AEE - Control Systems Most Expected Bits || SAIMEDHA KOTI - HYD

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[00:00:06]Hi everyone myself from space engineering academy.

[00:00:13]So control system most important questions by the series basic concepts signal flow and black diagram of stability response analysis.

[00:00:43]root locus.

[00:00:47]Okay. So online not only system every subject most expected bits.

[00:01:20]Every last Revision last minute online super online course complete 11,000 not only any kind of discussive numbers 984 4971 3451 98486925 admission and thank you so much for watching this video. This is the right video at the right time and please enjoy the video by Vishnuansar about the topic root locus and inverse root locus part two. Next question. The correct root locus diagram of the system is The correct root locus diagram of the system is first of all locate the poles and zeros.

[00:03:02]One pole is at origin remaining two poles are at plus J4 minus J4 because SS² equal to -6 therefore plus - J4.

[00:03:13]Next zeros + J8 minus Z8 + J8 minus J8 okay five root locus exist anyway because 1 2 3 4 5 sum of poles and zeros is odd number root locus exist in this section so root locus exist in this section on this real axis root locus exist but no option Next.

[00:03:44]Okay, no problem.

[00:03:46]And option A from pole root log is departing. Option B pole departing. And option three eliminated. Why? Because from root locus started from zero here.

[00:03:58]But actually root locus starts from pole. This is against the concept.

[00:04:01]Option four also correct. Next we have to calculate angle of departure and angle of arrival. Then only it is possible. So friends this is complex roots for complex roots only we have to calculate departure and arrival and angle made by this pole is 90° this pole also 90° angle made by all the poles is 90° so angle of departure formula is 180 minus 5 sorry these are zeros these are zeros 180 minus So with respect to this pole I'm calculating ph is angle made by poles this pole 190 this pole one also 90 180° next zero this is poles minus 0 + 90 this is making + 90 and this is making - 90 so power 3 is 180 sorry five is 180 So 180 minus 180 is 0°. Angle of departure is 0°. Therefore, so it is going to be 0°.

[00:05:15]Angle of arrival is plus - 360°.

[00:05:24]Angle of arrival plus - angle of departure is 0°. Arrival will be 360°.

[00:05:32]360° means it is root locus will be like this.

[00:05:38]So option four is suitable for this question.

[00:05:43]Next question. If damping ratio is 0.5 of the given openloop transfer function K by S into S + 10. What is the value of K? First of all one pole is at origin other pole is at minus 10. Damping ratio is 0.5 means cos 5 is equal to za from this 5 is equal to cos inverse of.5 cos inverse of 0.5 is 60° that means draw a 60° line this is 60° line okay what is the value of k first root locus exist root lo sorry not exist root locus exist root locus exist between these two then break point is average value of these 2 0 - 10 by 2 which is - 5 at -5 root locus branch is there. This is root locus branch at minus 5 root locus branches are this is the root locus branch one is going upward direction other is going downward direction. Now this 0.5 is touching at this point. This length is point sorry this length is five. This angle is 60.

[00:06:54]Then tan 60 is equal to opposite by adjacent. Opposite is unknown. Let's say y by adjacent is five. So y = 5 into tan 60 5 <unk>3.

[00:07:12]This value is 5 <unk>3.

[00:07:15]Next whenever this value is 5 <unk>3 how to calculate this by applying s or cos sin 60 is equal to opposite by hypotenuse that hypotenuse is z. So zed is equal to 5 <unk>3 by sin 60. Sin 60 is <unk>3x2 it is 10. So this value is 10. So from this pole to this point 10 definitely from here also it is 10.

[00:07:52]So k is equal to product of distance vectors from various poles. 10 into 10 divided by zeros are not there. Take it as one. So k value is 100. Therefore answer is 100 for this question.

[00:08:06]Or else take characteristic equation closer loop transfer function s² + 10 s + k numerator plus denominator equal to0 characteristic equation 2 into za into omega= 10 omega square = k so za value given.5 then omega is 10 k is equal to 100 so either value either way you can calculate the answer either you can use the root locus concept or else we can use the characteristic equation concept answer will be coming next. The root locus of a certain system is shown in figure the closed loop transfer function.

[00:08:46]The closed loop transfer function first of all he given for even number this is one pole this is one pole right side of the section is even number he given root locus means it is inverse root locus question even though he said root locus be careful this is inverse root locus question whenever it is exist for even number the concept is related to inverse root locus whenever it is exist for odd number the concept is related to root locus. So right now inverse root locus means inverse root locus concepts are using positive feedback principle. What is positive feedback principle? G of s by 1 - g of s into h of s. That's it.

[00:09:32]So g of s by 1. So three will be the correct answer. That means minus k. If it is negative feedback add this k to denominator. So if it is negative feedback add k to denominator. If it is positive feedback minus K we have to subtract from den numerator subtracted from denominator that will be positive feedback concept.

[00:09:55]Next the root locus diagram of a closed loop system shown figure the system is over damped. The system is over damped at this point. This is five critically damped. At this point this is one critically damped. Over damped is in between 0 to 1. In between 0 to 1 and here in between 5 to infinity 5 to infinity system is over damped in between 0 to 1 and k greater than five. Fourth will be the correct answer. And in between 1 and five under damped at this point wherever break points are there that is critically damped. K= 1 and five is critically damped. K is in between 1 and five is under damped. K greater than five that means answer is going to be fourth one for this question directly answer direct question.

[00:10:46]Next a transfer function has two zeros at infinity means two zeros are at infinity.

[00:10:55]Transfer function has two zeros at infinity then the relation between numerator degree n and denominator degree m of the transfer function. You know as totes formula is p minus z. Poles is represented right now by M.

[00:11:10]Number of asympto formula is modulus of P minus Z. So M poles given M zeros given N. So these as are 2. Therefore 2 is equal to M - N. From this is asking about N value. So mus N = 2. M = N + 2.

[00:11:31]Sorry, he's asking n value that is mus 2. n= mus 2. 2 will be the correct answer for this question.

[00:11:47]The openloop transfer function of a negative feedback system given the value of k at the breakaway point of the root locus of the above system.

[00:11:55]First of all, where is the breakaway point? Draw the root locus. One pole is at zero. Another pole is at minus2.

[00:12:03]Another pole is at minus 6. Root locus exists for odd number. Root locus not exist. Root locus exist. Root locus exist between 0 and minus2. Therefore breakaway point exists between them. So how to calculate breakaway point?

[00:12:16]Differentiate k.

[00:12:25]So differentiate k. K is going to be S into S S² means K is poles by zeros. I'm writing the expression S² + 8 S + 12 K is going to be. So next step K is going to be S cub + 8 S² + 12 S. So differentiation of this 3 S² + 16 S + 12 = 0.

[00:12:54]roots of this equation you will get minus.9 and other value minus.9 is valid because break point exist between 0 and minus2 then calculate k value at that point calculate k value at that point that is at minus.9 direct step at minus.9 we are calculating k value therefore k is equal to product of distance vectors from various poles how many poles three poles no zero take one so minus.5 9 to 0 will be the distance.9 minus.9 to2 it is distance 1.1 minus.9 to 6 distance is 5.1 that is nothing but k so k value is going to be so.9 into 1.1 into 5.1 so just calculate this value that itself is going to be k next the root locus of a system is shown in figure the possible openloop transfer function of the system is 100% It is going to be circle means K into S + B by S into S + A. This is the form.

[00:14:00]So S into S plus A. This is the first answer. Correct answer. So it is given circle. Definitely K into S + 3 by S into S plus A form only. You will get the circle not for remaining options.

[00:14:11]Direct answer dear engine is this is the shortcut. Next.

[00:14:16]Next question is openloop transfer function of a system its root locus diagram is first of all zeros are given at -1 and minus3. First of all, where the location of poles -2 + z2 -2 + z2 this is wrong answer because root log started from zero.

[00:15:00]So dear friends first of all -2 + z2 location of holes are at -2 + z2 - z2 location of zeros at -1 - 3 root locus not exist even number root locus exist root locus exist so definitely calculate angle of departure will be the answer like this.

[00:15:32]So one root locus ends here another root locus ends here right 100% break point is in between these two average value of these two will be minus2 that is the started lyrically I'm using so answer is going to be first option remaining options not matches right next question consider the following statements regarding the root locus technique for analyzing linear control system root locus is the locus of the roots of the characteristic equation as the closed loop gain varies from 0 to infinity.

[00:16:02]Perfectly correct. The number of root locus branches of the root loc is equal to number of poles of the open loop. No, it is equal to either open loop poles or open loop zeros whichever is higher. Not clearly with respect to open loop poles.

[00:16:16]Wrong. For a particular point in the splane to lie on the root locus, the angle criteria should be 2 L + 1 into pi that is odd multiple. Correct.

[00:16:24]Therefore, three is correct. So, which of the following statements is correct?

[00:16:29]Let me of these statements one and three is correct. One and three correct means three will be the correct answer for this question.

[00:16:37]Three will be the correct answer for this question. Okay. Next question. Open loop transfer function is given. The break points lies in the root locus.

[00:16:46]Just draw the poles and zero location.

[00:16:49]Poles are at minus2 and minus5 and 0 is at minus2. The break point exist. See root locus not exist. Root log is not a root locus exist between these two poles and from this 0 to infinity. Whenever root locus exist between two adjacent poles there is a breakaway point. When root locus exist between two adjacent zeros that is called breakin point. Already we discussed all these things. Therefore in between minus2 and minus5. So break point lies in between minus2 to minus 5.

[00:17:21]Three will be the answer for this question.

[00:17:25]Next. The root locus plot of a system is shown below. The root locus plot of a system is given shown below. The gain margin for k equal to 12 is first of all the given value of k at marginal stability is 48.

[00:17:41]Value of k for marginal stability is 48 and is asking at 12. Therefore k will be four. That means gain is going to be four. When gain is going to be four, gain margin is 20 log 1 by gain 20 log 1 by gain.

[00:18:00]So 20 log k 20 log k 20 log k is 2² 20 log 2 square is 12 decibb.

[00:18:11]So answer is going to be told us with this root locus concepts completed.

[00:18:15]Whenever this kind of questions came K is given 48 then value of K at that particular point you see for marginal stability or critical stability K is given 48 and he's asking at 12.

[00:18:27]Therefore K is equal to value of K at marginal stability divided by given value of K. This is the formula. So that you will get K. So gain margin is 20 log gain.

[00:18:39]20 L gain that is 20 L 2 L 2² automatically that gain margin is going to be 12 Christmas.