工作原理
An LLC converter regulates its output voltage by changing the switching frequency, so the voltage loop compensator outputs a frequency command rather than a duty cycle. Above resonance, raising the frequency lowers the output voltage, which means the plant gain is negative and the controller must act on the inverted error.
This tool first finds the operating point with the first harmonic approximation (FHA): it computes the resonant frequency, the inductance ratio m and the quality factor Q from your component values and load, then searches the inductive side of the gain curve for the switching frequency that gives the required voltage gain. The slope of the gain curve there is the low-frequency plant gain dV_out/df_s.
The small-signal plant combines that slope with the output capacitor and load (a single pole at 1/(2π·R·C_o)) and the ESR zero. A pure delay models sampling and computation in a digital controller. An optional double pole at the beat frequency |f_s − f_r| approximates the resonant tank dynamics that appear near resonance.
Auto-tune solves for the PI gains that put the crossover at your target frequency with the requested phase margin. The sliders then let you scale Kp and Ki and watch how the loop gain, margins and step response respond, which is the quickest way to build intuition for compensator design.
公式
- FHA voltage gain
- K = (m−1)·F² / √((m·F² − 1)² + F²·(F² − 1)²·(m − 1)²·Q²)
- Plant (small-signal)
- G_vf(s) = K_f · (1 + s·ESR·C_o) / (1 + s·(R + ESR)·C_o)
- Plant gain at the operating point
- K_f = (V_in,eff / n) · dK/dF / f_r
- PI controller
- C(s) = Kp + Ki / s
- Loop gain
- T(s) = C(s) · G_vf(s) · H · e^(−s·T_d)
- Auto-tune (at ω_c)
- φ_C = −180° + PM − ∠P(jω_c), Kp = cos φ_C / |P(jω_c)|, Ki = Kp·ω_c·tan(−φ_C)
计算示例
The default design is a 390 V half-bridge LLC delivering 48 V / 500 W with n = 4, Lr = 38 µH, Cr = 66.6 nF and Lm = 190 µH (f_r ≈ 100 kHz, m = 6, Q ≈ 0.40). It operates at about 104 kHz, where the plant gain is roughly −0.18 mV/Hz. With 1000 µF output capacitance, a 2.5 V sense divider and 15 µs control delay, auto-tuning for a 2 kHz crossover and 60° phase margin gives about 13.6 dB of gain margin and a step response with roughly 24% overshoot.
常见问题
Why is the controller output in Hz instead of duty cycle?
An LLC converter controls power flow with switching frequency. The PI output is a frequency command, which the PWM peripheral converts into a switching period.
What crossover frequency should I choose?
Voltage loops commonly cross over at a few hundred hertz to a few kilohertz, well below the switching frequency and below the beat frequency between switching and resonant frequency. Higher crossover gives faster transients but leaves less margin against unmodeled dynamics.
How accurate is the FHA plant model?
It captures the DC gain and the output filter pole well, which is enough for a first PI design. Near and below resonance the LLC has extra poles that FHA misses, so confirm the loop with an extended describing function model, simulation or a network-analyzer measurement.
What phase margin is enough?
Aim for at least 45°, and 60° for a well-damped response. Keep at least 6 dB of gain margin.
计算结果为工程估算值，请结合数据手册、仿真和实测验证设计。