norxs · IPMSM Field-Weakening Control & Functional-Safety Demonstrator

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

SPEED LOOPSpeed Tracking — Co-Simulationt = 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^*

CH.4Tracking Error & Lyapunov Bound

e(t) proposedresidual set ±B

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

CH.2.8Current Vector — i_d–i_q Plane|i_s| = 0 A

current limit I_maxvoltage ellipseMTPAoperating trail

CH.3.5Adaptive 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)

CH.3.4Open-Loop Phase — Iso-Damping

FOPI (λ tunable)Integer PI

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

CH.4/5A-MO-FOPSO Pareto Front

Pareto setbest compromiseStd PI

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

Self-contained browser simulation of the dissertation model (IPMSM parameters per Table 2.3: R_s=0.05Ω, L_d=0.4 mH, L_q=0.8 mH, ψ_f=0.08 Wb, p=4, J_m=0.01 kg·m², V_dc=360 V, I_max=250 A). Fractional integrator s^−λ realized as a true integrator cascaded with an Oustaloup recursive approximation (N=5) of s^(1−λ), normalized to unit gain at the loop crossover — the Oustaloup method deployed in the dissertation. Figures are illustrative of the closed-loop behaviour, not a substitute for the full MATLAB/Simulink–CarSim co-simulation. © 2026 norxs Technology LLC.