See a motor think.

Contents

1. 01

   Foundations

   Read any three-phase quantity as one rotating vector, and scale a drive so nothing overflows.

   • Space vectors Where the rotating field comes from, and why two numbers describe three phases.
   • Power in three phases Why one phase pulses to zero, three deliver a constant, and where the 3/2 comes from.
   • Clarke and Park abc to alpha-beta to dq, the 2/3 factor, and what an angle error costs.
   • Per-unit and scaling Normalised bases, fixed-point formats, and choosing them so nothing overflows.
2. 02

   The machine

   Move between abc, αβ and dq in either direction, and know which angle each step needs.

   • PMSM dq model The four parameters, the voltage equations, and measuring them without dropping factors.
   • Measuring the machine Where the four parameters come from, the factors that get dropped, and what heat does to them.
   • Torque and MTPA Magnet torque, reluctance torque, and why id = 0 is not always the optimum.
   • Field weakening What to do when the back-EMF reaches the DC link and negative id stops being optional.
3. 03

   The inverter

   Predict the voltage a machine demands, the torque it returns, and where its speed runs out.

   • The bridge Six devices, one gate pattern, which one is carrying the current right now, and what it dissipates.
   • Six-step commutation What FOC replaced: six fixed directions, 14% torque ripple, and 15.5% more voltage.
   • Space-vector PWM Sectors, dwell times, and why min-max injection is the same thing as SVPWM.
   • Deadtime The distortion a safety interlock costs you, and what compensation actually recovers.
4. 04

   Sensing

   Turn a voltage request into gate signals, and account for what deadtime takes back.

   • Current measurement One, two or three shunts, when to sample, and the signature each error leaves in dq.
   • The converter What a finite number of codes does to a current, and why dq rounds differently from the phases.
   • The DC link The bridge from the supply side: ripple current, sag, and where braking energy goes.
   • Position sensors What each sensor really tells you, and the d-axis offset that stands between a count and an angle.
5. 05

   Control and estimation

   Place a sampling instant that measures current rather than switching noise.

   • The current loop Gains from the machine parameters, decoupling, and anti-windup that works.
   • Speed and position loops Why cascades work, how far apart the bandwidths must be, and startup saturation.
   • Sampled time The controller is a difference equation: which error sample it uses, and what aliasing does.
   • Sensorless position Flux and sliding-mode observers, the PLL, and which way each filter shifts the angle.
6. 06

   Implementation

   Tune a current loop from machine parameters, and stop an integrator winding up.

   • Timing and synchronisation The delay budget, phase margin from pure algebra, and where the ISR time goes.
   • The peripherals it needs PWM, triggered ADC, fault inputs — what the silicon must do, and the register rules that bite.
   • Software architecture Layers that point inwards, one owner of the inverter, and a witness the control law does not use.
   • Bringing a drive up The order to switch things on in, so that a regression has exactly one candidate cause.