Control System Synthesis¶

control.lqr(*args, **keywords)¶

Linear quadratic regulator design

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

$J = \int_0^\infty x' Q x + u' R u + 2 x' N u$

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

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

Returns:

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

Returns:

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])