Im trying to figure out how a certain example is working.(adsbygoogle = window.adsbygoogle || []).push({});

in this example the function

[tex]x = g - \frac{k}{m} \frac{(z-z0)^2}{(i-i0)^2}[/tex]

where g, k, m, z0, i0 are fixed values and z, i are variables

The function above is written as

[tex]x = f(i,z) ( \sqrt{g} (z-z0) - y (i-i0) )[/tex]

where f(i,z) is a new function as function of i, z and y is a new variable independent of i, z.

The idea is to use linearize the system around its equilibrium point (z0 = 0.072 and i0=1). But in the example they dont show how they have found f(i,z) (and f(i0,z0)) and y.

In order to reconstruct the example i need this so i tried to find f(i,z) by writing f(i,z) as (a+b) and solve the system as

[tex] f(i,z) = (a+b) ( \sqrt{g} (z-z0) - y (i-i0) ) = a \sqrt{g} (z-z0) - a y (i-i0) + b \sqrt{g} (z-z0) - b y (i-i0) [/tex]

thus if we compute a, b, y we get

[tex] a = \frac{\sqrt{g}}{z-z0} , \quad b =\sqrt{\frac{k}{m}}\frac{i-i0}{(z-z0)^2} , \quad y = \sqrt{\frac{k}{m}} [/tex]

thus

[tex] f(i,z) = a+b = \frac{ \sqrt{gm} (z-z0) + \sqrt{k}(i-i0) }{ \sqrt{m}(z-z0)^2 } [/tex]

if i now fill in i=i0 and z=z0 (equilibrium point) then the answer is infinity, which cant be correct.

Anyone knows where i make a mistake?

Thanks in advance

Azizz

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Control Theory Problem

Loading...

Similar Threads - Control Theory Problem | Date |
---|---|

Why are we still teaching Routh-Hurwitz criterion in Control | Feb 17, 2018 |

Control Theory Application? | Jan 3, 2015 |

Control Theory | Feb 1, 2012 |

Control Theory Book for a Mechanical Engineering | Sep 8, 2011 |

Aerospace Aileron-Air crafts/Rockets control theory | Aug 2, 2011 |

**Physics Forums - The Fusion of Science and Community**