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On/Off Control of a Thermal Actuator
Introduction
This example model consists of a two-hot-arm thermal actuator made of polysilicon. The actuator is activated through thermal expansion. The temperature increase required to deform the two hot arms, and thus displace the actuator, is obtained through Joule heating (resistive heating). The greater expansion of the hot arms, compared to the cold arm, causes a bending of the actuator.
This is a modified version of the Thermal Microactuator Simplified model from the COMSOL Multiphysics Application Library. In the present model, the applied current is controlled so that the actuator deflection does not exceed a given value. The on/off controller used in this example is implemented in Simulink.
Model Definition
The electro-thermal expansion problem is solved in COMSOL Multiphysics, while the control system is implemented in Simulink as an on/off controller.
The cosimulation with COMSOL Multiphysics and Simulink is set up by exporting a COMSOL Cosimulation file from the COMSOL model and then adding this file to the COMSOL Cosimulation block in the Simulink simulation diagram. The input of the block consists of the applied voltage. The block has two outputs: the tip displacement, which is used as control variable, and the maximum temperature in the actuator.
Figure 1 shows the full control simulation diagram in Simulink.
Figure 1: Simulink diagram of the thermal actuator controller.
Results and Discussion
Figure 2 below shows the actuator tip displacement at the communication time between COMSOL and Simulink. The tip displacement is always controlled between 0.71 μm and 0.81 μm. To reduce the variation in the displacement, you need to reduce the communication time and the settings in the relay block.
Figure 2: Actuator tip displacement at communication.
In COMSOL Multiphysics, the output time step used during the computation is set with a lower value than the communication time step. Figure 3 below shows the actuator tip displacement that is stored in the COMSOL model once the simulation is run. Notice that the results are much smoother.
Figure 3: Actuator tip displacement at computed time.
 
 
Figure 4 shows the applied voltage as an input to the COMSOL model. The plot clearly shows the on/off activation based on the tip displacement of the actuator.
Figure 4: Applied voltage vs. time.
The maximum temperature in the actuator is shown in Figure 5. The activation intervals are too short for the cooling as the temperature keeps increasing.
Figure 5: Actuator maximum temperature vs. time.
Setting Up the Cosimulation
Follow the workflow below to set up the cosimulation with COMSOL Multiphysics and Simulink:
1
Set up the COMSOL model and make sure that the study runs. Only studies with a single Stationary or Time Dependent study step are supported for cosimulation.
2
Save the COMSOL model. This step is important because the name of the model is needed to load the cosimulation file in Simulink.
3
Add the Cosimulation for Simulink feature node to the COMSOL model. Use this to define the inputs, outputs, and study for the cosimulation.
4
From the Cosimulation for Simulink feature node, export the file for cosimulation. Any location will work, but it is good practice to export this file to the location where the MPH-file has been saved.
5
Create or load the simulation diagram in Simulink, and add the COMSOL Cosimulation block.
6
Double-click the COMSOL Cosimulation block, and enter the name of the cosimulation file exported from COMSOL Multiphysics.
Application Library path: LiveLink_for_Simulink/Tutorials/thermal_actuator_llsimulink
Modeling Instructions — COMSOL Desktop
In this example you will start from an existing model which is an example in the COMSOL Multiphysics.
Application Libraries
1
From the File menu, choose Application Libraries.
2
In the Application Libraries window, select COMSOL Multiphysics>Multiphysics>thermal_actuator_simplified in the tree.
3
Click  Open.
Definitions
Domain Point Probe 1
1
In the Model Builder window, expand the Thermal Actuator (comp1) node.
2
Right-click Thermal Actuator (comp1)>Definitions and choose Probes>Domain Point Probe.
3
In the Settings window for Domain Point Probe, locate the Point Selection section.
4
In row Coordinates, set x to L.
5
Select the Snap to closest boundary check box.
Point Probe Expression 1 (ppb1)
1
In the Model Builder window, expand the Domain Point Probe 1 node, then click Point Probe Expression 1 (ppb1).
2
In the Settings window for Point Probe Expression, locate the Expression section.
3
In the Expression text field, type v.
Maximum 1 (maxop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Maximum.
2
In the Settings window for Maximum, locate the Source Selection section.
3
From the Selection list, choose All domains.
Variables 1
In the Model Builder window, right-click Definitions and choose Variables.
Solid Mechanics (solid)
Linear Elastic Material 1
In the Model Builder window, expand the Thermal Actuator (comp1)>Solid Mechanics (solid) node, then click Linear Elastic Material 1.
Damping 1
1
In the Physics toolbar, click  Attributes and choose Damping.
2
In the Settings window for Damping, locate the Damping Settings section.
3
In the αdM text field, type 1e-6.
4
In the βdK text field, type 1e-6.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select General Studies>Time Dependent.
4
Right-click and choose Add Study.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2
Step 1: Time Dependent
1
In the Settings window for Time Dependent, locate the Study Settings section.
2
In the Output times text field, type range(0,1e-6,1e-4).
Solution 2 (sol2)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 2 (sol2) node.
3
In the Model Builder window, expand the Study 2>Solver Configurations>Solution 2 (sol2)>Dependent Variables 1 node, then click Temperature (comp1.T).
4
In the Settings window for Field, locate the Scaling section.
5
From the Method list, choose Manual.
6
In the Scale text field, type 300.
7
In the Model Builder window, under Study 2>Solver Configurations>Solution 2 (sol2)>Dependent Variables 1 click Electric potential (comp1.V).
8
In the Settings window for Field, locate the Scaling section.
9
From the Method list, choose Manual.
10
In the Study toolbar, click  Compute.
Results
1D Plot Group 12
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, locate the Data section.
3
From the Dataset list, choose Study 2/Solution 2 (sol2).
Global 1
1
Right-click 1D Plot Group 12 and choose Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
-comp1.ppb1
µm
Tip displacement
4
Click to expand the Legends section. Clear the Show legends check box.
Save the COMSOL Model
1
In the Model Builder window, under Results click Temperature (ht).
2
From the File menu, choose Save As.
3
Browse to a suitable folder, enter the filename thermal_actuator_llsimulink.mph, and then click Save.
Exporting the Cosimulation File
In the following configure the cosimulation, and export the file for cosimulation that will be loaded into Simulink.
Global Definitions
Cosimulation for Simulink 1
1
In the Study toolbar, click  Cosimulation for Simulink.
2
In the Settings window for Cosimulation for Simulink, locate the Filename section.
3
In the Filename text field, type thermal_actuator_llsimulink.
4
Locate the Inputs section. Click  Add.
5
In the table, enter the following settings:
Parameter name
Initial value
Unit
DV (Applied voltage)
5
V
6
Locate the Outputs section. In the table, enter the following settings:
Expression
Unit
Name
-comp1.ppb1
m
Disp
maxop1(T)
 
Max temp
7
Locate the Study section. From the Study list, choose Study 2.
8
Locate the Image section. Click  Set from Graphics WindowThis sets the current temperature plot (if a solution is available) as the thumbnail used for the COMSOL Cosimulation block inside Simulink.
9
Click  Export.
Modeling Instructions — Simulink
Once you have created the COMSOL model and saved the cosimulation file you can start Simulink to continue with the setup there.
1
Start COMSOL with Simulink.
2
In MATLAB enter the command mphapplicationlibraries to start the GUI for viewing models from the LiveLink for Simulink application library.
3
Browse to the folder LiveLink_for_Simulink/Tutorials, and select thermal_actuator_llsimulink.slx.
4
Click Open to get the simulation diagram as in Figure 1.
The included COMSOL Cosimulation block is already configured with a cosimulation file based on the model from the COMSOL Application Library and ready to run. If you want to run the simulation directly, go to Step 7 below. Else, if you want to use the model file and cosimulation file you have created by following the steps in the section Modeling Instructions — COMSOL Desktop, you can continue with Step 5 below.
5
Double-click the COMSOL Cosimulation block.
6
In the COMSOL Cosimulation window settings, in the Filename edit field enter the name of the file for cosimulation for Simulink as created in the section Exporting File for Cosimulation for Simulink.
Note: In case the folder path of the file for cosimulation for Simulink is not set in MATLAB enter the full filename.
For this simulation the stop time is set to 10−4 s and the communication step size is set to 5 μs.
7
To run the simulation, click Run.
Postrocessing the Solution in the COMSOL Desktop
To reproduce Figure 3 follow the steps below:
1
Once you have run the simulation in Simulink, in the MATLAB prompt enter mphlaunch. This automatically start the COMSOL Desktop with the model loaded.
2
In the Model Builder, under Results select 1D Plot Group 10.
Note: Close the COMSOL Desktop before running a new simulation in Simulink.