# 5.2.1. AN1292 Phase-locked Loop (PLL)

## 5.2.1.1. Overview

The sensorless estimator used to estimate position and velocity is essentially the same one described in application note AN1292.

Figure 5.5 AN1292 Phase-locked loop block diagram

Stationary-frame voltages \(V_{\alpha\beta}\) and currents \(I_{\alpha\beta}\) are used to estimate back-emf components \(E_{\alpha\beta}\) using a discrete-time approximation of the equation

(5.1)\[E_{\alpha\beta} = V_{\alpha\beta} - R_sI_{\alpha\beta} - L_s\tfrac{d}{dt}I_{\alpha\beta}\]

The feedback loop shown in Figure 5.5 is then used to rotate \(E_{\alpha\beta}\) into the synchronous (dq) frame to produce an error signal and update the electrical angle \(\theta_e\) (rather than \(\rho_{estim}\) shown in the diagram) used for rotation, where

(5.2)\[\theta_e = \rho_{estim} + \rho_{ofs}\]

and \(\rho_{ofs}\) (`motor.estimator.pll.rhoOffset` in firmware) is a parameter that defaults to zero, but can be adjusted manually with real-time diagnostic tools.