types.control_classical.PolePlacementResult

types.control_classical.PolePlacementResult()

Pole placement (eigenvalue assignment) result.

Design state feedback gain K such that closed-loop system (A - BK) has desired eigenvalues (poles).

Fields

gain : GainMatrix State feedback gain K (nu, nx) desired_poles : np.ndarray Desired closed-loop eigenvalues achieved_poles : np.ndarray Actual achieved eigenvalues of (A - BK) is_controllable : bool System must be controllable for arbitrary placement

Examples

>>> A = np.array([[0, 1], [-2, -3]])
>>> B = np.array([[0], [1]])
>>>
>>> # Place poles for faster response
>>> desired_poles = np.array([-5, -6])
>>> result: PolePlacementResult = pole_placement(A, B, desired_poles)
>>>
>>> K = result['gain']
>>> print(result['is_controllable'])  # True
>>> print(np.allclose(result['achieved_poles'], result['desired_poles']))  # True
>>>
>>> # Verify
>>> A_cl = A - B @ K
>>> actual_poles = np.linalg.eigvals(A_cl)
>>> print(np.sort(actual_poles))  # [-6, -5]