Motor Fcs Mpc Trivector

motor-fcs-mpc-trivector — PMSM Three-Vector Finite-Control-Set MPC Builder

Three-phase 2-level voltage-source inverter + PMSM (SPMSM / mild-saliency IPMSM via parameterization). Inner loop = three-vector FCS-MPC current control in the dq frame: each control period synthesizes an expected voltage vector per sector from the two adjacent active vectors u_i, u_j plus a zero vector, and splits the period into three sub-intervals — u_i for t_i, u_j for t_j, zero for t_z = Tsc − t_i − t_j — chosen so that both i_d and i_q reach their references in one period (dual-axis deadbeat). Outer loop = speed PI providing iq_ref, id_ref = 0. Synthesizing an arbitrary-direction, arbitrary-amplitude voltage vector and nulling both axes drives switching-cycle current ripple below single- and dual-vector FCS-MPC at the same Tsc.

Distilled from Xu Yanping et al. 2018 (Three-Vector Model Predictive Current Control for PMSM, Trans. China Electrotech. Soc. 33(5):980-986). Control-law formulas are the signed T2(b)–T6(b) in pmsm_formulas.md §F; plant physics, prediction, speed PI, Clarke/Park, the 8-vector set and the 6-sector decode are reused by pointer from pmsm_formulas.md (incl. §B.4/§B.5). The q-axis slope (T2a) is reused by pointer from §E.1 (N2), and the cost criterion from §F.0 (control strategy, non-signed).

Layered on motor-pmsm-base. All base discipline applies (Goto TagVisibility, Vdc/BEMF rule, Visual 4-check, broken-FOC defense).

What makes three-vector different (vs dual-vector motor-fcs-mpc-dualvector and single-vector)

There is no SVPWM and no Anti_Park — the selected discrete vectors are applied directly; the gate comes from a 3-segment time-slicer, not a PWM modulator.

Must-Follow Rules

1. Plan first. Before any add_block, write a numbered plan: parameter table, design-decision choices (design_decisions.md), build-script structure. Get user approval.
2. One-click reproducibility. Inject all parameters via set_param(mdl, 'InitFcn', sprintf(...)). Model must Run from .slx double-click in a fresh MATLAB session. See crit_conditions.md §J-CRIT.
3. Controller chart hardcodes machine params via sprintf. The TVMPCC chart embeds Rs/Ld/Lq/psif as numeric literals at build time; the literals MUST equal the InitFcn values digit-for-digit (assert it in the build). See crit_conditions.md §K-CRIT.
4. Two-rate DISCRETE sample times (the validated structure — see crit_conditions.md §G-CRIT):
   • TVMPCC and ThetaSrc → MATLABFunctionConfiguration.UpdateMethod='Discrete', SampleTime='Tsc'.
   • Slicer → Discrete, SampleTime='Ts' (must run at the fast plant rate to slice three segments within the period), fed by a Digital Clock @ Ts.
   • SampleTime is silently ignored unless UpdateMethod='Discrete' is set first. A continuous/inherited gate fails to propagate into the discrete SimPowerSystems bridge (Stateflow:SignalTypePropagationError).
5. gate is a 6-element COLUMN vector. The Slicer output must be [Sa+;Sa−;Sb+;Sb−;Sc+;Sc−] (column) so the inferred size [6 1] matches the Universal_Bridge gate port [6]; a [1 6] row triggers DataBackPropagationSizeSuffix. See crit_conditions.md §D-CRIT.
6. R2024b: set the MATLAB-Function code via the config object, not the wrong Stateflow class. The chart class is Stateflow.EMChart (NOT EMLChart); the robust route is get_param(blk,'MATLABFunctionConfiguration').FunctionScript = code. See crit_conditions.md §G-CRIT, anti_patterns.md #2.
7. DC bus polarity must match. DC +(RConn) → UB RConn(1)(+), DC −(LConn) → UB RConn(2)(−). Reversed polarity clamps the link via the freewheel diodes → vds=vqs=0, zero current, rotor stalls (no error). See crit_conditions.md §DC-CRIT, anti_patterns.md #6.
8. One theta_e, integrated at Tsc, feeds both Plark and the controller. theta_e += Tsc·(Pn·w) persistent, wrapped via atan2(sin,cos). Do NOT use the PMSM bus theta. Goto/From ⇒ TagVisibility='global'. See crit_conditions.md §A-CRIT.
9. Outer PI saturation is mandatory. LimitOutput='on', [−iq_max, +iq_max], 1.5·Pn·psif·iq_max ≥ 1.3·TL_max, back-calculation anti-windup. See parameter_defaults.md.
10. Keep all three vectors live. The T5 three-case clamp must degrade gracefully (drop the out-of-range vector) — not silently collapse to a single/dual vector. Confirm in acceptance that t_i, t_j, t_z are all meaningfully nonzero in steady state. See anti_patterns.md #5.

Build Flow

If issues arise, consult crit_conditions.md (A/D/G/J/K/DC) and anti_patterns.md.

Required User Inputs

Ask the user before starting. Defaults in parameter_defaults.md.

Triggers / Skip

Generalization Across Machine Sub-Types

Topology does not change — same blocks, same wiring, same controller+slicer charts, same CRIT conditions. Only parameters and id_ref strategy differ. Out-of-scope: SynRM (psif ≈ 0), IM, BLDC trapezoidal — different prediction equations.

Sibling Skills

• motor-pmsm-base — base infrastructure (this skill layers on it)
• motor-fcs-mpc-dualvector — dual-vector FCS-MPC (the direct predecessor; q-only deadbeat)
• motor-fcs-mpc — single-vector FCS-MPC
• motor-dtc-pmsm — Direct Torque Control alternative
• motor-smc-pmsm — Sliding Mode Control alternative