 Hello, I am Milka Jagale working as assistant professor in Department of Mechanical Engineering, Walton Institute of Technology, Solapur. Today, we are going to see block diagram reduction rules, learning outcome. At the end of the session, students will understand the rules to reduce the block diagrams in the control system. So, the content for today's presentation is rules for block diagram reduction. So, these four rules we have already studied in the previous video. So, just have a look over them. When two blocks are connected in series, then they can be algebraically multiplied. When two blocks are connected in parallel, then they can be algebraically added or subtracted depending on the sign of the feedback. For eliminating the feedback loop, we have seen if there is a negative sign, then if there is a negative feedback, we have to say we have to take positive. The third rule states eliminate the feedback loop in which we are, if the system has one feedback, one forward, one takeoff and one summing, then these can be reduced to a single block which states G of S upon 1 plus or minus G of S H of S. And the fourth law is associative law for summing point. So, it states that the position of a two summing points can be changed if the both are connected in series without presence of summing or takeoff. Now these rules we are going to see in detail today that is fifth rule shifting summing point before a block or after the block and shifting takeoff point before a block, after a block and then shifting takeoff point after a summing point, shifting takeoff point before a summing point. So, before going to the laws, I want to tell you why these rules are used. These rules are very important because these are used to reduce the block diagram into a single equivalent block. So, when a complicated block diagram is given with n number of blocks, so by using these rules we can reduce the block diagram. So, let us see. Rule number 5 states shifting summing point before a block. Now shifting summing point before a block. To shift a summing point before a block, another block having transform function 1 by g is added before the summing point. Now, if you see in this figure, this is a summing point and this is a g block and I need to shift to the summing point before the block, then I need to add one more block having transfer function 1 by g before that summing point. If you see the output of this is x plus g into r of s. How this came? Output is x plus g that is gain of this block into reference signal. So, that is x plus g into r of s is the output of this and what is the output of this? Before you are shifting the takeoff summing or you are using the rules, keep in mind that the output should not be changed. By doing this or by applying the rules before and after the procedure, the output should remain same like if you see here, the output of this is also same that is g r plus x. So, this states that when you need to shift a summing point before a block, one more block is added with this transfer function 1 by g that is whatever this function is present over here that is added over here so that we can shift that summing point before a block. So, these was the rule number 5. Now, rule number 6 that is a reverse shifting a summing point after a block. Now summing point is present over here and I want to shift the summing point after a g block after g block. So, what is the procedure? First, let us see what the rule states. To shift a summing point after a block, add a block having same transfer function at the summing point. So, this is what I have shown here. If I want to shift the summing point after a block, I need to add the same block, I need to add the same transfer function at that summing point. Now if you see the output of this is r plus x into g that is r plus x into the gain of this block. So, let us see what is this? If you see the output at this point, see of us nothing but x into g plus r into g which is both same. The output gain by this and output gain here both are same even after making the shifting procedure the output has not changed. So, we have got our requirement without changing the output. So, this is rule number 6 where we can shift the summing point after a block. Now our rule number 7 is shifting takeoff point before a block. Now, let me tell you what is this takeoff point, takeoff point or branch point. To shift a takeoff point before a block, add a block having transfer function g in series with the signal taking from the takeoff point. Now if this is the problem and you want to shift to this takeoff point before the block. So, what can I do? If you see in this figure you see this x this point x point is taken before the block. So, to do that a transfer function having whatever the transfer function was present over there that is added in series with the takeoff point can see here and the output of both that is output of figure A is r into g plus x into g. So, what is the output of this figure C? It is same. So, that is why when you want to shift the takeoff point before a block you need to add a block having transfer function g in series with the takeoff point from that takeoff point. So, this is what we have added g in series with the takeoff point. Next rule number 8 reverse shifting takeoff point after the block. This is nothing but reverse of the previous case now I want to shift this takeoff point after the block g. If you see this figure A this is the takeoff point I want to shift this takeoff point after point g. So, let us see what is the output at this C of s is nothing but r into g. If I shift this takeoff point I need to add a block having transfer function 1 by g in series with the signal taking from that takeoff point. In the previous case we have added only g whereas in this case we have added a transfer function having 1 by g in series with that takeoff point ok. This was rule number 8 and in both case the output is same that is C equal to rg and C equal to rg. So, this is same next rule number 9 shifting takeoff point after a summing point. Now, I want to shift this takeoff point after the summing point. Let us see what the rule states to shift a takeoff point after a summing point one more summing point is added in series with takeoff point. So, I want to shift to this takeoff point after the summing point. So, what is done one more summing point is added in series with the takeoff point. So, this is what is the case I want like this for this they have done they have added one more summing in series with that takeoff point. The output at this and this both are same. So, that is why this was rule number 9. Now, shifting takeoff point so, the output in both case this is same that is C equal to r plus or minus y and this is also same. So, that is why this is done. Now, to shift the takeoff point rule number 10. Rule number 10 states that to shift a takeoff point before a summing point we need to add a summing point in series with takeoff point. So, this is the situation we need to shift the takeoff point before the block. This is the situation and we need this. So, for this we have to add one more summing point in series with that takeoff point. So, if you see the output at this and output in this both are same. So, there is no change in output that is why this is valid rule. We can use this rule for shifting so, that the block diagram is reduced. These are the references. Thank you, thank you, thank you.