3-phase BLDC motor analysis and control using Tensor Product Transformation

Abstract

This thesis designs and tests an angle-scheduled tensor-product (TP) state-feedback controller for speed control of a three-phase BLDC motor, modelled as an LPV system whose matrices depend on electrical rotor angle. The angle dependence is approximated by a 12-vertex polytopic model, and vertex gains are computed via LMIs with a common quadratic Lyapunov function; in real time the controller interpolates these gains and applies rate-limited, saturated phase voltages through a PWM interface. In nonlinear Simulink simulations of a 0–3000 rpm step, the TP and composite PI+TP controllers achieve 5–6 ms rise time, 10–15 ms settling time and 3–4% overshoot, whereas a tuned PI loop shows similar rise time but about 12% overshoot and ~45 ms settling. Steady-state results show that PI and PI+TP have essentially zero error and negligible ripple, while pure TP leaves a small bias and ~75 rpm peak-to-peak ripple, so the PI+TP architecture is identified as the best compromise between fast dynamics and smooth steady state.