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control.matlab.dlqr — Python Control Systems Library 0.10.2 documentation

control.matlab.dlqr(A, B, Q, R[, N])[source]

Discrete-time linear quadratic regulator design.

The dlqr() function computes the optimal state feedback controller u[n] = - K x[n] that minimizes the quadratic cost

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

• dlqr(dsys, Q, R)

• dlqr(dsys, Q, R, N)

• dlqr(A, B, Q, R)

• dlqr(A, B, Q, R, N)

where dsys is a discrete-time StateSpace system, and A, B, Q, R, and N are 2d arrays of appropriate dimension (dsys.dt must not be 0.)

Parameters:

A, B2D array

Dynamics and input matrices.

dsysLTI StateSpace

Discrete-time linear system.

Q, R2D array

State and input weight matrices.

N2D array, optional

Cross weight matrix.

integral_actionndarray, 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.

methodstr, 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’.

Returns:

K2D array

State feedback gains.

S2D array

Solution to Riccati equation.

E1D array

Eigenvalues of the closed loop system.

Examples

>>> K, S, E = dlqr(dsys, Q, R, [N])                         
>>> K, S, E = dlqr(A, B, Q, R, [N])                         

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