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**1. Homework Statement**

Welding robot is defined by the block diagram attached/ excuse the paint work.

(hope that worked)

find:

a)maximum value of K required to achieve stability.

b)roots of the characteristic equation, at half the maximum K value.

c)estimated percentage overshoot, if the complex roots determined

in part (b) are dominant and half the maximum K is considered.

**2. Homework Equations**

NA

**3. The Attempt at a Solution**

Pretty sure that the first step is reducing the three blocks to a single transfer function?

This is pretty simple, two top blocks are cascaded then using the feedback formula gives.

Gives:

[tex] \frac{K}{(0.5s+1)(s+1)(s+2)}[/tex]

Using the feedback formula gives:

[tex]\frac{\frac{K}{(0.5s+1)(s+1)(s+2)}}{1\pm\frac{K}{(0.5s+1)(s+1)(s+2)}* \frac{1}{0.005s+1}} [/tex]

a) Max value of K to achieve stability:

simplifying - getting tired of LaTex, so:http://www.wolframalpha.com/input/?i=%28k%2F%28%280.5s%2B1%29%28s%2B1%29%28s%2B2%29%29%29%2F%28PlusMinus%5B1%2C%28k%2F%28%280.5s%2B1%29%28s%2B1%29%28s%2B2%29%29%29*1%2F%280.005s%2B1%29%5D%29

There are poles and zeroes at s=0 - have to consult my textbook but I cant see how it can be simultaneously asymptotic and 0 ?? - zeroes at s = -1, -2.................I'm a bit stuck here - Routh table??????

Thanks, any help appreciated.