00:01
In this question, we have been given the block diagram of the control system as we can see here.
00:06
We need to first find out the transfer function which is denoted by g of s and it is equals to y of s divided by r of s.
00:18
So let us see how can we do this.
00:20
We know that our standard circuit for the system is shown as this.
00:26
Correct so if i draw my standard system it will be somewhat of this same so this is here g of s the transfer function and here it is h of s correct and then they give us c of s so this is a standard one and here i'm having my r of s so now if i consider so let g of s is equal to n divided by d then what will be value of t of s so that we know it is c of s divided by r of s it equals to g divided by one plus gh correct or this is further equal to n divided by d plus n of h so this is what we are getting here.
01:28
Now what we can do, if i now find out the ratio, c .s divided by r of s.
01:37
So it will be what, 36 divided by.
01:40
Here we have been given 36 divided by 3 and this is 1 divided by s.
01:46
So from there i'm getting s times of s plus 3 plus 36k plus 36.
01:56
So i can say now my the transfer function, which is denoted by g of s equals to y of s divided by r of s, it will be given by 36 divided by s squared plus 3 plus 36k times s plus 36.
02:24
Okay, so this is my required transfer function here now we will see the next part what have been asked in the next part let's see that so in the second part we have to find out the value of k such that the damping ratio is point seven so we need to find out the value of k for which the damping ratio of the system okay? we just denoted by a zeta is equals to zeta is equals to 0 .7 we have been given correct this is a damping ratio so let's see how can we do this part so to see this we know that the peak time which is denoted by tp is equal to pi divided by wd and it will be pi divided by wd is further equals to w n under root of 1 minus zeta square correct so it becomes pi divided by six under root 1 minus.
03:35
This is given to be 0 .7.
03:37
So this will be coming out to be 0 .73 second.
03:42
So this is my peak time.
03:44
Now what i will get with this, peak overshoot if i find out, peak overshoot with given by p raise to minus the stamping ratio times pi.
04:03
Divided by under root 1 minus damping ratio square.
04:08
Correct.
04:10
Multiplied with undread.
04:12
So solving this, we know all the values here.
04:15
So solving this, what i'm going to get is 4 .59 %...