# Difference between revisions of "Errata: In Example 6.10, the system input for the linearized model should be w instead of u"

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{{errata page | {{errata page | ||

− | | chapter = | + | | chapter = State Feedback |

− | | page = | + | | page = 196 |

− | | line = | + | | line = 19, 23 |

− | | contributor = | + | | contributor = J. W. Kim |

− | | date = | + | | date = 5 Nov 2011 |

− | | rev = 2. | + | | rev = 2.11a |

| version = Third printing | | version = Third printing | ||

− | | text = | + | | text = The dynamics at the top of the example use the linearized input <amsmath>w = u-u_e</amsmath> and hence the input for the remainder of the example is <amsmath>w</amsmath> and not <amsmath>u</amsmath>. This affects the two displayed equations in lines 19 and 23. The first displayed equation should read |

+ | <center><amsmath> | ||

+ | \frac{d}{t} \begin{bmatrix} x \\ z \end{bmatrix} = \begin{bmatrix} | ||

+ | a & 0 \\ | ||

+ | 1 & 0 | ||

+ | \end{bmatrix} \begin{bmatrix} x \\ z \end{bmatrix} + | ||

+ | \begin{bmatrix} b \\ 0 \end{bmatrix} {\color{blue} w} + \begin{bmatrix}-b_g \\ 0 \end{bmatrix} \theta + \begin{bmatrix} 0 \\ v_e - v_r \end{bmatrix}. | ||

+ | </amsmath></center> | ||

+ | and the second should read | ||

+ | <center><amsmath> | ||

+ | \aligned | ||

+ | \frac{dz}{dt} &= y - v_r, \qquad | ||

+ | {\color{blue} w} &= -k_p x - k_i z + k_r v_r, | ||

+ | \endaligned | ||

+ | </amsmath></center> | ||

}} | }} |

## Latest revision as of 17:34, 6 September 2012

Return to Errata page |

Location: page 196, line 19, 23

The dynamics at the top of the example use the linearized input and hence the input for the remainder of the example is and not . This affects the two displayed equations in lines 19 and 23. The first displayed equation should read

and the second should read

(Contributed by J. W. Kim, 5 Nov 2011)