BUILT-IN MATHEMATICA SYMBOL

LQOutputRegulatorGains

gives the optimal state feedback gain matrix for the StateSpaceModel object ss and the quadratic cost function with output and control weighting matrices q and r.

includes the output-control cross-coupling matrix p in the cost function.

LQOutputRegulatorGains

specifies sensors as the measured outputs of ss.

LQOutputRegulatorGains

specifies finputs as the feedback inputs of ss.

MORE INFORMATION

The state-space model ss can be given as StateSpaceModel, where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:

		continuous-time system
		discrete-time system

The argument sensors is a list of integers specifying the positions of the measured outputs in .

Similarly, finputs is a list of integers specifying the positions of the feedback inputs in .

LQOutputRegulatorGains is equivalent to LQOutputRegulatorGains[{ss, All, All}, {...}].

The cost function is:

		continuous-time system
		discrete-time system

In LQOutputRegulatorGains, the cross-coupling matrix p is assumed to be zero.

The optimal control is given by , where is the computed feedback gain matrix.

For continuous-time systems, the optimal feedback gain is computed as , where and . The matrix is the solution of the continuous Riccati equation .

For discrete-time systems, the optimal feedback gain is computed as , where and . The matrix is the solution of the discrete Riccati equation .

The subscript denotes the submatrix associated with the feedback inputs , and the subscript denotes the submatrix associated with the sensors .

EXAMPLES

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Basic Examples (3)

A set of optimal output-weighted state feedback gains for a continuous-time system:

LQ output regulator gains for a discrete-time system:

A set of optimal output-weighted state feedback gains for a continuous-time system:

In[1]:=

Out[1]//MatrixForm=

LQ output regulator gains for a discrete-time system:

In[1]:=

Out[1]=

Scope (6)

Compute a set of optimal output-weighted state feedback gains of a continuous-time system:

The gains for a cost function with input-output coupling:

The gains for a discrete-time system:

The gains computed using only the first output as the measurement:

Use all outputs as measurements:

The gains using only the first input as the feedback input:

Options (0)

Applications (1)

Construct an output-weighted state-feedback gain matrix for an aircraft model:

Plot the closed-loop output response and the control signals:

Properties & Relations (4)

The output regulator gains can be computed using LQRegulatorGains and equivalent weighting matrices:

LQOutputRegulatorGains gives the same result:

Compute the LQ output regulator gains by solving the underlying Riccati equation:

LQOutputRegulatorGains gives the same result:

Compute the gains for a discrete-time system using DiscreteRiccatiSolve:

LQOutputRegulatorGains gives the same result: