Thread: 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!!!

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

Originally Posted by Plato

The LCD is

Thanks for the swift reply. But where does the 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...

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

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!