Control System Synthesis¶

control.lqr(*args, **keywords)

The lqr() function computes the optimal state feedback controller that minimizes the quadratic cost

The function can be called with either 3, 4, or 5 arguments:

• lqr(sys, Q, R)
• lqr(sys, Q, R, N)
• lqr(A, B, Q, R)
• lqr(A, B, Q, R, N)
Parameters: A, B: 2-d array : Dynamics and input matrices sys: Lti (StateSpace or TransferFunction) : Linear I/O system Q, R: 2-d array : State and input weight matrices N: 2-d array, optional : Cross weight matrix K: 2-d array : State feedback gains S: 2-d array : Solution to Riccati equation E: 1-d array : Eigenvalues of the closed loop system

Examples

>>> K, S, E = lqr(sys, Q, R, [N])
>>> K, S, E = lqr(A, B, Q, R, [N])

control.place(A, B, p)

Place closed loop eigenvalues

Parameters: A : 2-d array Dynamics matrix B : 2-d array Input matrix p : 1-d list Desired eigenvalue locations K : 2-d array Gains such that A - B K has given eigenvalues

Examples

>>> A = [[-1, -1], [0, 1]]
>>> B = [[0], [1]]
>>> K = place(A, B, [-2, -5])