control.step_info

control.step_info(sysdata, T=None, T_num=None, yfinal=None, params=None, SettlingTimeThreshold=0.02, RiseTimeLimits=(0.1, 0.9))[source]

Step response characteristics (Rise time, Settling Time, Peak and others).

Parameters

  • sysdata (StateSpace or TransferFunction or array_like) – The system data. Either LTI system to simulate (StateSpace, TransferFunction), or a time series of step response data.

  • T (array_like or float, optional) – Time vector, or simulation time duration if a number (time vector is autocomputed if not given, see step_response() for more detail). Required, if sysdata is a time series of response data.

  • T_num (int, optional) – Number of time steps to use in simulation if T is not provided as an array; autocomputed if not given; ignored if sysdata is a discrete-time system or a time series or response data.

  • yfinal (scalar or array_like, optional) – Steady-state response. If not given, sysdata.dcgain() is used for systems to simulate and the last value of the the response data is used for a given time series of response data. Scalar for SISO, (noutputs, ninputs) array_like for MIMO systems.

  • params (dict, optional) – If system is a nonlinear I/O system, set parameter values.

  • SettlingTimeThreshold (float, optional) – Defines the error to compute settling time (default = 0.02)

  • RiseTimeLimits (tuple (lower_threshold, upper_theshold)) – Defines the lower and upper threshold for RiseTime computation

Returns

S – If sysdata corresponds to a SISO system, S is a dictionary containing:

RiseTime:

Time from 10% to 90% of the steady-state value.

SettlingTime:

Time to enter inside a default error of 2%

SettlingMin:

Minimum value after RiseTime

SettlingMax:

Maximum value after RiseTime

Overshoot:

Percentage of the Peak relative to steady value

Undershoot:

Percentage of undershoot

Peak:

Absolute peak value

PeakTime:

time of the Peak

SteadyStateValue:

Steady-state value

If sysdata corresponds to a MIMO system, S is a 2D list of dicts. To get the step response characteristics from the j-th input to the i-th output, access S[i][j]

Return type

dict or list of list of dict

See also

step, lsim, initial, impulse

Examples

>>> sys = ct.TransferFunction([-1, 1], [1, 1, 1])
>>> S = ct.step_info(sys)
>>> for k in S:
...     print(f"{k}: {S[k]:3.4}")
...
RiseTime: 1.256
SettlingTime: 9.071
SettlingMin: 0.9011
SettlingMax: 1.208
Overshoot: 20.85
Undershoot: 27.88
Peak: 1.208
PeakTime: 4.187
SteadyStateValue: 1.0

MIMO System: Simulate until a final time of 10. Get the step response characteristics for the second input and specify a 5% error until the signal is considered settled.

>>> from math import sqrt
>>> sys = ct.StateSpace([[-1., -1.],
...                   [1., 0.]],
...                  [[-1./sqrt(2.), 1./sqrt(2.)],
...                   [0, 0]],
...                  [[sqrt(2.), -sqrt(2.)]],
...                  [[0, 0]])
>>> S = ct.step_info(sys, T=10., SettlingTimeThreshold=0.05)
>>> for k, v in S[0][1].items():
...     print(f"{k}: {float(v):3.4}")
RiseTime: 1.212
SettlingTime: 6.061
SettlingMin: -1.209
SettlingMax: -0.9184
Overshoot: 20.87
Undershoot: 28.02
Peak: 1.209
PeakTime: 4.242
SteadyStateValue: -1.0