control.flatsys.SystemTrajectory

class control.flatsys.SystemTrajectory(sys, basis, coeffs=[], flaglen=[], params=None)[source]

Bases: object

Trajectory for a differentially flat system.

The SystemTrajectory class is used to represent the trajectory of a (differentially flat) system. Used by the point_to_point and solve_flat_optimal functions to return a trajectory.

Parameters
sysFlatSystem

Flat system object associated with this trajectory.

basisBasisFamily

Family of basis vectors to use to represent the trajectory.

coeffslist of 1D arrays, optional

For each flat output, define the coefficients of the basis functions used to represent the trajectory. Defaults to an empty list.

flaglenlist of int, optional

For each flat output, the number of derivatives of the flat output used to define the trajectory. Defaults to an empty list.

paramsdict, optional

Parameter values used for the trajectory.

Methods

eval

Compute state and input for a trajectory at a list of times.

response

Compute trajectory of a system as a TimeResponseData object.
eval(tlist)[source]

Compute state and input for a trajectory at a list of times.

Evaluate the trajectory at a list of time points, returning the state and input vectors for the trajectory:

x, u = traj.eval(tlist)

Parameters
tlist1D array

List of times to evaluate the trajectory.

Returns
x2D array

For each state, the values of the state at the given times.

u2D array

For each input, the values of the input at the given times.

response(timepts, transpose=False, return_x=False, squeeze=None)[source]

Compute trajectory of a system as a TimeResponseData object.

Evaluate the trajectory at a list of time points, returning the state and input vectors for the trajectory:

response = traj.response(timepts) time, yd, ud = response.time, response.outputs, response.inputs

Parameters
timepts1D array

List of times to evaluate the trajectory.

transposebool, optional

If True, transpose all input and output arrays (for backward compatibility with MATLAB and scipy.signal.lsim). Default value is False.

return_xbool, optional

If True, return the state vector when assigning to a tuple (default = False). See forced_response for more details.

squeezebool, optional

By default, if a system is single-input, single-output (SISO) then the output response is returned as a 1D array (indexed by time). If squeeze = True, remove single-dimensional entries from the shape of the output even if the system is not SISO. If squeeze = False, keep the output as a 3D array (indexed by the output, input, and time) even if the system is SISO. The default value can be set using config.defaults['control.squeeze_time_response'].

Returns
responseTimeResponseData

Time response data object representing the input/output response. When accessed as a tuple, returns (time, outputs) or (time, outputs, states if return_x is True. If the input/output system signals are named, these names will be used as labels for the time response. If sys is a list of systems, returns a TimeResponseList object. Results can be plotted using the plot method. See TimeResponseData for more detailed information.

response.timearray

Time values of the output.

response.outputsarray

Response of the system. If the system is SISO and squeeze is not True, the array is 1D (indexed by time). If the system is not SISO or squeeze is False, the array is 2D (indexed by output and time).

response.statesarray

Time evolution of the state vector, represented as a 2D array indexed by state and time.

response.inputsarray

Input(s) to the system, indexed by input and time.