0806thermalsystems_webinar_2015
DESCRIPTION
ESTE DOCUMENTO ES INTRODUCTORIA AL ANALISIS DE SISTEMAS TERMICOS POR ELEMENTOS FINITOSTRANSCRIPT
Modeling Feedback Control of Thermal Systems in COMSOL
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Lexi Carver Technical Marketing
Engineer COMSOL
Jon Ebert, PhD Director
SC SOLUTIONS
Agenda• Introduction to COMSOL
Multiphysics® software• Simulating Feedback Control
of Thermal Systems• Demo: Rapid Thermal
Processing (RTP) System• Q&A• How To– Try COMSOL Multiphysics®– Contact Us
Prestressed plated metal layers in a model of a micromirror
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Displacement induced by thermal strains and applied pressure in a model of a capacitive pressure sensor
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Feedback Control of Thermal Systemsin COMSOL
Jon EbertSC Solutions, Inc.
Email: [email protected]
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Overview
Feedback control of temperature is important in many manufacturing processes.
At SC we have developed methods for the model-based control of systems where we use physics-based models to develop high-performance temperature control.
This presentation will give an example of one method for designing a simple PID feedback controller (Q-Design).
We will present a simple example of feedback control within a COMSOL model.
A demo with 5-zone temperature control of a Rapid Thermal Processing (RTP) system will be shown.
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Closed-Loop Transfer Function
The Closed-Loop System
PC
Closed-Loop Response:
For a scalar system
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Proportional + Integral + Derivative Control (PID)
This is the most common type of feedback controller
The “gains”, Kp, Ki, and Kd (and td) must be selected by the engineer
There are systematic methods
Here we’ll outline ‘Q’-design
To limit high-frequency noise amplification, we usually low-pass filter the error driving the derivative control:
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Model-Based Control (Q-Design)
Incorporate a mathematical model of the system directly into the controller.
Often referred to as Q-parameterization or Youla parameterization.
References for Q-parameterization Control Design
For stable P, ALL stable controllers can be expressed in this form!
Control design becomes choice of transfer function Q
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A Model-Based Design (‘Q-Design’)
Closed-Loop Response:
If we select T and we know P, we can calculate C
For scalar (single input, single output)
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Selecting T (Closed-Loop Transfer Function)
Or, in time domain
Or, in time domain
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Solving for Model-Based Controller Gains
where and select
Resulting controller:
Our PID form:
Tuning PID
It turns out that if you pick T as we have done for the second order P, the controller is in the form of a PID controller.
Assume the system (P) is a second order system
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PID Example (w=1, z=1)
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PID Example (w=2, z=1)
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Implementing PID in COMSOL (An Example)
One dimensional heat transfer in a plate
Governing Equations:
Measure y on this surface
Heat surface at x=0 and measure temperature at surface x=L (y=T2)
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Build the Model in COMSOL
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Model Parameters
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Apply Boundary Conditions
Control input
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Create Mesh and Run the Simulation
This is not a second order system, but a much higher order PDE.
When we discretize the PDE using finite elements, we create a system of ODE’s.
For the mesh used here, there are 101 differential equations, or degrees of freedom (DOF).
Still, we will look for a PID controller based on a second order system.
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Open-Loop Response
We step the input flux from 0 to qmax*uctrl
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Measure Model Response Properties from OL Step
Time where y crosses 63% of final value
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Finding Approximate Time Constants
Measure the rate of change in y.Maximum is approximately 18[K/s]
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Approximate 2nd Order Model Parameters
We can use these to compute controller parameters.
We also need to pick the closed-loop speed, w, and damping, z.
Approximate 2nd order model parameters for plate model:
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Implementing PID in COMSOL
Proportional control:
Integral control:
Derivative control:
We solve these differential equations in COMSOL.
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Implementing PID in COMSOLAdd “Global ODEs and DAEs” to Model
Enter the Equations
State variableEquation
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Implementing PID in COMSOLDefine T2 as the plate temperature at x=L
Define control variables
The control: limit to 0<= uctrl <=1
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Define the Reference
Define the reference using an interpolation table.
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Controller Parameters
Tuning PID
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Closed-Loop Response
Works pretty well.
The open-loop response took almost 100s to reach the setpoint, the closed loop gets there in 12s.
Sensor
ref
Actuator face
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More Advanced Model-based Control
(MIMO) Multi-input (u)/Multi-output (y) require more complicated methods.
Each operation is a matrix operation…
The design principle is the same, but the difficulty of control design is balancing the tradeoffs between bandwidth, noise, and actuator saturation.
PC
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Summary
A methodology for tuning a PID controller has been presented.
A model for the system is built and an approximate second order model is assumed for choosing the PID parameters.
A desired closed-loop transfer function (T) is selected. Here we selected it so the resulting controller has the same form as the PID.
The PID gains were derived that give the desired closed-loop response.
An example of implementing PID in COMSOL was presented.
Poll QuestionHow do you model your feedback control law in your application?• In the same software that I use for studying
thermal systems.• In a different software that I interface.• In COMSOL using the Global ODEs and DAEs
interface.• In COMSOL with LiveLink™ for MATLAB®.• I haven't done it yet and want to learn how.
DemoClosed-Loop Temperature Control of a Rapid
Thermal Processing (RTP) System
Wafer (200mm dia.)
Lamps (5)
FeedbackControllerS
Rapid Thermal Processor (RTP)
-+ Lamp
power commands
Wafer temperature sensors
Temperature reference
Cold walls600°C
1000°C
Conclusion• A model-based method of tuning a PID
controller has been presented (Q-Design).
• For many thermal systems an open-loop step response can be used to characterize parameters (time-constants and gain) needed to tune the PID controller.
• COMSOL provides a simple ODE interface that allows quick implementation of PID control.
Q&A Session
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