motor-fcs-mpc-dualvector

name	motor-fcs-mpc-dualvector
description	PMSM Dual-Vector Finite-Control-Set MPC Builder. Build an inner-loop two-vectors-per-period finite-control-set MPC current controller for a three-phase voltage-source-inverter-driven PMSM (SPMSM / mild-saliency IPMSM via parameterization) in Simulink, with an outer speed PI providing iq_ref. Two vectors per control period (V_opt1 + V_j) with q-axis-deadbeat time allocation cut switching-cycle current ripple ~3-5x below single-vector FCS-MPC. Use when constructing, reproducing, porting, or extending a dual-vector / two-vector FCS-MPC current-control simulation in Simulink (keywords dual-vector MPC, two-vector MPC, double-vector MPCC, deadbeat time allocation, duty-cycle MPC, 双矢量模型预测, 占空比 MPC). Skip for single-vector FCS-MPC (use motor-fcs-mpc), FOC, DTC, SMC, sensorless, scalar V/Hz, BLDC trapezoidal, induction-motor MPC, three-or-more-vector / multi-step-horizon MPC, strong-saliency IPMSM MTPA, weak-field, or pure theory questions. Layered on motor-pmsm-base.
metadata	{"version":"1.0"}

motor-fcs-mpc-dualvector — PMSM Dual-Vector Finite-Control-Set MPC Builder

Three-phase 2-level voltage-source inverter + PMSM (SPMSM / mild-saliency IPMSM via parameterization). Inner loop = dual-vector FCS-MPC current control in the dq frame: each control period applies two voltage vectors — the first optimal active vector V_opt1 for a deadbeat-computed on-time t_opt1, then a second vector V_j for the remainder Tsc − t_opt1. Outer loop = speed PI providing iq_ref. The second vector + intra-period time split drive switching-cycle current ripple far below single-vector FCS-MPC at the same Tsc.

Distilled from Xu Yanping et al. 2017 (Two-Vector Model Predictive Current Control for PMSM, Trans. China Electrotech. Soc. 32(20):222-230). Control-law formulas are the signed N2–N5 in pmsm_formulas.md §E; plant physics, prediction, speed PI, Clarke/Park and the 8-vector set are reused by pointer from the same file (§0-§7 / §A / §B.5).

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

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

Aspect	Single-vector (motor-fcs-mpc)	Dual-vector (this skill)
Vectors per period	1 (held the whole Tsc)	2: V_opt1 for t_opt1, then V_j
Modulator	none; one switch state per period	none; time-slicer sequences two states within Tsc
Extra novelty	—	q-axis deadbeat time allocation (N3), duty-weighted average voltage (N4)
Chart sample-time	INHERITED + dual ZOH	two-rate DISCRETE: controller @ Tsc, slicer @ Ts (see rule 4)
Cost (this reference)	L2 weighted	L1 unweighted (paper eq 7)
Ripple @ same Tsc	baseline	~3-5x lower (paper Table 2)

There is no SVPWM and no Anti_Park — the selected discrete vectors are applied directly; the gate comes from the 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 DualVecMPC 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). Never put them in an external .m file (drifts from the plant). See crit_conditions.md §K-CRIT.
4. Two-rate DISCRETE sample times (the validated structure — see crit_conditions.md §G-CRIT):
   • DualVecMPC and ThetaSrc → MATLABFunctionConfiguration.UpdateMethod='Discrete', SampleTime='s_Tsc' (compute once per control period and hold).
   • TimeSlicer → Discrete, SampleTime='s_Ts' (must run at the fast plant rate to slice 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.
5. DC bus polarity must match. Wire DC +(RConn) → UB RConn(1)(+) and DC −(LConn) → UB RConn(2)(−). Reversed polarity forward-biases the bridge freewheel diodes, clamps the DC link to ≈0, and the motor sees no voltage (vds=vqs=0, zero current, rotor stalls). See anti_patterns.md #1 — this is the most common dual-vector build failure.
6. gate is a 6-element COLUMN vector. The TimeSlicer 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 a back-propagation size error. See crit_conditions.md §D-CRIT.
7. One theta_e, integrated at Tsc, feeds both Plark and the controller. theta_e += Tsc·(Pn·w) in a persistent var, wrapped via atan2(sin,cos). Do NOT use the PMSM bus theta. If routed via Goto/From, TagVisibility='global'. See crit_conditions.md §A-CRIT.
8. Outer PI saturation is mandatory. LimitOutput='on', limits [−iq_max, +iq_max] with 1.5·Pn·psif·iq_max ≥ 1.3·TL_max, back-calculation anti-windup. See parameter_defaults.md.

Build Flow

Phase	Action	Reference
0	Validate inputs + sanity grid	base/pre_build_grid.md
1	Plant layer (powergui Discrete @ Ts, DC, UB Inverter, PMSM Salient-pole, TL) — check DC polarity	crit_conditions.md, anti_patterns.md #1
2	Measurement layer (BusSelector → Clark → Plark, theta_e source)	crit_conditions.md §A
3	Outer speed PI (RPM↔rad/s, mandatory saturation)	parameter_defaults.md, scripts/speed_pi_design.m
4	DualVecMPC two-stage controller chart	algorithm_pseudocode.md + crit_conditions.md §G/§K
5	TimeSlicer two-vector sequencer + Digital Clock	algorithm_pseudocode.md §slicer + crit_conditions.md §G/§D
6	Logging (To Workspace @ fast rate Ts for ripple signals i_d/i_q; controller outputs may log @ Tsc)	acceptance_criteria.md
7	Solver (fixed-step discrete, FixedStep = Ts; powergui Discrete) + InitFcn injection	crit_conditions.md §J
8	Self-tests + acceptance (visual 4-check, then §E ripple vs operating point)	acceptance_criteria.md

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

Required User Inputs

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

Group	Parameter
Machine	Rs (Ω), Ld, Lq (H; SPMSM: Ld=Lq=Ls), psif (V·s), Pn, J (kg·m²), F (N·m·s)
Power stage	Vdc (V) — BEMF margin; ripple scales with Vdc·Tsc/L, so it co-sets the ripple level
Sampling	Ts (plant solver, ~1 μs), Tsc (control period, paper 100 μs @ 10 kHz; Tsc/Ts ≥ 50)
Outer loop	Kp_w, Ki_w (recommend speed_pi_design.m; B=0 ⇒ Symmetric Optimum a=4), iq_max
MPC	cost form (L1-unweighted = paper / L2-weighted = production option), id_ref (SPMSM/mild-IPMSM: 0)
Scenario	StopTime, omega_ref profile (RPM), TL_step_time, TL_value (< 1.5·Pn·psif·iq_max)

Triggers / Skip

✅ Use	❌ Skip
Build / port / extend a dual-vector (two-vector) FCS-MPC simulation in Simulink	Single-vector FCS-MPC → motor-fcs-mpc
Two vectors/period, q-deadbeat time allocation, duty-cycle MPC	FOC, DTC, SMC, sensorless, scalar V/Hz, BLDC trapezoidal
Generalizing dual-vector MPC to a new SPMSM / mild-saliency machine	Three-or-more vectors, multi-step horizon (N>1), induction-motor MPC
	Strong-saliency IPMSM MTPA, weak-field; pure theory questions

Generalization Across Machine Sub-Types

Sub-type	Parameter constraint	Strategy
SPMSM	Ld == Lq	id_ref = 0. The N2–N5 general (Ld,Lq) form reduces verbatim to the paper's SPMSM equations.
IPMSM mild saliency	Lq > Ld, Lq/Ld ≤ 1.5	id_ref = 0 workable; the general form already carries the salient cross-terms.
IPMSM strong saliency	Lq/Ld ≥ 2	id_ref from MTPA (out of v1 scope; ask user)

Topology does not change — same blocks, same wiring, same two-stage chart, 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 — single-vector FCS-MPC (the natural comparison baseline)
• motor-dtc-pmsm — Direct Torque Control alternative
• motor-smc-pmsm — Sliding Mode Control alternative