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constructs the feedback regulator for the StateSpaceModel object ss with estimator and feedback gain matrices l and , respectively.
uses only sensors as the measured outputs of ss.
specifies finputs as the feedback inputs of ss.
specifies einputs as the exogenous deterministic inputs.
  • 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 input can include stochastic inputs , feedback inputs , and exogenous deterministic inputs .
  • The arguments finputs and einputs are lists of integers specifying the positions of and in .
  • The output consists of the noisy measurements as well as other outputs.
  • The argument sensors is a list of integers specifying the positions of in .
  • Block diagram of the system with its regulator:
Construct a state-feedback regulator from known estimator and state-feedback gains:
Construct a state-feedback regulator from known estimator and state-feedback gains:
Click for copyable input
The regulator for a SISO system with estimator gain and regulator gain :
Its transfer function:
The closed-loop system:
A state-feedback regulator for a system with two sensor outputs, one feedback input, one exogenous deterministic input, and one stochastic input:
An observer-based optimal regulator for a deterministic continuous-time system:
The transfer function of the estimator-regulator:
A state-feedback regulator for the discrete-time model of a satellite's attitude control system:
A regulator for a simple pendulum:
An LQ regulator for a SISO system:
The closed-loop poles are the poles of the state-feedback and estimator subsystems:
Construct an LQG regulator using optimal estimator gains and state-feedback gains:
LQGRegulator gives the same result:
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