control.NonlinearIOSystem
- class control.NonlinearIOSystem(updfcn, outfcn=None, params=None, **kwargs)[source]
Bases:
InputOutputSystem
Nonlinear I/O system.
Creates an
InputOutputSystem
for a nonlinear system by specifying a state update function and an output function. The new system can be a continuous or discrete time system (Note: discrete-time systems are not yet supported by most functions.)- Parameters
updfcn (callable) –
Function returning the state update function
updfcn(t, x, u, params) -> array
where x is a 1-D array with shape (nstates,), u is a 1-D array with shape (ninputs,), t is a float representing the currrent time, and params is a dict containing the values of parameters used by the function.
outfcn (callable) –
Function returning the output at the given state
outfcn(t, x, u, params) -> array
where the arguments are the same as for upfcn.
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 (timebase, optional) –
The timebase for the system, used to specify whether the system is operating in continuous or discrete time. It can have the following values:
dt = 0: continuous time system (default)
dt > 0: discrete time system with sampling period ‘dt’
dt = True: discrete time with unspecified sampling period
dt = None: no timebase specified
name (string, optional) – System name (used for specifying signals). If unspecified, a generic name <sys[id]> is generated with a unique integer id.
params (dict, optional) – Parameter values for the systems. Passed to the evaluation functions for the system as default values, overriding internal defaults.
See also
InputOutputSystem
Input/output system class.
Notes
The
InputOuputSystem
class (and its subclasses) makes use of two special methods for implementing much of the work of the class:_rhs(t, x, u): compute the right hand side of the differential or difference equation for the system. If not specified, the system has no state.
_out(t, x, u): compute the output for the current state of the system. The default is to return the entire system state.
Methods
Make a copy of an input/output system
Compute the dynamics of a differential or difference equation.
Feedback interconnection between two input/output systems
Find the index for an input given its name (None if not found)
Return list of indices matching input spec (None if not found)
Find the index for an output given its name (None if not found)
Return list of indices matching output spec (None if not found)
Find the index for a state given its name (None if not found)
Return list of indices matching state spec (None if not found)
Check to see if a system is a continuous-time system.
Check to see if a system is a discrete-time system
Check to see if a system is single input, single output.
Linearize an input/output system at a given state and input.
Compute the output of the system
Set the number/names of the system inputs.
Set the number/names of the system outputs.
Set the number/names of the system states.
- __call__(u, params=None, squeeze=None)[source]
Evaluate a (static) nonlinearity at a given input value
If a nonlinear I/O system has no internal state, then evaluating the system at an input u gives the output y = F(u), determined by the output function.
- Parameters
params (dict, optional) – Parameter values for the system. Passed to the evaluation function for the system as default values, overriding internal defaults.
squeeze (bool, optional) – If True and if the system has a single output, return the system output as a 1D array rather than a 2D array. If False, return the system output as a 2D array even if the system is SISO. Default value set by config.defaults[‘control.squeeze_time_response’].
- copy(name=None, use_prefix_suffix=True)[source]
Make a copy of an input/output system
A copy of the system is made, with a new name. The name keyword can be used to specify a specific name for the system. If no name is given and use_prefix_suffix is True, the name is constructed by prepending config.defaults[‘iosys.duplicate_system_name_prefix’] and appending config.defaults[‘iosys.duplicate_system_name_suffix’]. Otherwise, a generic system name of the form sys[<id>] is used, where <id> is based on an internal counter.
- dynamics(t, x, u, params=None)[source]
Compute the dynamics of a differential or difference equation.
Given time t, input u and state x, returns the value of the right hand side of the dynamical system. If the system is continuous, returns the time derivative
dx/dt = f(t, x, u[, params])
where f is the system’s (possibly nonlinear) dynamics function. If the system is discrete-time, returns the next value of x:
x[t+dt] = f(t, x[t], u[t][, params])
where t is a scalar.
The inputs x and u must be of the correct length. The params argument is an optional dictionary of parameter values.
- Parameters
t (float) – the time at which to evaluate
x (array_like) – current state
u (array_like) – input
params (dict, optional) – system parameter values
- Returns
dx/dt or x[t+dt]
- Return type
ndarray
- feedback(other=1, sign=-1, params=None)[source]
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
- Raises
ValueError – if the inputs, outputs, or timebases of the systems are incompatible.
- isctime(strict=False)[source]
Check to see if a system is a continuous-time system.
- Parameters
sys (Named I/O 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)[source]
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.
- linearize(x0, u0, t=0, params=None, eps=1e-06, name=None, copy_names=False, **kwargs)[source]
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.
- ninputs
Number of system inputs.
- noutputs
Number of system outputs.
- nstates
Number of system states.
- output(t, x, u, params=None)[source]
Compute the output of the system
Given time t, input u and state x, returns the output of the system:
y = g(t, x, u[, params])
The inputs x and u must be of the correct length.
- Parameters
t (float) – the time at which to evaluate
x (array_like) – current state
u (array_like) – input
params (dict, optional) – system parameter values
- Returns
y
- Return type
ndarray
- set_inputs(inputs, prefix='u')[source]
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')[source]
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')[source]
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].