# Feedback control systems

(Difference between revisions)
 Revision as of 07:30, 2 July 2009 (view source)← Previous diff Revision as of 16:43, 4 July 2009 (view source)Next diff → Line 10: Line 10: A control system is given by $\frac{dx}{dt} = Ax + Bu$ A control system is given by $\frac{dx}{dt} = Ax + Bu$ + + + For testing Math + + These are for testing Purpose by Nasir:- + + $\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds + = \int_a^x f(y)(x-y)\,dy$ + + $\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} + {3^m\left(m\,3^n+n\,3^m\right)}$ + + $u'' + p(x)u' + q(x)u=f(x),\quad x>a$ + + $\phi_n(\kappa) = + \frac{1}{4\pi^2\kappa^2} \int_0^\infty + \frac{\sin(\kappa R)}{\kappa R} + \frac{\partial}{\partial R} + \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR$ + + $\phi_n(\kappa) = + 0.033C_n^2\kappa^{-11/3},\quad + \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}$ + + $+ f(x) = + \begin{cases} + 1 & -1 \le x < 0 \\ + \frac{1}{2} & x = 0 \\ + 1 - x^2 & \mbox{otherwise} + \end{cases} +$ + + ${}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) + = \sum_{n=0}^\infty + \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n} + \frac{z^n}{n!}$ + + $\frac {a}{b}\ \tfrac {a}{b}$

## 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

• Ishtiaq Maqsood
• Hassan Mohy-ud-Din
• Suleman Sami Qazi

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

For testing Math

These are for testing Purpose by Nasir:-

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

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

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

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

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

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

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

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