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MTPA Derivation Placeholder

Sat, 16 May 2026 00:10:00 +0800

This placeholder exists so cross references work from the current-loop demo.

For an IPMSM, MTPA trades reluctance torque and magnet torque. A compact torque expression is:

$$T_e = \frac{3}{2}p\left(\psi_f i_q + (L_d - L_q)i_d i_q\right)$$

Sat, 16 May 2026 00:00:00 +0800

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Sat, 16 May 2026 00:00:00 +0800

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For a surface-mounted PMSM current loop, a simplified q-axis equation can be written as:

$$ u_q = R_s i_q + L_q \frac{di_q}{dt} + \omega_e \psi_f$$

Inline math works too: $i_d = 0$ is a common starting point before field weakening.

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Kp = Lq * wc;
Ki = Rs * wc;

Read the companion note: MTPA derivation.