# Thread: Partial Fractions...I think...on a Transfer Function

1. ## Partial Fractions...I think...on a Transfer Function

Hello there! My problem is probably really simple to solve however, I have managed to confused myself to a point of no return to I ask for whoever is on here to explain how to solve the equation found in the attached image. The equation is obtained from a Z-Transform control system time description along with a specific controller which gives a transfer function (equation 1). Once all the math-magic has been applied the transfer function will then be equation 2. My problem is I have no idea what steps are used to get equation 1 to equation 2. I assume partial fractions are used along with the Gaussian Elimination (which i really don't understand). Is it possible someone could show me the steps in detail as if i was an idiot? My math skills are beyond useless and I'm sure I have just missed something really simple.

Thank you!!!

2. ## Re: Partial Fractions...I think...on a Transfer Function

Originally Posted by fattonytm
Hello there! My problem is probably really simple to solve however, I have managed to confused myself to a point of no return to I ask for whoever is on here to explain how to solve the equation found in the attached image. The equation is obtained from a Z-Transform control system time description along with a specific controller which gives a transfer function (equation 1). Once all the math-magic has been applied the transfer function will then be equation 2. My problem is I have no idea what steps are used to get equation 1 to equation 2. I assume partial fractions are used along with the Gaussian Elimination (which i really don't understand). Is it possible someone could show me the steps in detail as if i was an idiot? My math skills are beyond useless and I'm sure I have just missed something really simple.
The LCD is $\displaystyle (z-0.3)(z-0.6)=z^2-0.9z+0.18$

3. ## Re: Partial Fractions...I think...on a Transfer Function

Originally Posted by Plato
The LCD is $\displaystyle (z-0.3)(z-0.6)=z^2-0.9z+0.18$
Thanks for the swift reply. But where does the $\displaystyle z+0.5$ come from on the denominator of equation 2?. I assume the denominator in equation 1 (the whole fraction) would become the reciprocal and multiplied with the numerator, however, when I multiply out and simplify i never get the correct answer so I assume I'm doing something wrong but not sure what exactly...

4. ## Re: Partial Fractions...I think...on a Transfer Function

multiplying the numerator and denominator of equation 1 by the LCD will clear the fractions in the numerator and denominator, and will yield equation 2

5. ## Re: Partial Fractions...I think...on a Transfer Function

After much thinking and fretting I managed to solve the equation and turns out it's simple errors that caused me the problem. As I believe probably a few people do this I have made a detailed step-by-step process to obtain the answer. Please feel free to move it to another part of the forum. Thank you Skeeter and Plato for steering me towards to right direction!