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Fix false positive algebraic loop in interconnect for MIMO feedthrough (#1257) #1258

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Fix false positive algebraic loop in interconnect for MIMO feedthrough (#1257) #1258

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10 changes: 7 additions & 3 deletions control/nlsys.py
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Original file line number Diff line number Diff line change
Expand Up @@ -951,10 +951,14 @@ def _compute_static_io(self, t, x, u):
ylist = np.zeros((noutputs + ninputs,))

# To allow for feedthrough terms, iterate multiple times to allow
# feedthrough elements to propagate. For n systems, we could need to
# cycle through n+1 times before reaching steady state
# feedthrough elements to propagate. For an interconnected system,
# an acyclic feedthrough path can traverse through multiple channels
# of the same subsystem in MIMO blocks. The maximum number of feedthrough
# propagation steps before reaching steady state (or confirming convergence)
# is therefore bounded by the number of internal inputs ninputs (or
# the number of subsystems).
# TODO (later): see if there is a more efficient way to compute
cycle_count = len(self.syslist) + 1
cycle_count = max(len(self.syslist), ninputs) + 1
while cycle_count > 0:
state_index, input_index, output_index = 0, 0, 0
for sys in self.syslist:
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49 changes: 49 additions & 0 deletions control/tests/interconnect_test.py
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Expand Up @@ -746,3 +746,52 @@ def test_parallel_interconnect():
np.testing.assert_allclose(sys_bd.B, sys_ic.B)
np.testing.assert_allclose(sys_bd.C, sys_ic.C)
np.testing.assert_allclose(sys_bd.D, sys_ic.D)


# Bug identified in issue #1257: MIMO feedthrough path visiting a subsystem multiple times
def test_interconnect_mimo_feedthrough_no_algebraic_loop():
# 2-input, 2-output plant with direct feedthrough only in g11
A = np.array([[-2.0, 0.0], [0.0, -3.0]])
B = np.array([[1.0, 0.0], [0.0, 1.0]])
C = np.array([[1.0, 0.0], [0.0, 1.0]])
D = np.array([[1.0, 0.0], [0.0, 0.0]])
plant = ct.ss(
A, B, C, D, inputs=['u[0]', 'u[1]'], outputs=['y[0]', 'y[1]'],
name='plant')

# PI controllers with D = 1
A_pi = np.array([[0.0]])
B_pi = np.array([[1.0]])
C_pi = np.array([[1.0]])
D_pi = np.array([[1.0]])
pi1 = ct.ss(A_pi, B_pi, C_pi, D_pi, inputs='e[0]', outputs='u[1]', name='pi1')
pi2 = ct.ss(A_pi, B_pi, C_pi, D_pi, inputs='e[1]', outputs='u[0]', name='pi2')

err = ct.summing_junction(
inputs=['r', '-y'], outputs='e', dimension=2, name='err')

# Without the fix, this raises RuntimeError: algebraic loop detected
sys = ct.interconnect(
[err, pi1, pi2, plant], inplist=['r'], outlist=['y'])

# Compare closed loop poles against ct.feedback
K_ss = ct.ss(
np.zeros((2, 2)),
np.eye(2),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]])
)
expected_poles = np.sort_complex(ct.feedback(plant, K_ss).poles())
np.testing.assert_allclose(
np.sort_complex(sys.poles()), expected_poles, rtol=1e-5)


def test_interconnect_algebraic_loop_detection():
# True algebraic loop: feedback through static feedthrough blocks
P = ct.ss([], [], [], [[1.0]], inputs='u', outputs='y', name='P')
sumj = ct.summing_junction(inputs=['r', 'y'], outputs='u', name='sumj')
with pytest.raises(RuntimeError, match='algebraic loop detected'):
ct.interconnect(
[sumj, P], connections=[['P.u', 'sumj.u'], ['sumj.y', 'P.y']],
inplist=['r'], outlist=['P.y'])

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