Wolfram Language & System 11.0 (2016)|Legacy Documentation

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gives the state feedback gain matrix for the state-space model ssm, such that the poles of the closed-loop system are pi.

specifies control inputs ini to use.

Details and OptionsDetails and Options

  • StateFeedbackGains is also known as pole placement gains.
  • The state-space model ssm can be given as StateSpaceModel[{a,b,}], where a and b represent the state and input matrices in either a continuous-time or a discrete-time system:
  • continuous-time system
    discrete-time system
  • If ssm is controllable, the eigenvalues of will be {p1,p2,,pn}, where is the computed state feedback 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 controllability of the system.
  • StateFeedbackGains also accepts nonlinear systems specified by AffineStateSpaceModel and NonlinearStateSpaceModel.
  • For nonlinear systems, the operating values of state and input variables are taken into consideration, and the gains are computed based on the approximate Taylor linearization and returned as a vector.
  • StateFeedbackGains[{ssm,{in1,}},] is equivalent to StateFeedbackGains[ssm1,], where ssm1SystemsModelExtract[ssm,{in1,}].
  • StateFeedbackGains accepts a Method option with settings given by:
  • Automaticautomatic method selection
    "Ackermann"Ackermann method
    "KNVD"KautskyNicholsVan Dooren method

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Place the poles at :

Click for copyable input

Place all the eigenvalues of a discrete-time system at the origin:

Click for copyable input
Click for copyable input
Click for copyable input

Eigenvalue assignment for a two-input system:

Click for copyable input

Calculate the feedback gains for a two-input system, using the first input:

Click for copyable input
Introduced in 2010
| Updated in 2014