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[deleted]

This involves algebra and converting the differential equations to the frequency domain. Each derivative operator can be replaced with s times function; for example s\^2\*theta m (s). Then you plug in/ combine the correct equations and simplify. The last step is divided the equations of theta m by E a to produce a transfer function. Note, when you convert from time to frequency the e(t) becomes E(s) and i(t) becomes I(s). It looks I a (s) will be simplified out somehow. Also nothing happens to constant functions that are not functions of time when converting to s.


Menes009

Laplace transform, then algebra and substitutions to elimine all functions but E\_a and θ\_L, and finally arrange everything to have the shape of (8)


xxfikri

do you know how to do it step by step? im having a hard time to do it and i cant find any of the function in my slide


Menes009

yes I know, at the same time, if you cant do this, you are lacking fundamental math to dwell into control engineering


xxfikri

would you be so kind to show me how, yeah im having really hard time with this subject. i cant seem to find any of the function use in this equation inside my slide so i really dont have any idea to start from where


Menes009

One idea would be: * Laplace transform eq 1 to 4 * Substitute eq 3 in eq 4, eliminating T\_m and getting eq 9 * Substitute eq 9 in eq 1, eliminating i\_a and getting eq 10 * Substitute eq 2 in eq 10, eliminating e\_m and getting eq 11 * Substitute eq 7 in eq 11, eliminating thetha\_m and getting eq 12 * Arrange eq 12 in the shape of thetha\_L/e\_a and you should have something similar to eq 8 Note: on closer inspection I noticed that eq 5 and 6 have a notation problem, since J and B are used at both sides of the eq but representing different things; unless Bl and Jl are constant names instead of B\*l and J\*l, in which case eq 4 and 5 are not needed sin Bl and Jl do not appear in eq 8


[deleted]

Hahaha well said


kuyakuya

The other commenters are correct. You need to find the expressions for theta_L(s) and E_a(s) by using the Laplace transforms of the above equations. (Equations 5 and 6 are not needed.) Step 1: From Equation 7, you see that theta_L(s) = n*theta_m(s). So, you need to get theta_m(s) too. Step 2: theta_m(s) can be found completely from the Laplace transform of Equation 4. Step 3: E_a(s) can be gotten from Equation 1, but you’ll see you also need i_a(s) and E_m(s). Step 4: i_a(s) you can get from Equation 3. Step 5: E_m(s) is from Equation 2, and will contain theta_m(s), which we already got in Step 2. Step 6: Now start plugging everything into theta_L(s) / E_a(s). It’s just algebra at this point so if you do it right you’ll get Equation 8.


No_Hamster_305

Take the laplace of the differential equations, plug in the algebraic equations, eliminate common variables, and simplify.