 Welcome to the session. I am Priyanka Vedla and today we will see about block diagram reduction rules. These are the learning outcomes. At the end of the session students will be able to apply the rules for reducing the block diagram and second evaluate transfer function of the system. These are the contents of this video lecture. Already you know block diagram is a pictorial representation of the given system and there is a relationship between input and output of a system. The entire complete system can be splitted into number of blocks and each block analyzed separately conveniently. Now recall few rules for block diagram reduction that I studied in previous video lecture. Now pause the video for a minute and you have to recall few rules for block diagram reduction. So rule one is associative law. There in this we have to consider two summing points. If we change the position of two summing points, that time also the output remains same in both conditions. Blocks in series that is a rule two. There is a the transfer function of the blocks if connected in series then get multiplied with each other. Rule three block in parallel. The transfer function of the blocks which are connected in parallel at that time the blocks are the transfer function of that system get added algebraically. If there is a negative sign then you have to consider the negative sign. Then rule four is eliminate feedback loop. Before moving towards to rule four we have to recall the transfer function of closed loop system. Now pause the video for a minute and you have to recall transfer function of closed loop system. So transfer function is nothing but output upon input. So c of s upon r of s is equal to g of s divided by 1 plus or minus g of s into h of s. So we see the rule four. Now consider a system. Here the r of s and the feedback signal input is given to the summing point. Here the points are added. The inputs are added here then it is given to g1. In this system g1 and g2 are connected in series. So we have to reduce this block diagram. If the blocks are in series then we get multiplied with each other. So here g1 and g2 the transfer function of the systems are multiplied and then connect the feedback loop that is a h. So how it is calculated the transfer function of the system that is nothing but c of s upon r of s. Here if the sign is negative at that time you have to consider the positive sign. Means c of s divided by r of s is equal to g1 g2 upon 1 plus g1 g2 into h. So in this way you have to eliminate the feedback loop from the block diagram. If there is a negative sign here we get the positive. If there is positive then here we get negative. Then rule five shifting a summing point before the block. In this case in this system r of s into g here we get r of s into g then this input signal is added at summing point with input x. So here we get r of s into g plus x. Now shifting a summing point before the block. One thing remember always each time before shifting and after shifting the output must be same. So for that purpose we make some arrangement for each time. So in this case first the summing point is shifted before the block. For that output remains same. We will do some changes in that. What is the changes? The input x is multiplied with the inverse of the transfer function of the system that is a 1 by g then added at summing point in series with all other signals. So here we get r of s plus x by g and this signal is given to the this second system. Then we get c of s is equal to g into this one. After simplification we get this. So this is a rule five. Then rule six shifting a summing point after the block. Shifting a summing point this is a summing point. You have to shift this summing point after the block. So first before shifting first you have to calculate the output. So here r of s plus x this is given to this and here we get g into r of s plus x. So after shifting the summing point here we will do some changes. Again x is multiplied with the same transfer function of the g and then added at summing point in series with all other signals. So here we get r of s into g plus x into g. So after simplification we get the same output. Shifting a summing point after the block at that time you have to consider the same transfer function is added at summing point. Rule seven shifting a takeoff point before the block. This is a takeoff point a point from which a signal is taken for the feedback purpose. So here we get two equations for x and for c of s. So for x and c of s we get the same equation that is r of s into g this one. So shifting a takeoff point before the block. In this case we get x is equal to r of s and c of s is equal to r of s into g. If we compare these outputs at that time x is different. So again we will do some changes in that. When we shift a takeoff point before the block at that time same transfer function is connected is in series with all other input signals. So here x is multiplied with g and then it is given to the next block. So here we get x is equal to r s into g and c of s is equal to r s into g. So shifting a takeoff point before the block at that time you have to multiply directly transfer function that is a g with input signal. Rule eight shifting a takeoff point after the block. In this case before shifting here we get two equations again x is equal to r of s and c of s is equal to r of s into g. Now shifting a takeoff point after the block. So to shift a takeoff point after the block. So again in this case we get x is equal to and c s is equal to same equation x is equal to r s into g and c of s is equal to r s into g. So this is a first case but we want same output. So again the input x is multiplied with reciprocal of the transfer function of the system in series with all other signals. So here x again we get the two equations x is equal to r s into g into 1 by g. So here we get r of s and then for c of s is equal to r s into g. Here we will get same output. Then rule nine shifting a takeoff point after the summing point. Here there are the two rules rule nine and rule ten are critical rules. So in this case here we will shift the takeoff point after the summing point means takeoff point and summing point both are considered here. So here z is equal to r of s and c of s is equal to r of s plus or minus y. Now we consider the second case that is a shifting a takeoff point after the summing point. In this case one more summing point is added c of s is equal to r of s plus or minus y. Here we get but for z is equal to means for getting z is equal to r of s we will do some changes that is here we get r of s plus or minus y. So here for z is equal to r of s for that we will y is inverted means y is added with inverting sign. So minus plus is connected to this summing point means z is equal to r of s plus minus y and invert of y signal minus plus y. So here we get z is equal to r of s and c of s is equal to r of s plus minus y. Then rule ten shifting a takeoff point before the summing point for that before shifting here we get z is equal to r of s plus or minus y and c of s also same r of s plus or minus y. But after shifting to consider the same summing point means we can add one more summing point and in this case see z is equal to r of s and this y is again added here. So z is equal to r of s plus or minus y and for c of s r of s plus or minus y. These are the references. Thank you.