diff --git a/control/margins.py b/control/margins.py
index 20da2a879..fc2a20d7c 100644
--- a/control/margins.py
+++ b/control/margins.py
@@ -156,13 +156,14 @@ def _poly_z_real_crossing(num, den, num_inv_zp, den_inv_zq, p_q, dt, epsw):
return z, w
-def _poly_z_mag1_crossing(num, den, num_inv, den_inv, p_q, dt, epsw):
+def _poly_z_mag1_crossing(num, den, num_inv_zp, den_inv_zq, p_q, dt, epsw):
# |H(z)| = 1, H(z)*H(1/z)=1, num(z)*num(1/z) == den(z)*den(1/z)
- p1 = np.polymul(num, num_inv)
- p2 = np.polymul(den, den_inv)
+ p1 = np.polymul(num, num_inv_zp)
+ p2 = np.polymul(den, den_inv_zq)
if p_q < 0:
+ # * z**(-p_q)
x = [1] + [0] * (-p_q)
- p2 = np.polymul(p2, x)
+ p1 = np.polymul(p1, x)
z = np.roots(np.polysub(p1, p2))
eps = np.finfo(float).eps**(1 / len(p2))
z, w = _z_filter(z, dt, eps)
@@ -171,7 +172,7 @@ def _poly_z_mag1_crossing(num, den, num_inv, den_inv, p_q, dt, epsw):
return z, w
-def _poly_z_wstab(num, den, num_inv, den_inv, p_q, dt, epsw):
+def _poly_z_wstab(num, den, num_inv_zp, den_inv_zq, p_q, dt, epsw):
# Stability margin: Minimum distance to -1
# TODO: Find a way to solve for z or omega analytically with given
diff --git a/control/tests/margin_test.py b/control/tests/margin_test.py
index 4965bbe89..fbd79c60b 100644
--- a/control/tests/margin_test.py
+++ b/control/tests/margin_test.py
@@ -338,13 +338,19 @@ def test_zmore_stability_margins(tsys_zmore):
'cnum, cden, dt,'
'ref,'
'rtol',
- [([2], [1, 3, 2, 0], 1e-2, # gh-465
- (2.9558, 32.8170, 0.43584, 1.4037, 0.74953, 0.97079),
- 0.1 # very crude tolerance, because the gradients are not great
- ),
- ([2], [1, 3, 3, 1], .1, # 2/(s+1)**3
- [3.4927, 69.9996, 0.5763, 1.6283, 0.7631, 1.2019],
- 1e-3)])
+ [( # gh-465
+ [2], [1, 3, 2, 0], 1e-2,
+ [2.9558, 32.390, 0.43584, 1.4037, 0.74951, 0.97079],
+ 2e-3), # the gradient of the function reduces numerical precision
+ ( # 2/(s+1)**3
+ [2], [1, 3, 3, 1], .1,
+ [3.4927, 65.4212, 0.5763, 1.6283, 0.76625, 1.2019],
+ 1e-4),
+ ( # gh-523
+ [1.1 * 4 * np.pi**2], [1, 2 * 0.2 * 2 * np.pi, 4 * np.pi**2], .05,
+ [2.3842, 18.161, 0.26953, 11.712, 8.7478, 9.1504],
+ 1e-4),
+ ])
def test_stability_margins_discrete(cnum, cden, dt, ref, rtol):
"""Test stability_margins with discrete TF input"""
tf = TransferFunction(cnum, cden).sample(dt)
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