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control.find_operating_point — Python Control Systems Library 0.10.2 documentation

control.find_operating_point(sys, initial_state=0.0, inputs=None, outputs=None, t=0, params=None, input_indices=None, output_indices=None, state_indices=None, deriv_indices=None, derivs=None, root_method=None, root_kwargs=None, return_outputs=None, return_result=None, **kwargs)[source]

Find an operating point for an input/output system.

An operating point for a nonlinear system is a state and input around which a nonlinear system operates. This point is most commonly an equilibrium point for the system, but in some cases a non-equilibrium operating point can be used.

This function attempts to find an operating point given a specification for the desired inputs, outputs, states, or state updates of the system.

In its simplest form, find_operating_point finds an equilibrium point given either the desired input or desired output:

xeq, ueq = find_operating_point(sys, x0, u0)
xeq, ueq = find_operating_point(sys, x0, u0, y0)

The first form finds an equilibrium point for a given input u0 based on an initial guess x0. The second form fixes the desired output values and uses x0 and u0 as an initial guess to find the equilibrium point. If no equilibrium point can be found, the function returns the operating point that minimizes the state update (state derivative for continuous-time systems, state difference for discrete-time systems).

More complex operating points can be found by specifying which states, inputs, or outputs should be used in computing the operating point, as well as desired values of the states, inputs, outputs, or state updates.

Parameters:

sysNonlinearIOSystem

I/O system for which the operating point is sought.

initial_state (or x0)list of initial state values

Initial guess for the value of the state near the operating point.

inputs (or u0)list of input values, optional

If y0 is not specified, sets the value of the input. If y0 is given, provides an initial guess for the value of the input. Can be omitted if the system does not have any inputs.

outputs (or y0)list of output values, optional

If specified, sets the desired values of the outputs at the operating point.

tfloat, optional

Evaluation time, for time-varying systems.

paramsdict, optional

Parameter values for the system. Passed to the evaluation functions for the system as default values, overriding internal defaults.

input_indices (or iu)list of input indices, optional

If specified, only the inputs with the given indices will be fixed at the specified values in solving for an operating point. All other inputs will be varied. Input indices can be listed in any order.

output_indices (or iy)list of output indices, optional

If specified, only the outputs with the given indices will be fixed at the specified values in solving for an operating point. All other outputs will be varied. Output indices can be listed in any order.

state_indices (or ix)list of state indices, optional

If specified, states with the given indices will be fixed at the specified values in solving for an operating point. All other states will be varied. State indices can be listed in any order.

derivs (or dx0)list of update values, optional

If specified, the value of update map must match the listed value instead of the default value for an equilibrium point.

deriv_indices (or idx)list of state indices, optional

If specified, state updates with the given indices will have their update maps fixed at the values given in dx0. All other update values will be ignored in solving for an operating point. State indices can be listed in any order. By default, all updates will be fixed at dx0 in searching for an operating point.

root_methodstr, optional

Method to find the operating point. If specified, this parameter is passed to the scipy.optimize.root function.

root_kwargsdict, optional

Additional keyword arguments to pass scipy.optimize.root.

return_outputsbool, optional

If True, return the value of outputs at the operating point.

return_resultbool, optional

If True, return the result option from the scipy.optimize.root function used to compute the operating point.

Returns:

op_pointOperatingPoint

The solution represented as an OperatingPoint object. The main attributes are states and inputs, which represent the state and input arrays at the operating point. If accessed as a tuple, returns states, inputs, and optionally outputs and result based on the return_outputs and return_result parameters. See OperatingPoint for a description of other attributes.

op_point.statesarray

State vector at the operating point.

op_point.inputsarray

Input vector at the operating point.

op_point.outputsarray, optional

Output vector at the operating point.

Notes

For continuous-time systems, equilibrium points are defined as points for which the right hand side of the differential equation is zero: . For discrete-time systems, equilibrium points are defined as points for which the right hand side of the difference equation returns the current state: .

Operating points are found using the scipy.optimize.root function, which will attempt to find states and inputs that satisfy the specified constraints. If no solution is found and return_result is False, the returned state and input for the operating point will be None. If return_result is True, then the return values from scipy.optimize.root will be returned (but may not be valid). If root_method is set to ‘lm’, then the least squares solution (in the free variables) will be returned.

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