control.step_info

control.step_info(sysdata, timepts=None, timepts_num=None, final_output=None, params=None, SettlingTimeThreshold=0.02, RiseTimeLimits=(0.1, 0.9), **kwargs)[source]

Step response characteristics (rise time, settling time, etc).

Parameters
sysdataStateSpace or TransferFunction or array_like

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

timepts (or T)array_like or float, optional

Time vector, or simulation time duration if a number (time vector is auto-computed if not given, see step_response for more detail). Required, if sysdata is a time series of response data.

timepts_num (or T_num)int, optional

Number of time steps to use in simulation if T is not provided as an array; auto-computed if not given; ignored if sysdata is a discrete-time system or a time series or response data.

final_output (or 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.

paramsdict, optional

If system is a nonlinear I/O system, set parameter values.

SettlingTimeThresholdfloat, optional

Defines the error to compute settling time (default = 0.02).

RiseTimeLimitstuple (lower_threshold, upper_threshold)

Defines the lower and upper threshold for RiseTime computation.

Returns
Sdict or list of list of dict

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 that the first peak value is obtained.

  • ‘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 jth input to the ith output, access S[i][j].

See also

step_response, forced_response, initial_response, impulse_response

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