide an opportunity
  to online adjust control factors to compensate
  the change of noise factors, which is expected
  to achieve a better performance than offline RPD.

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Motivation of Using APC
y(x,e)
xx1
?b
?a
e
noise distribution
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The Objective and Focus
The research focuses on the development of
automatic process control (APC) methodologies
based on DOE regression models and real-time
measurement or estimation of noise factors for
complex mfg processes
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Literature Review

• For complex discrete manufacturing processes, the
  relationship between the responses (outputs) and
  process variables (inputs) are obtained by DOE
  using a response surface model, rather than using
  dynamic differential/difference equations
• offline robust parameter design (RPD) (Taguchi,
  1986)
• Improve robust parameter design based on the
  exact level of the observed uncontrollable noise
  factors (Pledger,1996)
• Existing APC literature are mainly for automatic
  control of dynamic systems that are described by
  dynamic differential/difference equations.
• Certainty Equivalence Control (CEC) (Stengel,
  1986) The controller design and state estimator
  design are conducted separately (The uncertainty
  of system states is not considered in the
  controller design)
• Cautious Control (CC) (Astrom and Wittenmark,
  1995) The controller is designed by considering
  the system state estimation uncertainty, which is
  extremely difficult for a complex nonlinear
  dynamic system.
• Jin and Ding (2005) proposed Doe-Based APC
  concepts
• considering on-line control with estimation of
  some noise factors.
• No interaction terms between noise and control
  factors in their model.

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Objective

• Develop a general methodology for controller
  design based on a regression model with
  interaction terms.
• Investigate a new control law considering model
  parameter estimation uncertainties
• Compare the performances of CC, CEC, and RPD, as
  well as performance with sensing uncertainties.

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Methodology Development Procedures ? APC Using
Regression Response Models
Obtain significant factors estimated process
model
S1 Conduct DOE and process modeling
Based on key process variable



S2 Determine APC control strategy (considering
model errors
Use certainty equivalence control or cautious
control
Based on observation uncertainty


Based on process operation constraints on
controller
S3 Online adjust controllable factors

Obtain reduced process variation


S4 Control performance evaluation


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1. Process Variable Characterization
Process Variables
Noise Factors
Controllable Factors
Off-line setting Factors
Unobservable Noise Factors
On-line adjustable Factors
Observable Noise Factors
Y f (X, U, e, n)
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2. Control System Framework
Observable Noise Factors (e)
Unobservable Noise Factors (n)
Noise Factors
Target
Feedforward Controller
Manufacturing Process
Response (y)
Controllable Factors (x)
Predicted Response
In-Process Sensing of e
Observer for Noise Factors (e)
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3 Controller Design3.1 Problem Assumptions

• The manufacturing process is static with smoothly
  changing variables over time Parameter Stability

• e, n and e are independent, with E(e)0,
  Cov(e)Se, E(n)0, Cov(n)Sn, E(e)0, Cov(e)Se.
  e are i.i.d.

• Estimated process parameters denoted by
  ,
• is estimated from
  experimental data.

• Observations of measurable noise factors, denoted
  by , are unbiased, i.e.,
  and .

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3 Controller Design 3.2 Objective Function
Objective Function (Quadratic Loss)
Optimization Problem
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3 Controller Design 3.3 Control Strategy
Procedure for Solving Optimization Problem
Step 2 obtain X by solving optimization problem
of JAPC
Process Control Strategy Two Step Procedure
Step 1 Off-line Controllable Factors Setting
Step 2 On-line Automatic Control Law
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4. Case Study An Injection Molding Process
Process Description
Response Variable (y) Percentage
Shrinkage of Molded Parts
Process Variables
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DOE Modeling
Designed Experiment Result (Engel, 1992)
Reduced DOE Model after Coefficient Significance
Tests
Parameter Estimation Error
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Robust Parameter Design
Response Model
Variance Model
RPD Settings
u1 and x3 are adjusted according to target values
as in right table
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DOE-Based APC
Objective Loss Function
Optimal Settings
where
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Simulation Results
Comparison of RPD, CE control and Cautious Control
Assuming
Optimal Off-line Setting
Cautious control law performs much better than RPD
Control Strategy Evaluation
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Simulation Results - 2
Certainty Equivalence assume observation perfect
CE controller performs much better than RD when
the measurement is perfect, but its advantage
decreases when the measurement is not perfect,
and will cause a larger quality loss than RPD
controller under high measurement uncertainty.
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Control strategy with partial sensing failure 1

• Sensor noise level change no modeling error

150 observations, sensor noise level increased
from point 51 to 100, then restored. t1.6
CE Control suffers greatly from noise level change
Mean of RPD has deviated from target
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Control strategy with partial sensing failure 2

• Sensor noise level change

APC considering modeling error
255 observations, sensor noise level increased
from point 101 to 200, then restored
Overall J/J_ce16.8. APC performance is steady
over different noise levels.
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Control strategy with partial sensing failure 3

• Sensor failure

- Assume no modeling error, - 250 observations,
sensor failed from point 51 to 150, then repaired
Control Strategy
Switch to RPD setting after the detection of
sensor failure - Actual system will have step
response
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Industrial Collaboration with OG Technologies
DOE-Based APC Test bed in Hot Deformation
Processes
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Summary

• DOE-Based APC performs better than RPD when
  measurable noise factors are present with not too
  large measurement uncertainty.
• RPD should be employed in case of too large
  measurement uncertainty or there are no
  observable noise factors.
• Cautious control considering measurable noise
  factors and model estimation uncertainty performs
  better than RPD and CE strategy.
• Model updating and adaptive control with
  supervision are promising or the future study.

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Impacts

• Expanding the DOE from off-line design and
  analysis to on-line APC applications, and
  investigates the associated issues in the DOE
  test design and analysis
• Developing a new theory and strategy to achieve
  APC by using DOE-based models including on-line
  DOE model updating, cautious control, and
  supervision.