Saturday 2 August 2014

motor - Modeling scalar control of PMSM


I have met with a scalar control algorithm for a permanent magnet synchronous motor. I haven´t heard about it before so I decided to develop a dynamic model to further analyze this control algorithm. Unfortunatelly I haven´t got the Matlab with the SimPowerSystems library so I decided to create this model in Scilab.


I have been using below given equations for PMSM simulation:


\$\frac{\mathrm{d}i_d}{\mathrm{d}t} = \frac{1}{L_d}\cdot(u_d-R\cdot i_q+L_q\cdot\omega_e\cdot i_q), \\ \frac{\mathrm{d}i_q}{\mathrm{d}t} = \frac{1}{L_q}\cdot(u_q-R\cdot i_q-L_d\cdot\omega_e\cdot i_d - \omega_e\cdot\psi_m), \\ \frac{\mathrm{d}\omega_m}{\mathrm{d}t} = \frac{1}{J}\cdot(1.5\cdot p\cdot\psi_m\cdot i_q - T_l),\\ \omega_e = p\cdot\omega_m\$


where \$p\$ is number of pole pairs


The parameters of the model:


\$L_d = 1.365\cdot10^{-3}\,H \\ L_q = 1.365\cdot10^{-3}\,H \\ R = 0.416\,\Omega \\ \psi_m = 0.166\,Wb \\ p = 2 \\ J = 3.4\cdot10^{-4}\,kg\cdot m^2 \\ kF= \frac{3.2}{(2\cdot\pi\cdot\frac{1200}{60})^2}\,\frac{N\cdot m}{(rad\cdot s^{-1})^2}\$



Here is my overall simulation model enter image description here


The motor is loaded by below given torque


\$T_l = kF\cdot\omega^2\$ which is removed in step wise manner at \$t=0.4\,s\$


The U/f block enter image description here


The PMSM Model block enter image description here


The Inverse Park Transform block enter image description here


The Inverse Clarke Transform block enter image description here


Ther results are following


Stator currents enter image description here


Motor torque enter image description here



Reference and actual mechanical speed enter image description here


Stator voltage in q axis enter image description here


I have doubts about correctness of my model due to the fact that the actual motor speed differs from the reference speed. I expected that they will equal because of the modeled machine is a synchronous motor. Does anybody know where I did a mistake? Thanks in advance for any suggestions.




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