EstimatorRegulator

EstimatorRegulator[ssm,{l,κ}]

constructs the feedback regulator for the StateSpaceModel ssm with estimator and feedback gain matrices l and κ, respectively.

EstimatorRegulator[{ssm,sensors},{l,κ}]

uses only sensors as the measured outputs of ssm.

EstimatorRegulator[{ssm,sensors,finputs},{l,κ}]

specifies finputs as the feedback inputs of ssm.

EstimatorRegulator[{ssm,sensors,finputs,einputs},{l,κ}]

specifies einputs as the exogenous deterministic inputs.

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
  • EstimatorRegulator also accepts nonlinear systems specified by AffineStateSpaceModel and NonlinearStateSpaceModel.
  • For nonlinear systems, the operating values of state and input variables are taken into consideration when constructing the EstimatorRegulator.
  • 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 .
  • EstimatorRegulator[ssm,{}] is equivalent to EstimatorRegulator[{ssm,All,All,None},{}].
  • The estimator gains l can be computed using EstimatorGains, LQEstimatorGains, or DiscreteLQEstimatorGains.
  • The feedback gains κ can be computed using StateFeedbackGains, LQRegulatorGains, or DiscreteLQRegulatorGains.
  • Block diagram of the system with its regulator:

Examples

open allclose all

Basic Examples  (1)

Construct a state-feedback regulator from known estimator and state-feedback gains:

In[1]:=
Click for copyable input
Out[1]=

Scope  (5)

Applications  (3)

Properties & Relations  (2)

See Also

LQGRegulator  StateOutputEstimator  EstimatorGains  LQEstimatorGains  KalmanEstimator  DiscreteLQEstimatorGains  StateFeedbackGains  LQRegulatorGains  DiscreteLQRegulatorGains

Introduced in 2010
(8.0)
| Updated in 2014
(10.0)