PowerCraftMotion
POWER CONVERSION / MOTOR CONTROLGaN HEMT / MOTOR DRIVE

POWER INMOTION.

GaN inverter design.
For efficient motor drives.

We develop GaN HEMT inverters for PMSM and BLDC motors. Our design work addresses power loss, cooling and current control to improve efficiency and output capability.

GaN inverter dynamometer concept with a differential-voltage probe, U/V/W current clamps, an AI test-automation simulation on the PC and calculated instrument waveforms, power and power factors.
INVERTER / MOTORConcept artwork
GaN INVERTER / DESIGN TARGETS150 × 95 × 30 mm

MAX 80 V DC250 A rms · phase

AXIAL-FLUX MOTOR CONCEPT · LIQUID / AIR COOLING OPTIONSResolver, Hall, Encoder

POSITION FEEDBACK OPTIONS UNDER REVIEW

POWER INTO MOTIONPOWER INTO
MOTION.
01 POWER ELECTRONICS02 THERMAL DESIGN03 MOTOR CONTROL

Power. Thermal. Control.
Designed together.

We review the power stage, cooling structure and control requirements against device characteristics and operating conditions.

GaN HEMT INVERTER

The following sections explain design principles and review criteria. They do not report product test results or confirmed specifications.

01POWER ELECTRONICSPower electronics

Fast transitions can reduce switching loss, but high current slew rates can also produce voltage overshoot across parasitic inductance. Device selection and PCB layout need to be considered together.

Gate voltage and drive impedance must suit the selected device. Power loops, gate loops and return paths influence ringing, unintended switching and electromagnetic emissions.

DESIGN REVIEW POINTS

Loops & layout
Power and gate loop parasitics; decoupling placement
Transition quality
Voltage and current waveforms; overshoot, ringing and drive conditions
02THERMAL DESIGNThermal design

Conduction and switching losses are major sources of heat in the power stage. Loss estimates depend on current, switching frequency and device temperature; thermal design must also account for the path from the device to the cooling system.

Continuous operation and short peak loads produce different thermal responses. Estimating peak junction temperature requires load duration, repetition and transient thermal response as well as average loss and steady-state thermal resistance.

DESIGN REVIEW POINTS

Steady state
Ambient and cooling conditions; junction temperature under continuous load
Transient response
Peak-load duration, repetition and transient thermal impedance

Conduction and switching loss

Simplified estimates for understanding a single device.

Channel conduction loss

P_cond approximately equals I_rms squared times R_DS on

At constant on-resistance, conduction loss is proportional to RMS current squared. Iᵣₘₛ is the on-state channel current of one device evaluated over the full period, with off intervals set to zero. It differs from motor phase RMS or RMS over only the on interval; do not apply duty again. In practice, RDS(on) varies with temperature and other operating conditions.

Switching transition loss

P_sw approximately equals f_sw times the sum of E_on and E_off

For fixed Eon and Eoff, switching loss increases with switching frequency. The equation assumes one turn-on and turn-off pair per period. Both energies depend on operating voltage, current and gate-drive conditions.

Total inverter loss requires a separate calculation. Check the scope of measured loss terms to avoid omissions or double counting.

03MOTOR CONTROLMotor control

Motor control and overcurrent protection require current measurements at appropriate sampling instants. Switching noise, signal settling, sensing topology, PWM timing and ADC latency determine the usable measurement window.

Dead time is used to avoid simultaneous conduction of the upper and lower switches in the same leg, but also affects reverse-conduction loss. Gate-drive delays and switching timing must be reviewed together. Fault detection and shutdown response require a separate timing assessment.

DESIGN REVIEW POINTS

Sensing & control
Sensing location, settling, sampling timing and motor feedback
Protection & timing
Gate-drive delay, dead time and the fault-to-shutdown path

FROM DC POWER TO MOTOR DRIVE

From a DC supply to motor voltage.

The inverter switches a DC supply to produce motor terminal voltages. Current measurements and motor feedback inform control and protection design.

INPUTDC source
CONVERSIONGaN HEMTInverter
MOTIONPMSM / BLDCMotor

Conceptual energy flow. Not a product configuration or specification.

WHY GaN / BEYOND THE DEVICE

GaN characteristics.
Design implications.

Gate charge, reverse conduction and switching frequency affect power-stage losses and operation. Evaluate each under the intended circuit and operating conditions.

02REVERSE CONDUCTION

Reverse conduction.

E-mode GaN has no p–n body-diode reverse-recovery charge.

Reverse conduction and output-capacitance charging currents still occur. Review dead-time voltage drop and duration separately from capacitance-related switching loss.

GaN reverse conduction · TI (opens in a new tab)
03SYSTEM TRADE-OFF

Switching frequency.

Fast switching provides greater flexibility in selecting the switching frequency.

Review transition and drive losses, current ripple and emissions together. Output-capacitance charging and its associated losses also depend on the circuit and switching conditions.

GaN loss mechanisms · TI (opens in a new tab)

ENGINEERING / LOSS & HEAT

Power loss and thermal response.

Compare semiconductor conduction and switching losses with magnetic core and winding losses, then examine how heat flows to the cooling system.

LOSS ATLAS / DEVICE TO SYSTEM

Inverter loss analysis

Compare models for conduction, switching and magnetic-component losses, including the boundaries and conditions needed to calculate total inverter loss.

System boundary for total loss

The boundary here is the inverter. Magnetic losses apply only to inductors or transformers actually inside that boundary. Motor iron and copper losses are separate. Align time intervals and measurement boundaries to avoid double counting.

Ploss,inv = ΣjPcond,j+ Psw,Σ + Prev,Σ+ Σm(Pcore,m + Pcu,m)+ Paux + Pother

j: semiconductor device · m: magnetic component · cond: on-state conduction · sw: transitions · rev: separate reverse conduction · core/cu: core/winding · aux: remaining drive/control/supply losses not counted above · other: capacitors, interconnects and remaining losses

Preparing the calculator. Its controls will be available shortly.

CONDUCTION / SENSITIVITY

Current waveform and effective on-resistance

GaN conduction loss depends on the current waveform, conduction intervals, junction temperature, gate-drive conditions and preceding voltage stress. These conditions must also be considered when applying an I²R model.

Current sensitivity of conduction loss
Loss relative to referenceP / Pref
Current ratio from 0.5 to 2 on the horizontal axis; loss ratio from 0 to 4 vertically. The curve is current ratio squared at fixed resistance.012340.51.01.52.0
On-state device RMS current ratioI / Iref
Positive reference values · dimensionless axes · not product measurements. Control and plot ranges are chosen for comparison; they are not physical limits or allowable operating ranges of a device or material.

Educational assumption: fixed on-resistance, temperature and conduction pattern; the entire device-current waveform scales uniformly. I is full-interval on-state device RMS current; Pref is conduction loss at Iref. Pcond / Pref = (I / Iref)².

1.00
Loss relative to reference1.000×
Pcond = Irms,on2· RDS(on)
Detailed models · equations and boundaries
Pcond = (1/Tobs)∫0Tobs g(t) Reff(t) i2(t) dt
Reff(t) = RDS(on)(Tj(t), VGS(t), i(t), h(t))

In the resistive on-state, treat RDS(on) as an effective resistance dependent on Tj, VGS, device current i and stress/recovery history h. The mask g(t) is 1 during on-state channel-conduction intervals and 0 otherwise. Exclude transition intervals and off-state reverse conduction.

Dynamic on-resistance in GaN can differ from the DC value. Characterization must match off-state voltage, stress duration, switching conditions and observation time. The graph intentionally omits these dependencies to isolate the I²R relationship.

Tobs [s]: averaging interval · i [A]: device current · RDS(on) [Ω] · Tj: junction temperature · VGS [V] · g: dimensionless. At fixed resistance, I²rms,on = (1/Tobs)∫g(t)i²(t)dt: full-interval RMS with off intervals set to zero. Conduction duty is already included; do not multiply by duty again or directly substitute motor phase-current RMS.

Each graph uses a different loss reference. The normalized curves cannot be added to calculate total loss or efficiency. Actual prediction requires device, magnetic-material, winding and operating-point data.

02 / THERMAL PATH

Junction temperature and cooling.

The package, PCB and cooling structure determine how heat leaves the device. To estimate junction temperature, account for power loss, thermal resistance and the temperature of the ambient air or coolant.

  1. Device junctionWhere heat is generated
  2. Package / PCBHeat transfer and spreading
  3. Thermal structureInterfaces and heat-flow path
  4. Ambient / coolantAmbient air or cooling fluid
Single equivalent heat-flow path
ΔT≈Ploss × Rθ

This steady-state approximation represents heat flow from one device, dissipating Ploss [W], through one equivalent path. ΔT [K] is the junction-to-ambient or junction-to-coolant difference; Rθ [K/W] must span the same two points. Do not multiply total inverter loss by one device’s Rθ. Mutual heating, parallel paths and transient response require separate analysis.

Five relationships behind thermal designConduction · contact · convection · radiation · coolant balance

HEAT TRANSFER / FROM MATERIAL TO SYSTEM

Where does heat go, and how quickly?

Power dissipation generates heat. Junction temperature follows from the heat-flow path and its cooling boundary. Conduction through materials, temperature drops at contacts and convection into a fluid connect the heat source to the cooling system.

01 / CONDUCTION

Conduction / heat through a material

For heat flowing through a uniform flat layer, greater thickness increases thermal resistance. Greater conductivity and cross-sectional area reduce it.

Rcond = L / (kA)Q̇ = (Thot − Tcold) / Rcond

Steady, one-dimensional conduction; constant k and A; no heat generation within the layer. L is thickness [m], k conductivity [W/(m·K)], and A area normal to heat flow [m²]. Q̇ is heat-transfer rate [W]; R is thermal resistance [K/W].

02 / CONTACT

Contact / a temperature drop at the interface

Surface roughness, flatness and clamping pressure affect thermal contact. Bulk conduction through a TIM and contact resistance at its two faces are separate terms.

Rct = 1 / (hcAct)ΔTct = Q̇Rct

hc is areal contact conductance [W/(m²·K)]; Act is the contact area to which it applies [m²]. Do not add the same contact resistance again to measured TIM resistance that already includes it.

03 / CONVECTION

Convection / heat from a surface to a fluid

The surface-to-fluid temperature difference drives heat transfer. Fluid properties, velocity, channel geometry and flow regime determine h.

Q̇conv = hAwet(Ts − Tfluid)Rconv = 1 / (hAwet)

A lumped approximation using h [W/(m²·K)] and representative surface and bulk-fluid temperatures. Wetted area Awet [m²] is distinct from TIM contact area.

04 / RADIATION

Radiation / electromagnetic energy exchange

Radiation depends on the difference of fourth powers of absolute temperature. When a surface loses heat by both convection and radiation, add their heat-transfer rates.

Q̇rad = εσArad(Ts4 − Tsur4)

An isothermal diffuse-gray surface viewing only much larger isothermal surroundings, with view factor 1 and a nonparticipating medium. Arad is radiating area [m²]; ε is emissivity; Ts and Tsur must be in K. σ ≈ 5.6704 × 10⁻⁸ W/(m²·K⁴).

05 / COOLANT ENERGY BALANCE

Coolant / flow and inlet–outlet heat balance

The net heat-transfer rate into the coolant depends on its mass flow rate, specific heat capacity and temperature rise. For the same absorbed heat rate and specific heat capacity, a higher mass flow rate gives a smaller inlet–outlet temperature difference.

Q̇coolant = ṁcp(Tout − Tin)

Steady single-phase flow with constant cp; neglect shaft work and kinetic/potential energy changes. ṁ [kg/s], cp [J/(kg·K)], and Q̇coolant [W], the net heat-transfer rate entering the coolant.

Preparing the calculator. Its controls will be available shortly.

INTERACTIVE / STEADY-STATE RESISTANCE

Change thermal resistance. See the temperature change.

This steady-state example sends 100 W from one heat source through one series path to an isothermal fluid boundary at 25 °C. Adjust TIM thickness, conductivity and convection coefficient to compare the contributions.

The control ranges are for comparison, not physical limits of materials or cooling methods. Values are not product measurements; other resistances, including contact and spreading, and power loss remain fixed.

0.30 mm
3.0 W/(m·K)
1000 W/(m²·K)
Calculated junction temperature55.0 °C
Total resistance0.300 K/W
Junction–fluid rise30.0 K
Tj = Tfluid + PlossRtotalRtotal = Rfixed + RTIM + Rconv
Equivalent series heat-flow path Ploss = 100 W
Junction / heat source55.0 °C
Fixed resistance0.150 K/WΔT = 15.0 K
TIM conduction0.050 K/WΔT = 5.0 K
Surface → fluid0.100 K/WΔT = 10.0 K
Fluid boundary25.0 °C

Rfixed combines the remaining package, spreading and contact resistances into one fixed equivalent. The sequence above represents a resistance network, not the physical order of layers.

Contribution of each term to the current total thermal resistance
  • Fixed resistance50.0%
  • TIM conduction16.7%
  • Surface → fluid33.3%

ATIM = 0.002 m² · Awet = 0.010 m² · Rfixed = 0.150 K/W. This series example has no separate radiation or PCB parallel path. Fluid-boundary temperature is fixed; inlet–outlet temperature change can be calculated separately using the coolant heat balance above.

Improving the TIM still leaves the fixed and convective resistances. Finding the largest resistance across the whole path is the starting point for cooling design.

FIELD EQUATION → THERMAL CIRCUIT

From a temperature field to a transient response

Conduction, convection and radiation become internal transport and boundary conditions in the heat equation. Reducing the field to temperature nodes, resistances and capacitances gives a thermal circuit model.

Heat diffusion / a stationary solid
ρcp ∂T/∂t= ∇·(k∇T) + q‴

ρ is density [kg/m³], cp specific heat [J/(kg·K)], k isotropic thermal conductivity [W/(m·K)], and q‴ volumetric heat generation [W/m³]. With no phase change or thermomechanical coupling, the local energy-storage rate equals net conduction input plus internal generation, all per unit volume.

q″ = −k∇T [W/m²] is heat flux. Convection and radiation act as surface boundary conditions; contact interfaces have a heat-flux-dependent temperature jump. Specify the initial temperature and each boundary condition.

Lumped capacitance / one temperature node
Cθ dT/dt= P(t) − (T − Tb)/Rθ

For approximately uniform node temperature and volumetric heat capacity ρcp, Cθ = ρcpV [J/K], where V is node volume [m³]. The part of power loss P(t) [W] not yet leaving through the boundary increases internal energy. Tb is the constant reference-boundary temperature; t is time [s].

With constant Rθ and Cθ, T(0) = Tb and constant Pstep applied from t = 0, the step response below follows. τ = RθCθ [s] sets the timescale. Cθ does not change the steady-state rise.

ΔT(t) = PstepRθ(1 − e−t/τ)ΔT = T − Tb

Resolve a large temperature variation with multiple nodes. Distinguish a network representing physical heat paths from a fitted Foster network; its internal nodes do not represent literal layer interfaces.

FROM PRINCIPLES TO MODELS

Models for coordinate transforms, current control and thermal response.

GaN HEMTPOWER STAGE / CONCEPT
Three-phase power-stage concept with 24 GaN devices, vertically oriented MLCC banks and grouped control and protection circuits
Power-loop layout and flux cancellation

Closely coupled opposing current paths in the same loop partially cancel their magnetic fields, reducing parasitic loop inductance. Keep local DC-link connections to the switches short, while also considering switching-node parasitic capacitance.

Conceptual cross-section showing opposing currents in adjacent conductors L1 / POWER PATH → DIELECTRIC L2 / ← RETURN PATH

Cross-section of the outgoing and return current paths

EPC power-loop layout reference (opens in a new tab)
Power-stage design concept. Not an actual product photograph.

GaN HEMT.
Three-phase inverter.

We review supply voltage, motor characteristics, cooling and control requirements to define the inverter’s application scope and development priorities.

Power technology
GaN HEMT
Motor focus
PMSM / BLDC
Application focus
Student E-Formula · AGV · Robotics

Detailed specifications have not yet been released. The stated design targets are not test results or confirmed ratings.

ENGINEERING THE NEXT DRIVE

Designed around
your drive requirements.

Supply and motor characteristics, cooling conditions and control requirements define the design inputs. We evaluate conduction and switching losses, thermal limits and current-sensing constraints to set efficiency, power-density and control targets.

Four-wheel torque-vectoring development concept with four GaN inverters, a wireless VCU, GPU, underfloor battery, EV connectors and an EMI pre-scan spectrum analyzerEngineering concept image
WIRELESS TORQUE VECTORINGA development concept for four independent drives.
Concept of an inverter–motor test bench with a PowerCraft battery pack, active instrument displays, current probes and a ChatGPT laptopEngineering concept image
ENGINEER THE DETAILSA development setup for the inverter and motor.
01POWER CONVERSIONPower-stage loss reduction
We evaluate conduction and switching losses at the intended current and switching conditions. Gate drive and power-loop parasitics are reviewed to balance loss reduction against voltage overshoot.
02POWER DENSITYThermal design for continuous duty
We review heat paths through the devices, PCB and cooling structure. Junction temperature under continuous load remains a design constraint as the power stage becomes more compact.
03CURRENT CONTROLCurrent sensing and control response
Sensing location, PWM timing, signal settling and measurement delay are reviewed together. The measurement and processing paths must deliver current information in time for control and fault protection.
04SYSTEM INTEGRATIONMotor and system integration
We define the requirements of the motor, power supply, cooling system and supervisory controller. Their constraints inform the inverter’s application scope and the work to be agreed for joint development.

These are development objectives and design considerations. Specifications, supported functions and evaluation conditions are agreed for each product; performance must be established by testing under those conditions.

CO-DEVELOPMENT / FROM IDEA TO DRIVE

From requirements to a validation plan

  1. 01
    Define the drive targets

    Define efficiency, output, installation space and operating conditions

  2. 02
    Review the integrated design

    Review power, thermal and control needs to define the development scope

  3. 03
    Agree on validation criteria

    Define evaluation conditions and performance metrics

Discuss your application

FOUR-WHEEL CONTROL / DEVELOPMENT STUDY

Longitudinal force and yaw moment, allocated to four wheels.

Allocate force and moment requests to the wheels, then explore tire constraints and the vehicle response over time. Each stage uses its own inputs and model assumptions.

01 / BASIC ALLOCATION

Basic torque allocation

Longitudinal wheel forces sum to a total force; the left–right difference creates yaw moment. This static example calculates allocations that meet both requests under an assumed ±100 N·m torque limit at each wheel.

Force–moment allocation envelope

CALCULATED EXAMPLE
Yaw moment MzN·m
Allocation envelope from four wheel-torque limitsHorizontal force axis −1600 to 1600 N; vertical yaw-moment axis −960 to 960 newton meters. On and inside the diamond, each wheel torque magnitude is at most 100 newton meters. Selected point 800 N and 240 newton meters.-9600960-160001600
Longitudinal force FxN
Color bands: wheel-torque limit utilization≤ 25%≤ 50%≤ 75%≤ 100%
Preparing the calculator. Its controls will be available shortly.
800 N
240 N·m

Each slider endpoint is the maximum with the other request set to zero; the two maxima cannot be achieved together. Feasibility checks only this example’s wheel-torque limits. Tire grip and actual vehicle capability require additional constraints.

Allocation within torque limitsPeak wheel-limit utilization 75%
Calculated wheel-end torque requests N·m
WheelRequested torqueAllocated torque
FLFront left25.025.0
FRFront right75.075.0
RLRear left25.025.0
RRRear right75.075.0

Resultant: Fx = 800 N · Mz = 240 N·m. Minimum wheel-torque headroom 25.0 N·m.

Allocation equations, assumptions and development architecture

Four conditions define this map

Effective wheel radius r
0.25 m
Full track width t
1.20 m
Assumed torque limit per wheel
±100 N·m
Front / rear steering angles
0° / 0°

Allocation that preserves force and moment

For equal front/rear track widths and wheel radii, each side’s torque is split equally between its front and rear wheels. This minimizes the sum of squared torques among allocations satisfying both requests; it does not imply minimum electrical loss.

Axes are x forward, y left and z up; positive Mz is counterclockwise viewed from above. Wheel-end torque is positive when it produces forward force. Whether negative torque brakes or drives in reverse depends on wheel rotation. This static model neglects wheel angular acceleration and rolling resistance, so Fx,i = Ti/r. Tire friction, lateral forces, load transfer and speed-dependent motor and battery constraints belong in the vehicle model.

Development architecture for distributed drive

The concept would coordinate four GaN inverters through a VCU, with each inverter running its current loop locally. It would use an NVIDIA GPU for vehicle-model computation and allocation research, with torque commands and operating status exchanged wirelessly. Torque-command timing and communication-fault behavior are separate design tasks.

Preparing the calculator. Its controls will be available shortly.
02 / FRICTION CONSTRAINTSTire constraints and allocation principlesExplore static allocation with friction and load transfer, then the control principles

The vehicle controller decides which yaw moment is needed. The allocator decides how the four wheels can produce it. Lateral tire force consumes part of the same force budget used for driving and braking.

INTERACTIVE / FRICTION BUDGET

Friction headroom changes the envelope.

A static force budget with a = b and symmetric front/rear loads and lateral forces. Steering is zero; wheel inertia and rolling resistance are omitted. Each wheel has Fy = m ay/4. Prescribed ay sets quasi-static roll load transfer; longitudinal load transfer and aerodynamics are omitted. This does not solve steady cornering motion relating steering to ay.

800 N
-1600 N1600 N
480 N·m
-960 N·m960 N·m
0.60 —
0.2 —1.2 —
4.0 m/s²
-8 m/s²8 m/s²

m = 240 kg · h = 0.25 m
t = 1.20 m · rw = 0.25 m
g = 9.81 m/s² · T0 = 100 N·m

T0 is a symmetric torque cap per wheel. Motor speed and battery power are not variables in this plot.

Force–moment envelope with tire constraints

Requested and allocated force–moment pointsForce in N on the horizontal axis and moment in newton meters on the vertical axis. Constrained optimum · residual remains. Request 800 N and 480 newton meters.Mz [N·m]-9600960-160001600Fx [N]
Torque cap onlyWith frictionRequestAllocation

The shaded region preserves the specified lateral force. The dashed boundary uses only the ±100 N·m cap from the preceding example.

Constrained optimum · residual remainsResidual = allocation − request
Allocated Fx672.6 N
Allocated Mz403.6 N·m
Force residual-127.4 N
Moment residual-76.4 N·m
Load and torque at each wheel on a side
QuantityLeft FL / RLRight FR / RR
Fz [N]488.6688.6
Fy [N]240.0240.0
|T|max [N·m]42.184.1
Request [N·m]0.0100.0
Allocated [N·m]0.084.1

A torque cap of 0 means the prescribed lateral force is admissible but leaves no longitudinal headroom. A dash means wheel contact or lateral demand is already infeasible, so no admissible torque interval exists.

Load, friction and the exact optimum in this example

s is L or R; m is total mass, h is CG height above the ground, t is full track width and rw is effective wheel radius. The friction circle is admissible only for Fz > 0 and |Fy| ≤ μFz. Positive ay is leftward acceleration, increasing right-side load. Front and rear share load transfer equally, with one constant μ for all four tires.

The inverse allocation above gives TL* and TR*. With these normalization scales, J separates into two squared side-torque errors. Clipping each request to [−Ts,max, +Ts,max] is therefore the exact minimum. Unequal force/yaw weights or coupled battery constraints generally remove this simple solution.

Current minimum J: 0.01268 (dimensionless)

01Vehicle dynamics and reference response

Body axes are x forward, y left and z up. Yaw rate r = ψ̇ is in rad/s; body sideslip β ≈ vy/vx is in rad. Positive front steering δ points left. For constant vx > 0, small angles and linear tire response:

Cf and Cr [N/rad] are total front/rear axle cornering stiffnesses. Distances a and b [m] run from the CG to each axle; Iz [kg·m²] is yaw inertia. Mz [N·m] is the additional moment from longitudinal force differences, separate from aFyF − bFyR. The linear expression does not extend through vx → 0 or tire saturation.

r0 is the linear steady-cornering solution with Mz = 0; Ku has units s²/m. A near-zero denominator in an oversteer regime is not a useful reference target. The quasi-steady relation ay ≈ vx r gives the lateral-acceleration cap |rref| ≲ μ̂g/vx; it is not a complete stability or combined-friction boundary.

Separate reference generation, state estimation and feedback. Sideslip is estimated using signals such as IMU data, wheel speeds and a vehicle model. One additional Mz cannot independently impose arbitrary β and r targets. Design K for the speed and tire conditions, and return allocation residuals to limit integral windup during saturation.

02From steered wheels to a general allocation matrix

Rotate wheel-frame forces (Fxw, Fyw) by steering angle δi into body coordinates. Wheel position (xi, yi) is measured from the CG.

For v = [Fx, Mz]ᵀ, B has first-row units 1/m and a dimensionless second row. The vector d contains rotated lateral-force and external contributions. For a total force/moment target use u* = v* − d; do not subtract these terms twice when the target already specifies only the additional longitudinal-drive contribution. The dashboard uses δi = 0 with cancelling yaw contributions from symmetric lateral forces.

B uses Fxw,i ≈ Ti/rw,i by neglecting wheel acceleration and rolling resistance. Wheel-slip control also needs the rotational equation above and the tire slip–force relationship.

03Distinct tire, motor and battery constraints

The circle is an isotropic force budget with constant μ. Unequal longitudinal and lateral limits call for a friction ellipse and tire data. Vertical load, tire temperature and road-friction estimates change the admissible region.

Current, voltage and thermal limits make motoring and regenerative torque bounds speed-dependent. Tj is inverter semiconductor junction temperature; the expression shows representative inputs to a torque-limit map. Motor winding and magnet temperatures require additional limits. With gearing, convert motor-shaft torque and speed to the wheel basis using ratio and efficiency. In P = Tω, torque sign alone does not determine regeneration.

T is in N·m, ω in rad/s and P in W. Pbat is net DC power at the battery terminals: positive for discharge and negative for charging. Its port and sign convention differ from Pdc,inv in the regeneration section, where power entering the DC link from the inverter is positive. Pbat also accounts for drivetrain losses and auxiliaries, so it is not equal to mechanical output. Cancelling left/right Tω does not imply zero current or loss. Charge acceptance, DC-link voltage and battery state couple all wheels; independent torque clipping cannot enforce these limits.

04A normalized QP and the meaning of residuals

Positive scales Dv = diag(F0, M0) and DT = diag(T0,i) remove the units before Wv sets priorities. WT weights torque changes and λ ≥ 0. Changing weights does not relax physical limits; it chooses which errors to reduce within them.

With fixed B and linear constraints this is a convex QP. Prescribed lateral force reduces the friction circle to torque intervals as in the example. Optimizing longitudinal and lateral forces together under a circular constraint is not a linearly constrained QP; use a polygon approximation, conic or nonlinear optimization. Nonlinear efficiency maps also need separate treatment.

A small objective is not the same as feasibility. Both requests are met exactly only when ealloc = 0 and all constraints hold. A failed wheel changes its torque interval and the effective columns/rank of B. Penalizing Δτ smooths commands; it does not by itself minimize electrical loss.

05Wireless supervisory commands and local current loops
VCUState estimate · reference · allocation
Command receptionSequence · age · bounds · rate
Local inverterTorque-to-current · current loop · PWM/protection

Wireless packets carry supervisory torque requests and status. Each inverter closes its ADC–current-control–PWM path on a local timebase. Communication rate and current-loop frequency are distinct. Timestamp checks must include clock-synchronization uncertainty.

The phase expression is the frequency response of a constant pure delay td [s]. Here ωc [rad/s] is the angular frequency evaluated in the supervisory loop, not motor electrical speed or packet rate. This expression alone does not establish closed-loop stability with variable wireless delay or packet loss.

Assess jitter, the longest packet-loss burst and receive-to-apply delay as well as average latency. Stale or reordered commands must not refresh the request. Define timeout behavior and torque ramp rates for the vehicle state; immediate zero torque is not a universal response. Local electrical protection, such as overcurrent shutdown, follows a separate path that does not wait for wireless feedback.

The TI reference below illustrates local current loops in a wired distributed drive. It does not prescribe wireless latency or fault-policy values.

03 / VEHICLE RESPONSE

Vehicle yaw response

Compare target and actual yaw rates and the vehicle path under a fixed steering input. Change speed, steering and requested drive force, then explore how wheel friction, torque limits and drive faults affect the time response.

Preparing the vehicle yaw response.

ENGINEERED
FOR MOTION.

We review inverter requirements for Formula-style electric racing (Student E-Formula), automated logistics and robotics, based on the motor and operating conditions of each application.

AGV application concept02AUTONOMOUS MOBILITY

AGV

Traction drives for automated logistics.

Assess inverter power and control requirements against the vehicle’s traction load and operating conditions.

Discuss an application
Robotics application concept03ROBOTIC MOTION

Robotics

Motor drives for robotic systems.

Review inverter requirements and joint development needs for the robot’s motors and control system.

Discuss an application

POWERCRAFT.
IN MOTION.

A PowerCraft project.
Focused on GaN inverters.

PowerCraftMotion is PowerCraft’s GaN HEMT inverter development project. We define application requirements for the supply, motor and operating conditions, then identify the technical collaboration and joint development work required.

Project foundation
PowerCraft’s GaN inverter development project
Development focus
GaN power conversion and control for motor drives
ENGINEERING COLLABORATIONFROM REQUIREMENTS TO DESIGN.

LET’S ENGINEER
YOUR DRIVE.

Application reviews · Joint development · Investment

DEVELOPMENT OVERVIEW
In development

GaN HEMT
motor inverter

Define the development scope around your motor and operating conditions. Start with these three topics.

Supply & current
DC-voltage range, phase current and continuous or short-duration loads
Cooling & installation
Cooling method, installation space and operating environment
Control & feedback
Supervisory commands, communications and motor-sensor requirements

Detailed specifications have not yet been released. The stated design targets are not test results or confirmed ratings.

THREE-PHASE / ENGINEERING NOTES

Three-phase inverter principles

Loading theory and interactive diagrams.