Add a script used to generate plots for blog entries

utils/svpwm_test_plot.py

@@ -0,0 +1,124 @@
+#!/usr/bin/python
+
+# Copyright 2024 mjbots Robotic Systems, LLC.  [email protected]
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import argparse
+import math
+import matplotlib.pyplot as plt
+import numpy
+import sys
+
+
+SQRT3_4 = math.sqrt(3 / 4)
+
+
+class SinCos:
+    def __init__(self, theta):
+        self.s = math.sin(theta)
+        self.c = math.cos(theta)
+
+
+class InverseDqTransform:
+    def __init__(self, a, b, c):
+        self.a = a
+        self.b = b
+        self.c = c
+
+    @staticmethod
+    def from_dq(sc, d, q):
+        a = sc.c * d - sc.s * q
+        b = (SQRT3_4 * sc.s - 0.5 * sc.c) * d - (-SQRT3_4 * sc.c - 0.5 * sc.s) * q
+        c = (-SQRT3_4 * sc.s - 0.5 * sc.c) * d - (SQRT3_4 * sc.c - 0.5 * sc.s) * q
+
+        return InverseDqTransform(a, b, c)
+
+    @staticmethod
+    def from_values(a, b, c):
+        return InverseDqTransform(a, b, c)
+
+
+def main():
+    parser = argparse.ArgumentParser()
+
+    parser.add_argument('--vq', type=float, default=0)
+    parser.add_argument('--vd', type=float, default=0)
+    parser.add_argument('--title', type=str, default=None)
+    parser.add_argument('--offset-type', type=str, default=None)
+
+    args = parser.parse_args()
+
+    if args.offset_type is None:
+        args.offset_type = 'spwm'
+
+    limit = 2 * math.pi * 2
+    thetas = list(numpy.arange(0, limit, math.pi / 200))
+
+    def apply_pwm(theta):
+        if args.offset_type == 'spwm':
+            # Sinusoidal PWM
+            x = InverseDqTransform.from_dq(SinCos(theta), args.vd, args.vq)
+            return InverseDqTransform.from_values(x.a + 0.5,
+                                                  x.b + 0.5,
+                                                  x.c + 0.5)
+        elif args.offset_type == 'balanced':
+            # This is the approach used by moteus prior to SVPWM,
+            # which works out to be exactly the same as SPWM.
+            x = InverseDqTransform.from_dq(SinCos(theta), args.vd, args.vq)
+            center = (x.a + x.b + x.c) / 3
+            return InverseDqTransform.from_values(x.a + 0.5 - center,
+                                                  x.b + 0.5 - center,
+                                                  x.c + 0.5 - center)
+        elif args.offset_type == 'minmax':
+            # The "minmax" approach used to implement SVPWM in moteus.
+            x = InverseDqTransform.from_dq(SinCos(theta), args.vd, args.vq)
+            low = min(x.a, x.b, x.c)
+            high = max(x.a, x.b, x.c)
+            mid = 0.5 * (low + high)
+            return InverseDqTransform.from_values(x.a + 0.5 - mid,
+                                                  x.b + 0.5 - mid,
+                                                  x.c + 0.5 - mid)
+
+        raise RuntimeError(f'unknown offset type: {args.offset_type}')
+
+
+    phases = [apply_pwm(t) for t in thetas]
+    plt.plot(thetas, [x.a for x in phases], lw=3, label='a')
+    plt.plot(thetas, [x.b for x in phases], lw=3, label='b')
+    plt.plot(thetas, [x.c for x in phases], lw=3, label='c')
+
+    def motor_power(idt):
+        return (idt.a - idt.b) ** 2 + (idt.a - idt.c) ** 2 + (idt.b - idt.c) ** 2
+
+    plt.plot(thetas, [motor_power(x) for x in phases], lw=2, label='normalized power')
+
+    plt.xlabel('Electrical Angle (radians)')
+    plt.ylabel('Phase PWM')
+
+    plt.xticks(numpy.arange(0, limit, math.pi/4))
+    plt.yticks([0, 0.25, 0.5, 0.75, 1.0])
+
+    plt.legend(loc='upper right')
+    plt.grid()
+
+    if args.title is not None:
+        plt.title(args.title)
+
+    plt.show()
+
+
+
+
+if __name__ == '__main__':
+    main()