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avoid log(0) in automatic timevector calculation#441

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83 changes: 41 additions & 42 deletionscontrol/timeresp.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -61,7 +61,7 @@
Initial Author: Eike Welk
Date: 12 May 2011

Modified: Sawyer B. Fuller (minster@uw.edu) to add discrete-time
Modified: Sawyer B. Fuller (minster@uw.edu) to add discrete-time
capability and better automatic time vector creation
Date: June 2020

Expand DownExpand Up@@ -463,14 +463,14 @@ def step_response(sys, T=None, X0=0., input=None, output=None, T_num=None,
LTI system to simulate

T: array-like or number, optional
Time vector, or simulation time duration if a number. If T is not
provided, an attempt is made to create it automatically from the
dynamics of sys. If sys is continuous-time, the time increment dt
is chosen small enough to show the fastest mode, and the simulation
time period tfinal long enough to show the slowest mode, excluding
Time vector, or simulation time duration if a number. If T is not
provided, an attempt is made to create it automatically from the
dynamics of sys. If sys is continuous-time, the time increment dt
is chosen small enough to show the fastest mode, and the simulation
time period tfinal long enough to show the slowest mode, excluding
poles at the origin. If this results in too many time steps (>5000),
dt is reduced. If sys is discrete-time, only tfinal is computed, and
tfinal is reduced if it requires too many simulation steps.
dt is reduced. If sys is discrete-time, only tfinal is computed, and
tfinal is reduced if it requires too many simulation steps.

X0: array-like or number, optional
Initial condition (default = 0)
Expand All@@ -483,10 +483,10 @@ def step_response(sys, T=None, X0=0., input=None, output=None, T_num=None,
output: int
Index of the output that will be used in this simulation. Set to None
to not trim outputs

T_num: number, optional
Number of time steps to use in simulation if T is not provided as an
array (autocomputed if not given); ignored if sys is discrete-time.
Number of time steps to use in simulation if T is not provided as an
array (autocomputed if not given); ignored if sys is discrete-time.

transpose: bool
If True, transpose all input and output arrays (for backward
Expand DownExpand Up@@ -550,12 +550,12 @@ def step_info(sys, T=None, T_num=None, SettlingTimeThreshold=0.02,
LTI system to simulate

T: array-like or number, optional
Time vector, or simulation time duration if a number (time vector is
Time vector, or simulation time duration if a number (time vector is
autocomputed if not given, see :func:`step_response` for more detail)

T_num: number, optional
Number of time steps to use in simulation if T is not provided as an
array (autocomputed if not given); ignored if sys is discrete-time.
Number of time steps to use in simulation if T is not provided as an
array (autocomputed if not given); ignored if sys is discrete-time.

SettlingTimeThreshold: float value, optional
Defines the error to compute settling time (default = 0.02)
Expand DownExpand Up@@ -588,7 +588,7 @@ def step_info(sys, T=None, T_num=None, SettlingTimeThreshold=0.02,
sys = _get_ss_simo(sys)
if T is None or np.asarray(T).size == 1:
T = _default_time_vector(sys, N=T_num, tfinal=T)

T, yout = step_response(sys, T)

# Steady state value
Expand DownExpand Up@@ -640,7 +640,7 @@ def initial_response(sys, T=None, X0=0., input=0, output=None, T_num=None,
LTI system to simulate

T: array-like or number, optional
Time vector, or simulation time duration if a number (time vector is
Time vector, or simulation time duration if a number (time vector is
autocomputed if not given; see :func:`step_response` for more detail)

X0: array-like or number, optional
Expand All@@ -655,10 +655,10 @@ def initial_response(sys, T=None, X0=0., input=0, output=None, T_num=None,
output: int
Index of the output that will be used in this simulation. Set to None
to not trim outputs

T_num: number, optional
Number of time steps to use in simulation if T is not provided as an
array (autocomputed if not given); ignored if sys is discrete-time.
Number of time steps to use in simulation if T is not provided as an
array (autocomputed if not given); ignored if sys is discrete-time.

transpose: bool
If True, transpose all input and output arrays (for backward
Expand DownExpand Up@@ -730,7 +730,7 @@ def impulse_response(sys, T=None, X0=0., input=0, output=None, T_num=None,
LTI system to simulate

T: array-like or number, optional
Time vector, or simulation time duration if a number (time vector is
Time vector, or simulation time duration if a number (time vector is
autocomputed if not given; see :func:`step_response` for more detail)

X0: array-like or number, optional
Expand All@@ -746,8 +746,8 @@ def impulse_response(sys, T=None, X0=0., input=0, output=None, T_num=None,
to not trim outputs

T_num: number, optional
Number of time steps to use in simulation if T is not provided as an
array (autocomputed if not given); ignored if sys is discrete-time.
Number of time steps to use in simulation if T is not provided as an
array (autocomputed if not given); ignored if sys is discrete-time.

transpose: bool
If True, transpose all input and output arrays (for backward
Expand DownExpand Up@@ -830,56 +830,55 @@ def _ideal_tfinal_and_dt(sys):
constant = 7.0
tolerance = 1e-10
A = ssdata(sys)[0]
if A.shape == (0,0):
if A.shape == (0,0):
# no dynamics
tfinal = constant * 1.0
tfinal = constant * 1.0
dt = sys.dt if isdtime(sys, strict=True) else 1.0
else:
poles = sp.linalg.eigvals(A)
if isdtime(sys, strict=True):
poles = np.log(poles)/sys.dt # z-poles to s-plane using s=(lnz)/dt

# calculate ideal dt
if isdtime(sys, strict=True):
# z-poles to s-plane using s=(lnz)/dt, no ln(0)
poles = np.log(poles[abs(poles) > 0])/sys.dt
dt = sys.dt
else:
fastest_natural_frequency = max(abs(poles))
dt = 1/constant / fastest_natural_frequency

# calculate ideal tfinal
poles = poles[abs(poles.real) > tolerance] # ignore poles near im axis
if poles.size == 0:
if poles.size == 0:
slowest_decay_rate = 1.0
else:
slowest_decay_rate = min(abs(poles.real))
tfinal = constant / slowest_decay_rate
tfinal = constant / slowest_decay_rate

return tfinal, dt

# test below: ct with pole at the origin is 7 seconds, ct with pole at .5 is 14 s long,
# test below: ct with pole at the origin is 7 seconds, ct with pole at .5 is 14 s long,
def _default_time_vector(sys, N=None, tfinal=None):
"""Returns a time vector suitable for observing the response of the
both the slowest poles and fastest resonant modes. if system is
"""Returns a time vector suitable for observing the response of the
both the slowest poles and fastest resonant modes. if system is
discrete-time, N is ignored """

N_max = 5000
N_min_ct = 100
N_min_dt = 7 # more common to see just a few samples in discrete-time

ideal_tfinal, ideal_dt = _ideal_tfinal_and_dt(sys)

if isdtime(sys, strict=True):
if tfinal is None:
if tfinal is None:
# for discrete time, change from ideal_tfinal if N too large/small
N = int(np.clip(ideal_tfinal/sys.dt, N_min_dt, N_max))# [N_min, N_max]
tfinal = sys.dt * N
else:
else:
N = int(tfinal/sys.dt)
else:
if tfinal is None:
else:
if tfinal is None:
# for continuous time, simulate to ideal_tfinal but limit N
tfinal = ideal_tfinal
if N is None:
if N is None:
N = int(np.clip(tfinal/ideal_dt, N_min_ct, N_max)) # N<-[N_min, N_max]

return np.linspace(0, tfinal, N, endpoint=False)
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