EstimatorGains

EstimatorGains[ssm, {p1, p2, ..., pn}]
gives the estimator gain matrix for the StateSpaceModel ssm, such that the poles of the estimator are .

EstimatorGains[{ssm, {out1, ...}}, ...]
specifies the measured outputs to use.

Details and OptionsDetails and Options

  • EstimatorGains is also known as observer gains or observer pole placement.
  • The 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
  • If ssm is observable, the eigenvalues of will be , where is the computed estimator gain matrix.
  • For a descriptor system StateSpaceModel[{a, b, c, d, e}], the number of poles that can be specified is determined by the rank of e and the observability of the system.
  • EstimatorGains[{ssm, {out1, ...}}, ...] is equivalent to EstimatorGains[ssm1, ...], where ssm1=SystemsModelExtract[ssm, All, {out1, ...}].
  • The observer dynamics are given by:
  • continuous-time system
    discrete-time system
  • In the case of a square nonsingular matrix , the state vector can be computed as x=TemplateBox[{c}, Inverse].(y-d.u).
  • EstimatorGains accepts a Method option with settings given by:
  • Automaticautomatic method selection
    "Ackermann"Ackermann method
    "KNVD"Kautsky-Nichols-Van Dooren method
  • The estimator gains are computed as the state feedback gains of the dual system.

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

Compute estimator gains for a continuous-time system:

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A discrete-time system:

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Estimator gains for a two-output system with only the second output measured:

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