- control.lqr(A, B, Q, R[, N])¶
Linear quadratic regulator design
The lqr() function computes the optimal state feedback controller u = -K x that minimizes the quadratic cost
The function can be called with either 3, 4, or 5 arguments:
K, S, E = lqr(sys, Q, R)
K, S, E = lqr(sys, Q, R, N)
K, S, E = lqr(A, B, Q, R)
K, S, E = lqr(A, B, Q, R, N)
where sys is an LTI object, and A, B, Q, R, and N are 2D arrays or matrices of appropriate dimension.
A (2D array_like) – Dynamics and input matrices
B (2D array_like) – Dynamics and input matrices
sys (LTI StateSpace system) – Linear system
Q (2D array) – State and input weight matrices
R (2D array) – State and input weight matrices
N (2D array, optional) – Cross weight matrix
integral_action (ndarray, optional) – If this keyword is specified, the controller includes integral action in addition to state feedback. The value of the integral_action keyword should be an ndarray that will be multiplied by the current state to generate the error for the internal integrator states of the control law. The number of outputs that are to be integrated must match the number of additional rows and columns in the Q matrix.
method (str, optional) – Set the method used for computing the result. Current methods are ‘slycot’ and ‘scipy’. If set to None (default), try ‘slycot’ first and then ‘scipy’.
K (2D array (or matrix)) – State feedback gains
S (2D array (or matrix)) – Solution to Riccati equation
E (1D array) – Eigenvalues of the closed loop system
If the first argument is an LTI object, then this object will be used to define the dynamics and input matrices. Furthermore, if the LTI object corresponds to a discrete time system, the
dlqr()function will be called.
The return type for 2D arrays depends on the default class set for state space operations. See
>>> K, S, E = lqr(sys, Q, R, [N]) >>> K, S, E = lqr(A, B, Q, R, [N])