Question

course name: control system

topic about root locus

please show all your steps to make easier for understanding.

1. Determine the stability condition of the systems describe in the first column below. Justify your answer with reason. show all your answers steps Justification Stability condition Systems description dy y +2 y x +3 dt dy -6y= x + dt2 dt provide special condition provide special condition 2. Given the closed loop system in the figure below, analysis the systems given in the table below using the Root locus as follows: Ys) G(s) i. Determine the zeros and poles of the system ii. Sketch the root locus for the system with proper labeling. iii. Comment on the system dynamic stability (that is when the gain changes from zero to infinity.) show all your steps Poles = S-1 a. System1, G(s) = (s+2)(5+4) Zeros= Sketch root locus with proper label Determine break away point if applicable Comment on the stability of the system as K varies from zero to infinity. Clearly state your response provide clear and professional comment 3. Given the closed loop system in the figure below, analysis the systems given in the table below using the Root locus as follows: i. Determine the zeros and poles of the system. i. Sketch the root locus for the system with proper labeling ii. Determine break-away point iv. Determine the asymptote angles. G(6) K iv. Determine the critical gain above which the system is unstable Show all steps of answers v. comment on the system dynamic stability (that is when the gain changes from from zero to infinity See how well you understand root locus. Poles= 5 a. Systeml, G(s) = s(s+2)(s+4) Zeros = Sketch root locus with proper label Determine break away point if applicable Determine the asymptote angles. Critical gain: Kcr Comment on the stability of the system as K varies from zero to infinity Clearly state your response

Answer 1

As per HomeworkLib policy we need to answer only the first question if multiple questions are posted.... Please upload remaining questions separately... Please find the explanation below for 1st question.... Hope you understand... Thanks in advance....

+3 +ay =1 At bo5 sicles APply Laplace tronstomm on YC3YC)+ YC= XCs) Yo26-2] YCS s3t2 Farmi Rtt teble-forCbaractefctic eguation S 2s+2 c0 3 53x2. 2 Ala te Coetficients of 5e first Column Of RH positive Ssten is stab/c are table

at qt Applt Laplace tron stefn on bo ciotes 6 YC)XCs) )Yes) XCs) St YCs

character jstic euatio Fming R teble for EP Coefficient in te One of 5e -first colunn V te System is ustele. stom s Cteriptior) stebility Concitp Justificatpr Coefficiets of AonySteble at First Colinn O Rtt tee ore tVe Ore Of 15e coefficient ot Alucays nstee at Pirst calumn ot Rtt teble is -ve