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Simulink® with MagNet - Response Surface Modeling of an Actuator
Gallery spotlightActuators
Modeling an electromagnetic actuator in a systems context is sometimes required to accurately simulate the dynamic interaction between drive circuit, actuator, and load. Co-simulation, where a systems simulator and MagNet run parallel transient solves, is one method that can be used. An alternative approach, Response Surface Modeling (RSM), creates a functionally equivalent model of the actuator by performing a large number of static analyses at different currents and positions. Presented here is an example of an RSM, used in conjunction with the Simulink® system simulator from The MathWorks, Inc. The procedure is automated with the System Model Generator, which drives MagNet to execute its static solver and generates a file containing the RSM data. A plug-in to Simulink reads this file and provides a system block that can be connected to the rest of the system.
METHODS and RESULTS
SIMULINK SYSTEM DIAGRAM - ACTUATOR and DRIVE CIRCUIT
Shown here is the Simulink system diagram of the actuator and drive circuit. In this example, the coil is driven by a capacitor charged to 12 V. A spring holds the plunger against the upper stop. At time t=0, a switch closes to connect the charged capacitor to the coil. The RSM block has inputs for coil voltage (top) and external plunger force (bottom), and outputs for coil current (top), plunger position and velocity (center), and electromagnetic force (bottom). On the electrical side an integrator models the charged capacitor which discharges through the actuator's coil. On the mechanical side the spring, viscous damper, and upper and lower stops are modeled using appropriate Simulink blocks.
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CUTAWAY VIEW of ACTUATOR MODEL
The actuator model is shown in a cutaway view. Since this device has axial symmetry, the MagNet Static 2d solver is used to calculate force and flux-linkage at different positions and currents. (Note - This solver is also available in the MagNet Trial Edition, which is a free download.) The solution setup to create the Response Surface Model (RSM) is automated with the use of the System Model Generator.
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RSM of the FORCE - as a function of coil current and plunger position
The RSM of the force as a function of coil current and plunger position is shown here. The response surface models for both flux and force were created using the System Model Generator and required a total of 460 Magnetostatic 2d solutions.
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SIMULINK RESULT - position of the plunger as a function of time
This graph shows the position of the plunger as a function of time. The complicated behaviour arises from the transfer of energy between the potential energy of the capacitor, the energy stored in the magnetic field, the potential energy in the spring, and the kinetic energy of the plunger.
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MAGNET RESULT - position of the plunger as a function of time
This system can be modeled directly in MagNet's Transient with Motion solver, as shown here. The position is slightly different because MagNet can simulate an ideal bounce (instant velocity reversal), whereas a very large spring constant was used in Simulink. The small error at each bounce is amplified over time. Although the transient solution time is comparable to the time required to generate the RSM, the RSM allows changes in the drive circuit to be made and the result simulated almost instantly in Simulink.
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Number of time steps: 600
Transient solution time: 6 minutes 12 seconds
Number of static solutions in RSM: 460
Static solution time (total): 5 minutes 10 seconds
Simulink simulation time: 0.2 seconds
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