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 [pmsmformulas.md §F](../../../shared/formulas/pmsmformulas.md); 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](../motor-pmsm-base/SKILL.md). 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)

| Aspect | Single-vector | Dual-vector | Three-vector (this skill) | |---|---|---|---| | Vectors per period | 1 (held) | 2: V_opt1 + V_j | 3: u_i + u_j (adjacent active) + zero | | Deadbeat axes | none (search only) | q only (scalar t_opt1) | d AND q (2×2 solve for t_i,t_j,t_z) | | d-axis slope needed | no | no | yes (T2b) | | Candidate set | 7/8 basic vectors | vector pairs | 6 synthesized expected vectors (one per sector) | | Time allocation | — | q-deadbeat (N3) | dual-axis deadbeat 2×2 (T3) + 3-case clamp (T5) | | Chart sample-time | INHERITED + dual ZOH | two-rate DISCRETE | two-rate DISCRETE: controller/theta @ Tsc, slicer @ Ts | | Cost (this reference) | L2 weighted | L1 unweighted | L1 unweighted over the 6 expected vectors (paper eq 7) |

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 ([designdecisions.md](references/designdecisions.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 [critconditions.md §J-CRIT](references/critconditions.md).
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 [critconditions.md §K-CRIT](references/critconditions.md).
4. Two-rate DISCRETE sample times (the validated structure — see [critconditions.md §G-CRIT](references/critconditions.md)):

• 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).

1. 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 UniversalBridge gate port [6]; a [1 6] row triggers DataBackPropagationSizeSuffix. See [critconditions.md §D-CRIT](references/crit_conditions.md).
2. 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 [critconditions.md §G-CRIT](references/critconditions.md), [antipatterns.md](references/antipatterns.md) #2.
3. 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 [critconditions.md §DC-CRIT](references/critconditions.md), [antipatterns.md](references/antipatterns.md) #6.
4. 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 [critconditions.md §A-CRIT](references/critconditions.md).
5. 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 [parameterdefaults.md](references/parameterdefaults.md).
6. 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 [antipatterns.md](references/antipatterns.md) #5.

Build Flow

| Phase | Action | Reference | |---|---|---| | 0 | Validate inputs + sanity grid | base/[prebuildgrid.md](../motor-pmsm-base/references/prebuildgrid.md) | | 1 | Plant layer (powergui Discrete @ Ts, DC, UB Inverter, PMSM Salient-pole, TL) — check DC polarity | [critconditions.md §DC](references/critconditions.md), [antipatterns.md](references/antipatterns.md) #6 | | 2 | Measurement layer (BusSelector → Clark → Plark, thetae source) | [critconditions.md §A](references/critconditions.md) | | 3 | Outer speed PI (RPM↔rad/s, mandatory saturation) | [parameterdefaults.md](references/parameterdefaults.md), [scripts/speedpidesign.m](scripts/speedpidesign.m) | | 4 | TVMPCC controller chart (6-sector loop, 2×2 deadbeat, 3-case clamp, 6-candidate cost) | [algorithmpseudocode.md](references/algorithmpseudocode.md) + [critconditions.md §G/§K](references/critconditions.md) | | 5 | Slicer 3-segment sequencer + Digital Clock | [algorithmpseudocode.md](references/algorithmpseudocode.md) §slicer + [critconditions.md §G/§D](references/critconditions.md) | | 6 | Logging (To Workspace @ fast rate for ripple; scopes) | [acceptancecriteria.md](references/acceptancecriteria.md) | | 7 | Solver (fixed-step discrete, FixedStep = Ts; powergui Discrete) + InitFcn injection | [critconditions.md §J](references/critconditions.md) | | 8 | Self-tests + acceptance (visual 4-check + 3-vector liveness, then §E ripple) | [acceptancecriteria.md](references/acceptance_criteria.md) |

If issues arise, consult [critconditions.md](references/critconditions.md) (A/D/G/J/K/DC) and [antipatterns.md](references/antipatterns.md).

Required User Inputs

Ask the user before starting. Defaults in [parameterdefaults.md](references/parameterdefaults.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), 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 T2–T6 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. The d-axis deadbeat (T3) genuinely uses Ld. | | 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 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](../motor-pmsm-base/SKILL.md) — base infrastructure (this skill layers on it)
• [motor-fcs-mpc-dualvector](../motor-fcs-mpc-dualvector/SKILL.md) — dual-vector FCS-MPC (the direct predecessor; q-only deadbeat)
• [motor-fcs-mpc](../motor-fcs-mpc/SKILL.md) — single-vector FCS-MPC
• [motor-dtc-pmsm](../motor-dtc-pmsm/SKILL.md) — Direct Torque Control alternative
• [motor-smc-pmsm](../motor-smc-pmsm/SKILL.md) — Sliding Mode Control alternative

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: calebzu
• Source: calebzu/pmsm-control-claude-skills-for-matlab
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.