BUILT-IN MATHEMATICA SYMBOL

LQOutputRegulatorGains

LQOutputRegulatorGains[ssm, {q, r}]
gives the optimal state feedback gain matrix for the StateSpaceModel ssm and the quadratic cost function, with output and control weighting matrices q and r.

LQOutputRegulatorGains[ssm, {q, r, p}]
includes the output-control cross-coupling matrix p in the cost function.

LQOutputRegulatorGains[{ssm, sensors}, {...}]
specifies sensors as the measured outputs of ssm.

LQOutputRegulatorGains[{ssm, sensors, finputs}, {...}]
specifies finputs as the feedback inputs of ssm.

Details and Options Details and Options

The standard state-space model ssm can be given as StateSpaceModel[{a, b, c, d}], 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 descriptor state-space model ssm can be given as StateSpaceModel[{a, b, c, d, e}] in either continuous time or discrete time:
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[ssm, {...}] is equivalent to LQOutputRegulatorGains[{ssm, All, All}, {...}].
The cost function is:
continuous-time system

discrete-time system
In LQOutputRegulatorGains[ssm, {q, r}], 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 $kappa=TemplateBox[{{r, _, 1}}, Inverse].x_1$ , where and . The matrix is the solution of the continuous Riccati equation $a.x_r+x_r.a-x_1.TemplateBox[{{r, _, 1}}, Inverse].x_1+c_s.q.c_s=0$ .
For discrete-time systems, the optimal feedback gain is computed as $kappa=TemplateBox[{{r, _, 1}}, Inverse].x_1$ , where and . The matrix is the solution of the discrete Riccati equation $a.x_r.a-x_r-x_1.TemplateBox[{{r, _, 1}}, Inverse].x_1+c_s.q.c_s=0$ .
The subscript denotes the submatrix associated with the feedback inputs , and the subscript denotes the submatrix associated with the sensors .