control.iosys.LinearIOSystem¶

class control.iosys.LinearIOSystem(linsys, inputs=None, outputs=None, states=None, name=None)¶

Input/output representation of a linear (state space) system.

This class is used to implementat a system that is a linear state space system (defined by the StateSpace system object).

__init__(linsys, inputs=None, outputs=None, states=None, name=None)¶

Create an I/O system from a state space linear system.

Converts a StateSpace system into an InputOutputSystem with the same inputs, outputs, and states. The new system can be a continuous or discrete time system

Parameters

linsys (StateSpace) – LTI StateSpace system to be converted
inputs (int, list of str or None, optional) – Description of the system inputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form s[i] (where s is one of u, y, or x). If this parameter is not given or given as None, the relevant quantity will be determined when possible based on other information provided to functions using the system.
outputs (int, list of str or None, optional) – Description of the system outputs. Same format as inputs.
states (int, list of str, or None, optional) – Description of the system states. Same format as inputs.
dt (None, True or float, optional) – System timebase. None (default) indicates continuous time, True indicates discrete time with undefined sampling time, positive number is discrete time with specified sampling time.
params (dict, optional) – Parameter values for the systems. Passed to the evaluation functions for the system as default values, overriding internal defaults.
name (string, optional) – System name (used for specifying signals). If unspecified, a generic name <sys[id]> is generated with a unique integer id.

Returns

iosys – Linear system represented as an input/output system

Return type

LinearIOSystem

Methods

`__init__`(linsys[, inputs, outputs, states, name])	Create an I/O system from a state space linear system.
`append`(other)	Append a second model to the present model.
`copy`([newname])	Make a copy of an input/output system.
`damp`()	Natural frequency, damping ratio of system poles
`dcgain`()	Return the zero-frequency gain
`evalfr`(omega)	Evaluate a SS system’s transfer function at a single frequency.
`feedback`([other, sign, params])	Feedback interconnection between two input/output systems
`find_input`(name)	Find the index for an input given its name (None if not found)
`find_output`(name)	Find the index for an output given its name (None if not found)
`find_state`(name)	Find the index for a state given its name (None if not found)
`freqresp`(omega)	Evaluate the system’s transfer function at a list of frequencies
`horner`(s)	Evaluate the systems’s transfer function for a complex variable
`is_static_gain`()	True if and only if the system has no dynamics, that is, if A and B are zero.
`isctime`([strict])	Check to see if a system is a continuous-time system
`isdtime`([strict])	Check to see if a system is a discrete-time system
`issiso`()	Check to see if a system is single input, single output
`lft`(other[, nu, ny])	Return the Linear Fractional Transformation.
`linearize`(x0, u0[, t, params, eps])	Linearize an input/output system at a given state and input.
`minreal`([tol])	Calculate a minimal realization, removes unobservable and uncontrollable states
`name_or_default`([name])
`pole`()	Compute the poles of a state space system.
`returnScipySignalLTI`()	Return a list of a list of `scipy.signal.lti` objects.
`sample`(Ts[, method, alpha, prewarp_frequency])	Convert a continuous time system to discrete time
`set_inputs`(inputs[, prefix])	Set the number/names of the system inputs.
`set_outputs`(outputs[, prefix])	Set the number/names of the system outputs.
`set_states`(states[, prefix])	Set the number/names of the system states.
`zero`()	Compute the zeros of a state space system.

Attributes

idCounter

append(other)¶

Append a second model to the present model.

The second model is converted to state-space if necessary, inputs and outputs are appended and their order is preserved

copy(newname=None)¶: Make a copy of an input/output system.

damp()¶

Natural frequency, damping ratio of system poles

Returns

wn (array) – Natural frequencies for each system pole
zeta (array) – Damping ratio for each system pole
poles (array) – Array of system poles

dcgain()¶

Return the zero-frequency gain

The zero-frequency gain of a continuous-time state-space system is given by:

and of a discrete-time state-space system by:

Returns: gain – An array of shape (outputs,inputs); the array will either be the zero-frequency (or DC) gain, or, if the frequency response is singular, the array will be filled with np.nan.
Return type: ndarray

evalfr(omega)¶

Evaluate a SS system’s transfer function at a single frequency.

self._evalfr(omega) returns the value of the transfer function matrix with input value s = i * omega.

feedback(other=1, sign=- 1, params={})¶

Feedback interconnection between two input/output systems

Parameters

sys1 (InputOutputSystem) – The primary process.
sys2 (InputOutputSystem) – The feedback process (often a feedback controller).
sign (scalar, optional) – The sign of feedback. sign = -1 indicates negative feedback, and sign = 1 indicates positive feedback. sign is an optional argument; it assumes a value of -1 if not specified.

Returns

out

Return type

InputOutputSystem

Raises

ValueError – if the inputs, outputs, or timebases of the systems are incompatible.

find_input(name)¶: Find the index for an input given its name (None if not found)

find_output(name)¶: Find the index for an output given its name (None if not found)

find_state(name)¶: Find the index for a state given its name (None if not found)

freqresp(omega)¶

Evaluate the system’s transfer function at a list of frequencies

Reports the frequency response of the system,

G(j*omega) = mag*exp(j*phase)

for continuous time. For discrete time systems, the response is evaluated around the unit circle such that

G(exp(j*omega*dt)) = mag*exp(j*phase).

Parameters

omega (array_like) – A list of frequencies in radians/sec at which the system should be evaluated. The list can be either a python list or a numpy array and will be sorted before evaluation.

Returns

mag ((self.outputs, self.inputs, len(omega)) ndarray) – The magnitude (absolute value, not dB or log10) of the system frequency response.
phase ((self.outputs, self.inputs, len(omega)) ndarray) – The wrapped phase in radians of the system frequency response.
omega (ndarray) – The list of sorted frequencies at which the response was evaluated.

horner(s)¶

Evaluate the systems’s transfer function for a complex variable

Returns a matrix of values evaluated at complex variable s.

is_static_gain()¶: True if and only if the system has no dynamics, that is, if A and B are zero.

isctime(strict=False)¶

Check to see if a system is a continuous-time system

Parameters

sys (LTI system) – System to be checked
strict (bool, optional) – If strict is True, make sure that timebase is not None. Default is False.

isdtime(strict=False)¶

Check to see if a system is a discrete-time system

Parameters: strict (bool, optional) – If strict is True, make sure that timebase is not None. Default is False.

issiso()¶: Check to see if a system is single input, single output

lft(other, nu=- 1, ny=- 1)¶

Return the Linear Fractional Transformation.

A definition of the LFT operator can be found in Appendix A.7, page 512 in the 2nd Edition, Multivariable Feedback Control by Sigurd Skogestad.

An alternative definition can be found here: https://www.mathworks.com/help/control/ref/lft.html

Parameters

other (LTI) – The lower LTI system
ny (int, optional) – Dimension of (plant) measurement output.
nu (int, optional) – Dimension of (plant) control input.

linearize(x0, u0, t=0, params={}, eps=1e-06)¶

Linearize an input/output system at a given state and input.

Return the linearization of an input/output system at a given state and input value as a StateSpace system. See linearize() for complete documentation.

minreal(tol=0.0)¶: Calculate a minimal realization, removes unobservable and uncontrollable states

pole()¶: Compute the poles of a state space system.

returnScipySignalLTI()¶

Return a list of a list of scipy.signal.lti objects.

For instance,

>>> out = ssobject.returnScipySignalLTI()
>>> out[3][5]

is a scipy.signal.lti object corresponding to the transfer function from the 6th input to the 4th output.

sample(Ts, method='zoh', alpha=None, prewarp_frequency=None)¶

Convert a continuous time system to discrete time

Creates a discrete-time system from a continuous-time system by sampling. Multiple methods of conversion are supported.

Parameters

Ts (float) – Sampling period
method ({"gbt", "bilinear", "euler", "backward_diff", "zoh"}) –
Which method to use:
- gbt: generalized bilinear transformation
- bilinear: Tustin’s approximation (“gbt” with alpha=0.5)
- euler: Euler (or forward differencing) method (“gbt” with alpha=0)
- backward_diff: Backwards differencing (“gbt” with alpha=1.0)
- zoh: zero-order hold (default)
alpha (float within [0, 1]) – The generalized bilinear transformation weighting parameter, which should only be specified with method=”gbt”, and is ignored otherwise
prewarp_frequency (float within [0, infinity)) – The frequency [rad/s] at which to match with the input continuous- time system’s magnitude and phase (the gain=1 crossover frequency, for example). Should only be specified with method=’bilinear’ or ‘gbt’ with alpha=0.5 and ignored otherwise.

Returns

sysd – Discrete time system, with sampling rate Ts

Return type

StateSpace

Notes

Uses scipy.signal.cont2discrete()

Examples

>>> sys = StateSpace(0, 1, 1, 0)
>>> sysd = sys.sample(0.5, method='bilinear')

set_inputs(inputs, prefix='u')¶

Set the number/names of the system inputs.

Parameters

inputs (int, list of str, or None) – Description of the system inputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form u[i] (where the prefix u can be changed using the optional prefix parameter).
prefix (string, optional) – If inputs is an integer, create the names of the states using the given prefix (default = ‘u’). The names of the input will be of the form prefix[i].

set_outputs(outputs, prefix='y')¶

Set the number/names of the system outputs.

Parameters

outputs (int, list of str, or None) – Description of the system outputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form u[i] (where the prefix u can be changed using the optional prefix parameter).
prefix (string, optional) – If outputs is an integer, create the names of the states using the given prefix (default = ‘y’). The names of the input will be of the form prefix[i].

set_states(states, prefix='x')¶

Set the number/names of the system states.

Parameters

states (int, list of str, or None) – Description of the system states. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form u[i] (where the prefix u can be changed using the optional prefix parameter).
prefix (string, optional) – If states is an integer, create the names of the states using the given prefix (default = ‘x’). The names of the input will be of the form prefix[i].

zero()¶: Compute the zeros of a state space system.