Calibrating Optimal PMSM Torque Control with Field-Weakening Using Model-Based Calibration

Permanent magnet synchronous motor (PMSM) calibration is an indispensable step in the design of high-performance electric traction drive controls. Traditionally, the calibration process involves extensive hardware dynamometer (dyno) testing and data processing, and its accuracy depends largely on the expertise of the calibration engineer.

Model-based calibration standardizes the PMSM calibration process, reduces unnecessary testing, and generates consistent results. It is an industry-proven, automated workflow that uses statistical modeling and numeric optimization to optimally calibrate complex nonlinear systems. It can be used in a wide range of applications and is well known for being adopted in internal combustion engine control calibration. When applied to e-motor control calibration, the model-based calibration workflow can help motor control engineers achieve optimal torque and field-weakening control for PMSMs.

PMSM Characterization and Calibration: Challenges and Requirements

PMSMs stand out from other types of e-motors because of their high efficiency and torque density. This is because the permanent magnets inside the machine can generate substantial air gap magnetic flux without external excitation. This special trait makes a PMSM an excellent candidate for both non-traction and traction motor drive applications.

大多数非吸引PMSM应用程序仅要求机器在其控制方案相对简单的恒定扭矩区域中操作。牵引PMSM控制，除了快速动态响应外，还需要准确的扭矩输出和恒定的恒定功率范围操作。为了实现这些控制目标，尤其是在电动或混合动力汽车中，牵引力PMSM必须在field-weakeningregion, where tradeoffs need to be made between torque, speed, and efficiency.

A huge part of designing a high-performance field-weakening control algorithm is calibrating the field-weakening control lookup tables. Before generating the table data, PMSM characterization tests often need to be performed either using a dyno setup or through an FEA tool like ANSYS Maxwell or JSOL JMAG.

After PMSM characterization testing, flux linkage tables and measured torque at different current and speed operating points can be obtained. Here we need to distinguish PMSMcharacterizationfrom校准. PMSM characterization involves performing a series of tests either on a dyno or using an FEA tool, with the goal of extracting important machine information, such as flux linkage and torque. PMSM control calibration involves calculating controller lookup tables that will generate maximum torque or optimal efficiency at different operating points. The control calibration process usually happens after PMSM characterization. Both processes are required for high-performance PMSM control design.

The Model-Based Calibration Workflow

When applied to PMSM control calibration, the model-based calibration workflow usually involves four steps (Figure 1):

1. 设计实验以进行表征。
2. 精准医疗process the PMSM characterization dataset.
3. Fit PMSM characterization models.
4. Optimize PMSM controller lookup table data.

1.设计实验以进行表征

物理功能上的完整阶乘表征是浪费的，因为它增加了实验时间，成本和维护。在基于模型的校准中，提出了统计间隔的工作点作为测试点。无论是在物理点还是在FEA环境中进行的实验，当前ID和智商的生成的测试点将作为控制命令给出，PMSM速度将由Dyno Machine调节或在FEA工具中设置。使用虚拟Dyno需要详细的PMSM FEA模型。但是，一旦创建了模型，就可以通过更全面的操作点进行测试，而不会产生额外的成本开销。

2.精准医疗processing the PMSM Characterization Dataset

在PMSM表征期间，扭矩和DQ轴通量链接数据直接在DYNO上测量，要么是从ID，IQ和速度的每个操作点源自FEA工具的。表征后，数据集通过扭矩轮廓和速度步骤重新排列，并且每个变量（例如，扭矩）以单列格式存储，然后将其导入基于模型的校准Toolbox™（图2）。如有必要，可以进行其他分析以删除外围数据。由于噪声和测量误差，异常值在物理测试中很常见。

3. Fitting PMSM Characterization Models

模型拟合是一种重要的基于模型的一部分校准workflow. (Note that the models referred to in this article are not electric motor or controller models; they arestatisticalmodels in which functions such as Gaussian process regression or radial basis function represent the relationship between variables in the imported dataset.) Specifically, two sets of models are created: iq as a function of id and torque, and voltage margin as a function of id and torque. Each is modeled at a common set of motor speeds. These speeds are used as breakpoints for the final controller lookup table. Figure 3 shows models grouped by two speed operating points:1000 rpm and 5000 rpm.

Both iq and voltage margin models vary based on speed operating points, as speed can directly affect the boundary of operation. It is impossible to exactly represent the operation boundary from a finite number of characterized data points. The actual operation boundaries for the PMSM under calibration are often imposed by external limiting factors such as the thermal limit of the drive system and the DC bus voltage level of the inverter.

In model-based calibration, the operation boundaries of fitted models are approximated by the convex hulls enclosing the dataset, as depicted by the edges of colored surfaces in Figure 3. These boundaries are important for step 4 of the calibration workflow, since they are used as constraints for the optimization problem.

4. Optimizing PMSM Controller Lookup Table Data

在基于模型的校准中，使用CAGE（基于模型的校准工具箱中的校准生成工具）执行运行优化例程和生成最终校准查找表的过程。在CAGE中，步骤3的模型用于目标函数模型或作为约束。例如，电压边距模型在不同速度下用作电压约束，以确保整体调制电压不超过直流总线电压施加的最大值。除了约束外，还可以根据这些拟合模型设置单个或多个目标。

A common objective for optimized field-weakening control is to maximize the PMSM’s efficiency while reaching the required torque. This is achieved by setting up torque-per-ampere (TPA) as the target to maximize and simultaneously enforce current and voltage constraints. The result is an optimized operation region that covers maximum torque per ampere (MTPA), maximum torque per volt (MPTV), and operation points in between.

图4显示了如何通过CAGE过程获得查找表中的优化操作点。浅蓝色和黄色阴影区域在特定的速度工作点上表示相应的电流和电压约束，绿色区域是满足这两个约束的可行区域。图中的扭矩轮廓表示特定的扭矩需求。为了实现PMSM的最大效率控制，沿着可行区域内的扭矩轮廓中的笼子搜索中的优化器找到了一个最大化TPA目标的点。结果，在图4所示的示例中，将选择A作为最佳。图4中的其他优化查找表点由笼中的同一例程计算出来。

You can accelerate the optimization routine described above by running it with Parallel Computing Toolbox™. With parallel computing enabled, the entire workflow converges in under 10 minutes on a typical four-core PC.

After running the optimization routine, you can fill in the final calibration lookup tables by the optimization results through various filling methods, such as interpolation or clipping. In theory, you can choose any torque and speed breakpoints for the lookup table, but a common choice of breakpoints for torque is the percentage of maximum torque. Choosing torque percentage of maximum achievable torque rather than absolute torque values ensures that the entire lookup table can be filled with valid optimization results (Figure 5).

Extending the Workflow

本文介绍了基于模型的基本校准工作流程，用于生成具有现场效果的最佳PMSM扭矩控制查找表。文章中描述的示例是基于磁场控制表，其中扭矩，速度和可能的直流总线电压是输入。

For an algorithm that uses torque command and maximum flux linkage as inputs to its lookup tables, the workflow is the same, only with slightly different function models. In addition, if your application requires a more accurate and refined calibration, you can consider more variables, such as inverter voltage drop, core loss, AC resistance, and windage or friction, during the model fitting and CAGE process.