How does bandwidth interact with decoupling and parameter mismatch? 带宽设计如何与前馈解耦和参数失配相互作用？

From frequency domain to time domain: bandwidth, decoupling, and robustness 从频域到时域：带宽、解耦与鲁棒性

A well-tuned controller is not just "fast." It must balance speed, stability, and robustness to model uncertainty. This project asks you to quantify these tradeoffs through simulation. 一个调好的控制器不只是"快"。它必须在速度、稳定性和对模型不确定性的鲁棒性之间取得平衡。本项目要求你通过仿真量化这些权衡。

Code entry points and setup references代码入口与环境参考

git clone https://github.com/horychen/ee275.git
cd ee275/simulation
python tutorials_ep6_svpwm.py

Variables you should know至少要熟悉这些变量

Base configuration dictionary基础配置字典

Use this as your starting point. The key fields you will modify are highlighted in comments.以此为出发点。你需要修改的关键字段在注释中标出。

d = {
    'CL_TS': 1e-4,
    'VL_EXE_PER_CL_EXE': 5,
    'MACHINE_SIMULATIONs_PER_SAMPLING_PERIOD': 1,
    'TIME_SLICE': 0.2,
    'NUMBER_OF_SLICES': 6,
    'init_npp': 22,
    'init_IN': 1.3*6/1.414,
    'init_R': 0.035,                # <-- Part 3: change this for mismatch
    'init_Ld': 0.036e-3,            # <-- Part 3: change this for mismatch
    'init_Lq': 0.036e-3,            # <-- Part 3: change this for mismatch
    'init_KE': 0.0125,
    'init_Rreq': 0.0,
    'init_Js': 0.44e-4,             # <-- Part 3: change this for mismatch
    'DC_BUS_VOLTAGE': 5,
    'user_system_input_code':
        "if ii < 1: CTRL.cmd_idq[0] = 0.0; CTRL.cmd_rpm = 50\n"
        "elif ii < 5: ACM.TLoad = 0.2\n"
        "elif ii < 100: CTRL.cmd_rpm = -50",
    'CTRL.bool_apply_speed_closed_loop_control': True,
    'CTRL.bool_apply_decoupling_voltages_to_current_regulation': False,  # <-- Part 2
    'CTRL.bool_apply_sweeping_frequency_excitation': False,
    'CTRL.bool_overwrite_speed_commands': True,
    'CTRL.bool_zero_id_control': True,
    'FOC_delta': 15,                 # <-- Part 1: damping factor
    'FOC_desired_VLBW_HZ': 120,     # <-- Part 1: sweep this
    'FOC_CL_KI_factor_when__bool_apply_decoupling_voltages_to_current_regulation__is_False': 10,
    'CL_SERIES_KP': None,           # None = auto-tune
    'CL_SERIES_KI': None,
    'VL_SERIES_KP': None,
    'VL_SERIES_KI': None,
    'VL_LIMIT_OVERLOAD_FACTOR': 3.0,
    'disp.Kp': 0, 'disp.Ki': 0, 'disp.Kd': 0,
    'disp.tau': 0, 'disp.OutLimit': 0, 'disp.IntLimit': 0,
}

How does bandwidth affect time-domain performance? 带宽如何影响时域性能？

Background: PI auto-tuning背景：PI 自动整定

When CL_SERIES_KP is None, the Simulation_Benchmark class calls tuner.tunner_wrapper(d), which iterates to find current-loop and speed-loop PI gains that achieve the desired bandwidths. The key formulas are: 当 CL_SERIES_KP 为 None 时，Simulation_Benchmark 类会调用 tuner.tunner_wrapper(d)，通过迭代找到满足期望带宽的电流环和速度环 PI 参数。核心公式：

where $\delta$ is FOC_delta (a damping-like factor) and $\omega_{ci}$ is the current-loop bandwidth in rad/s. 其中 $\delta$ 即 FOC_delta（类似阻尼比的参数），$\omega_{ci}$ 为电流环带宽（rad/s）。

Step response metrics阶跃响应指标

Code skeleton代码骨架

import copy
from tutorials_ep6_svpwm import Simulation_Benchmark

bandwidths = [20, 40, 60, 80, 100, 120]
results = {'rise_time': [], 'overshoot': [], 'ss_error': []}

for bw in bandwidths:
    d_run = copy.deepcopy(d)      # use a fresh copy each time
    d_run['FOC_desired_VLBW_HZ'] = bw
    d_run['CL_SERIES_KP'] = None  # force re-tune
    d_run['CL_SERIES_KI'] = None
    d_run['VL_SERIES_KP'] = None
    d_run['VL_SERIES_KI'] = None

    sim = Simulation_Benchmark(d_run)
    speed = sim.gdd['CTRL.omega_r_mech']
    time  = sim.global_machine_times

    # TODO: extract rise time, overshoot, steady-state error
    # Hint: find the step region, identify y_ss, then compute metrics
    # results['rise_time'].append(tr)
    # results['overshoot'].append(os_pct)
    # results['ss_error'].append(ess)

What does feedforward decoupling do, and what are its side effects? 前馈解耦的作用与副作用

Physics: cross-coupling in the dq frame物理：dq 坐标系中的交叉耦合

The dq-frame voltage equations of a PMSM are: PMSM 的 dq 坐标系电压方程为：

The underbraced terms act as disturbances to the PI current regulators. Feedforward decoupling adds compensation voltages to cancel them: 下划线部分是对 PI 电流调节器的扰动。前馈解耦通过补偿电压来抵消它们：

This corresponds to lines 696–699 in tutorials_ep6_svpwm.py. 这对应 tutorials_ep6_svpwm.py 的第 696–699 行。

Code: toggle decoupling代码：切换解耦

# Experiment A: Decoupling OFF
d_off = copy.deepcopy(d)
d_off['CTRL.bool_apply_decoupling_voltages_to_current_regulation'] = False
sim_off = Simulation_Benchmark(d_off)

# Experiment B: Decoupling ON
d_on = copy.deepcopy(d)
d_on['CTRL.bool_apply_decoupling_voltages_to_current_regulation'] = True
sim_on = Simulation_Benchmark(d_on)

What happens when the controller's model does not match reality? 当控制器的模型与实际不匹配时会发生什么？

The idea思路

In Simulation_Benchmark, both CTRL (controller) and ACM (plant) are initialized from the same d dictionary. The feedforward decoupling uses CTRL.Lq and CTRL.KA to compute the compensation voltages. If these values are wrong (i.e., they don't match the actual plant), the feedforward injects errors instead of cancelling disturbances. 在 Simulation_Benchmark 中，CTRL（控制器）和 ACM（被控对象）都从同一个 d 字典初始化。前馈解耦使用 CTRL.Lq 和 CTRL.KA 来计算补偿电压。如果这些值是错误的（即与实际被控对象不匹配），前馈就会注入误差而非抵消扰动。

Code: parameter mismatch experiment代码：参数失配实验

import copy

# Step 1: Tune with correct parameters
d_baseline = copy.deepcopy(d)
d_baseline['CL_SERIES_KP'] = None  # auto-tune
sim_matched = Simulation_Benchmark(d_baseline)

# Step 2: Save tuned gains
saved_gains = {
    'CL_SERIES_KP': d_baseline['CL_SERIES_KP'],
    'CL_SERIES_KI': d_baseline['CL_SERIES_KI'],
    'VL_SERIES_KP': d_baseline['VL_SERIES_KP'],
    'VL_SERIES_KI': d_baseline['VL_SERIES_KI'],
}

# Step 3: Run with parameter mismatch
d_mismatch = copy.deepcopy(d)
d_mismatch.update(saved_gains)  # use pre-tuned gains, skip re-tuning
d_mismatch['init_R']  = d['init_R']  * 1.5   # +50% resistance (thermal)
d_mismatch['init_Ld'] = d['init_Ld'] * 0.7   # -30% inductance (saturation)
d_mismatch['init_Lq'] = d['init_Lq'] * 0.7
d_mismatch['init_Js'] = d['init_Js'] * 2.0   # +100% inertia (load)

sim_mismatched = Simulation_Benchmark(d_mismatch)

Predict disturbances and actively compensate 预测扰动并主动补偿

The speed observer in the code (DYNAMICS_SpeedObserver, line 417) estimates not only rotor speed but also a disturbance state xS[2], which represents the total disturbance — including load torque and modeling errors. When the disturbance feedforward is enabled, this estimate is actively fed forward to the speed controller, compensating for disturbances before the PI regulator has to react. 代码中的速度观测器（DYNAMICS_SpeedObserver，第 417 行）不仅估计转子速度，还估计扰动状态 xS[2]，它代表总扰动——包括负载转矩和建模误差。启用扰动前馈时，该估计值会主动前馈给速度控制器，在 PI 调节器反应之前就补偿扰动。

Observer dynamics观测器动态

where $e_\theta = \theta_d - \hat{\theta}_d$ is the position estimation error and $\ell_1, \ell_2, \ell_3$ are observer gains (configured via omega_ob). 其中 $e_\theta = \theta_d - \hat{\theta}_d$ 是位置估计误差，$\ell_1, \ell_2, \ell_3$ 是观测器增益（通过 omega_ob 配置）。

How to enable如何启用

# After creating Simulation_Benchmark with bool_start_simulation=False,
# modify CTRL before running:
CTRL.index_separate_speed_estimation = 1      # use observer for speed
CTRL.use_disturbance_feedforward_rejection = 1 # feed xS[2] forward
# Mode 2: CTRL.use_disturbance_feedforward_rejection = 2
#   adds correction: xS[2] + ell2 * output_error (faster but noisier)

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