PI–FOPSOFWC · IPMSM Field-Weakening Control Demonstrator

01 / 08 Opening

RMSE · Proposed

0.0 rpm

vs reference

RMSE · Std PI

0.0 rpm

baseline

Improvement

RMSE reduction

Overshoot · Prop

0.0%

step transient

Energy index ∫i_q²

0 A²s

f₂ objective

Region

MTPA

below base speed

MOTORLive Motor State — Rotor, Flux & Current Vector0 rpm · MTPA

Speed

0 rpm

Region

MTPA

Torque T_e

0 N·m

|i_s|

0 A

|u_s|/V_max

d-axis (rotor flux)q-axis / current vector (MTPA)current vector (field-weakening)

θ_e = p·θ_m (electrical angle spins p× faster than the rotor) — watch the vector snap from cyan to amber as |u_s| hits V_max and field weakening engages.

SPEED LOOPSpeed Tracking — Livet = 0.00 s

Reference r(t)Proposed (PI-FOPSOFWC)Std PI (Ziegler-Nichols)

u_c(t) = K_p(e,ė)·e(t) + K_i(e,ė)·D^-λe(t) → i_q^*

STABILITYTracking Error & Lyapunov Bound

e(t) proposedresidual set ±B

V(e)=½J_me², V̇ < 0 outside {|e| ≤ B} ⇒ practical UUB

CURRENTCurrent Vector — i_d–i_q Plane|i_s| = 0 A

current limit I_maxvoltage ellipseMTPAoperating trail

ADAPTIVEAdaptive Fuzzy Gains K_p(t), K_i(t)

K_p(t)K_i(t)

K_p=K_p0+α_pΔK_p, K_i=K_i0+α_iΔK_i, ΔK∈[-1,1] (bounded)

ROBUSTNESSOpen-Loop Phase — Iso-Damping

FOPI (λ tunable)Integer PI

d∠L(jω)/dω ≈ 0 near ω_c ⇒ phase margin invariant to gain drift

TUNINGA-MO-FOPSO Pareto Front

Pareto setbest compromiseStd PI

min [ f₁=∫t|e|dt (ITAE), f₂=∫i_q²dt (energy) ]

Academic Info & Disclaimer

© 2026 Chih-Chung Chiu · National Yunlin University of Science & Technology.
Academic demonstrator for doctoral defense. Representative IPMSM Case-II parameters.
Fractional integration via Oustaloup (N=5).