Feedback control systems

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A control system is given by <math>\frac{dx}{dt} = Ax + Bu</math>
A control system is given by <math>\frac{dx}{dt} = Ax + Bu</math>
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For testing Math
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These are for testing Purpose by Nasir:-
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<math>\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds
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= \int_a^x f(y)(x-y)\,dy</math>
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<math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
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{3^m\left(m\,3^n+n\,3^m\right)}</math>
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<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>
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<math>\phi_n(\kappa) =
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\frac{1}{4\pi^2\kappa^2} \int_0^\infty
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\frac{\sin(\kappa R)}{\kappa R}
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\frac{\partial}{\partial R}
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\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math>
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<math>\phi_n(\kappa) =
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0.033C_n^2\kappa^{-11/3},\quad
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\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>
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<math>
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f(x) =
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\begin{cases}
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1 & -1 \le x < 0 \\
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\frac{1}{2} & x = 0 \\
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1 - x^2 & \mbox{otherwise}
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\end{cases}
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</math>
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<math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
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= \sum_{n=0}^\infty
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\frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
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\frac{z^n}{n!}</math>
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<math> \frac {a}{b}\  \tfrac {a}{b} </math>

Revision as of 16:43, 4 July 2009

We meet regularly on Thursdays at 10am to discuss various topics of feedback control and modeling of physical systems.

Participants

  • Asad Abidi
  • Ishtiaq Maqsood
  • Hassan Mohy-ud-Din
  • Suleman Sami Qazi
  • Abubakr Muhammad

A control system is given by \frac{dx}{dt} = Ax + Bu


For testing Math

These are for testing Purpose by Nasir:-

\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds
 = \int_a^x f(y)(x-y)\,dy

\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
 {3^m\left(m\,3^n+n\,3^m\right)}

u'' + p(x)u' + q(x)u=f(x),\quad x>a

\phi_n(\kappa) =
 \frac{1}{4\pi^2\kappa^2} \int_0^\infty
 \frac{\sin(\kappa R)}{\kappa R}
 \frac{\partial}{\partial R}
 \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR

\phi_n(\kappa) = 
 0.033C_n^2\kappa^{-11/3},\quad
 \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}


 f(x) =
 \begin{cases}
 1 & -1 \le x < 0 \\
 \frac{1}{2} & x = 0 \\
 1 - x^2 & \mbox{otherwise}
 \end{cases}

{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
 = \sum_{n=0}^\infty
 \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
 \frac{z^n}{n!}

 \frac {a}{b}\  \tfrac {a}{b}

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