By 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
- Plan first. Before any
add_block, write a numbered plan: parameter table, design-decision choices (design_decisions.md), build-script structure. Get user approval. - One-click reproducibility. Inject all parameters via
set_param(mdl, 'InitFcn', sprintf(...)). Model must Run from.slxdouble-click in a fresh MATLAB session. See crit_conditions.md §J-CRIT. - Controller chart hardcodes machine params via
sprintf. TheDualVecMPCchart embedsRs/Ld/Lq/psifas numeric literals at build time; the literals MUST equal theInitFcnvalues digit-for-digit (assert it in the build). Never put them in an external.mfile (drifts from the plant). See crit_conditions.md §K-CRIT. - Two-rate DISCRETE sample times (the validated structure — see crit_conditions.md §G-CRIT):
DualVecMPCandThetaSrc→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.SampleTimeis silently ignored unlessUpdateMethod='Discrete'is set first. A continuous/inherited gate fails to propagate into the discrete SimPowerSystems bridge.
- DC bus polarity must match. Wire
DC +(RConn) → UB RConn(1)(+)andDC −(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. gateis a 6-element COLUMN vector. TheTimeSliceroutput 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.- One
theta_e, integrated atTsc, feeds both Plark and the controller.theta_e += Tsc·(Pn·w)in a persistent var, wrapped viaatan2(sin,cos). Do NOT use the PMSM bustheta. If routed via Goto/From,TagVisibility='global'. See crit_conditions.md §A-CRIT. - Outer PI saturation is mandatory.
LimitOutput='on', limits[−iq_max, +iq_max]with1.5·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