control.model_reduction

control.model_reduction(sys, elim_states=None, method='matchdc', elim_inputs=None, elim_outputs=None, keep_states=None, keep_inputs=None, keep_outputs=None, warn_unstable=True)[source]

Model reduction by input, output, or state elimination.

This function produces a reduced-order model of a system by eliminating specified inputs, outputs, and/or states from the original system. The specific states, inputs, or outputs that are eliminated can be specified by either listing the states, inputs, or outputs to be eliminated or those to be kept.

Two methods of state reduction are possible: ‘truncate’ removes the states marked for elimination, while ‘matchdc’ replaces the eliminated states with their equilibrium values (thereby keeping the input/output gain unchanged at zero frequency [“DC”]).

Parameters

sysStateSpace: Original system to reduce.
elim_inputs, elim_outputs, elim_statesarray of int or str, optional: Vector of inputs, outputs, or states to eliminate. Can be specified either as an offset into the appropriate vector or as a signal name.
keep_inputs, keep_outputs, keep_statesarray, optional: Vector of inputs, outputs, or states to keep. Can be specified either as an offset into the appropriate vector or as a signal name.
methodstring: Method of removing states: either ‘truncate’ or ‘matchdc’ (default).
warn_unstablebool, option: If False, don’t warn if system is unstable.

Returns

rsysStateSpace: Reduced order model.

Raises

ValueError: If method is not either ‘matchdc’ or ‘truncate’.
NotImplementedError: If the ‘matchdc’ method is used for a discrete-time system.

Warns

UserWarning: If eigenvalues of sys.A are not all stable.

See also

balanced_reduction, minimal_realization

Notes

The model_reduction function issues a warning if the system has unstable eigenvalues, since in those situations the stability of the reduced order model may be different than the stability of the full model. No other checking is done, so users must to be careful not to render a system unobservable or unreachable.

States, inputs, and outputs can be specified using integer offsets or using signal names. Slices can also be specified, but must use the Python slice function.

Examples

>>> G = ct.rss(4)
>>> Gr = ct.model_reduction(G, [0, 2], method='matchdc')
>>> Gr.nstates
2