Solenoid modelling with basic blocks and physical modelling blocks¶
This example shows a solenoid with a return spring. The solenoid is modelled as an inductance whose value L depends on the piston position x. The inverse EMF for a time-varying inductance is defined as:
$$v=L{di\over dt}+i{dL\over dt}\quad\quad\quad(1)$$
Since L depends on x:
$$v=L{di\over dt}+i{dL\over dx}{dx\over dt}\quad\quad(2)$$
${dL\over dx}$ can be obtained using data from the manufacturer and using the ratio:
$$force = 0.5*i^2{dL\over dx}\quad(3)$$
Then ${dL\over dx}$ can be integrated to get L as a function of x.
In the model, equation (2) is recalculated to solve for i and then implemented using physical blocks. The controlled current source then limits the magnitude of the current by equating it to i.
Schematic of the model:¶
Simulation results:¶
Values of solenoid current over time, A:
Values of the force generated by the solenoid over time, N:
