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BUILT-IN MATHEMATICA SYMBOL

DiscreteLQRegulatorGains

gives the optimal discrete-time state feedback gain matrix with sampling period

for the continuous-time StateSpaceModel object ss and the quadratic cost function with state and control weighting matrices q and r.

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

specifies the feedback inputs of ss.

The state-space model ss can be given as StateSpaceModel, where a and b represent the state and input matrices in the continuous-time system .

The argument finputs is a list of integers specifying the positions of the feedback inputs in .

DiscreteLQRegulatorGains computes the regulator gains based on the emulated system with cost function .

The emulated closed-loop system with the computed feedback gain matrix k can be obtained from SystemsModelStateFeedbackConnect[ToDiscreteTimeModel[ss, , Method->"ZeroOrderHold"], k]

Compute a set of discrete-time regulator gains for a continuous-time system:

Out[1]=

Compute a set of discrete LQ regulator gains for a continuous-time state-space model:

Only use the first input as the feedback input:

Compute the gains with state-control coupling in the cost function:

Use only inputs 1 and 3 for feedback:

Design an optimal controller by emulation:

The step response of the emulated system:

Use LQRegulatorGains and the discretized system and weighting matrices to compute the discrete LQ regulator gains:

DiscreteLQRegulatorGains directly gives the same result:

It is not possible to compute an optimal regulator for a system that is not stabilizable:

The second mode is not stabilizable: