 I am Milka Jagle working as assistant professor in Department of Mechanical Engineering, Wolchen Institute of Technology, Solapur. Today we are going to learn about block diagram reduction rules. We have already seen why block diagrams are used and what is the use of block diagrams. So, today we are going to see how to reduce the complicated systems by using block diagram reduction rules. So, first in this video we will see about what are those rules. Let us see learning outcome. At the end of the session student will be able to understand the rules to reduce the block diagrams in the control system. So, these are the content canonical form rules for block diagram reduction and references. So, these are the rules. There are total 10 rules. In this video we are going to see four rules. So, rule number one blocks in series or cascade. Rule number two blocks in parallel. Rule three eliminate feedback loop and rule four associative law for summing point. So, before moving forward I want to ask a question. What is series connection or parallel connection? So, I want you to pause the video and think about what is series and parallel connection. Have you heard series connection and parallel connection like resistances connected in series, resistance connected in parallel. So, what is series connection? Let us see series connection is a connection where blocks are arranged one after the another or blocks are connected one after the another. That is known as a series connection or the things are called to be in series connection if the blocks are connected one after the another. Now, parallel connection. The system is parallely connected when the blocks are connected one below the other like the same signal flows but they are connected one above the another or one below the another. Let us see further. So, rule number one is blocks in series or cascade. So, why these rules are used? Let me tell you these rules are used to simplify the block diagrams. First rule is blocks in series or cascade. These rules are used when the blocks are connected in series like if you see in this figure number two that is G1 block and G2 block are connected one after the another then they are seriously connected. Now, if the blocks are connected in series that can be optimized or that can be concluded in a single block simplified block that is G1, G2, R of S. If you see the definition that is blocks in series, the blocks which are connected in series may be algebraically combined by multiplication. Whenever you see two blocks connected in series then the gain of two blocks are to be multiplied and an equivalent block is formed. But remember that if two blocks are connected in series there should be no any takeoff point or summing point. We will see what is takeoff point. We have already seen actually in the before in the previous video we have already seen what is takeoff point and summing point. If there is a takeoff point here then this rule is not applicable. This rule is applicable only if two blocks are connected in series and there is absence of takeoff or summing point. Let us move forward. Now, rule number two, blocks in parallel. The blocks which are connected in parallel get added algebraically. Now, what is blocks connected in parallel? If you see here G1 block G2 block and G3 block are connected one below the other and the same input signal goes through all and they are given to this summing point. So, the signal flowing through G1 block is the output of G1 block is RSG1. Here it is RSG2 whereas it is RSG3. These are given when blocks are connected in series then they can be algebraically added just make sure that what is the sign of the output. Here it is G1 plus G2 minus G3. If you see here G1 is plus G2 is plus and G3 is minus. So, these all complicated this complicated system can be converted into a single block that is this one. So, these were the second rule. Now, moving forward third rule that is eliminate the feedback block. This is the feedback control system where R of s is the reference signal E of s is the error signal B of s is the feedback signal taken from this output and given backed and then this is the takeoff point. Now, let us see how to eliminate this feedback loop. These complete feedback loop is converted in only one block that is this block G of s upon 1 plus or minus G of s H of s. What is this? How it can be converted? Let us see this. Here in figure you see here error signal is nothing but R of s reference signal plus feedback signal that is B of s. Now, what is this B of s feedback signal? Feedback signal is nothing but the signal with the output signal C of s and then H of s. And what is C of s is nothing but error signal into gain. What is this gain we have got? So, from these three equation we find that error signal is nothing but C of s upon G of s. But equation 3 states that C of s is nothing but error signal into gain of that block. So, in conclusion we see that this complete feedback loop is converted or transformed into a single block that is G of s upon 1 plus or minus G of s into H of s. Now, let me tell you what is this plus this is plus or minus. So, just ignore this one this is plus or minus. When to take plus sign, when the feedback is negative, when the feedback is negative then you need to take here plus sign 1 plus and if the feedback is positive then you need to take here negative that is 1 minus. So, this is how we can eliminate the loop that is feedback loop. I hope it is clear whenever this feedback loop is given which consists of one summing point, one takeoff point, one G block and H block that is one forward block and one backward block. We can also say it is forward path and reverse path. So, whenever this loop is given that is thus can be also known as a complete loop. This is given that time you need to write this equation that is converted into this equation G of s upon 1 plus or minus G of s H of s I repeat plus sign is taken if there is a negative feedback and minus is taken when positive feedback. Next rule. So, as I have discussed here you see here G 1 G 2 are multiplied here they are seriously connected and then there is a feedback loop. This is what we got these are converted into a single block. This is the output when we have input given is this we have the system. This system is converted into single block. Next associative law for summing point. This states that this law states that the order of summing point can be changed if two or more summing point are in series. Let me tell you if two or more summing points are connected one after the another without any block or without any takeoff point in between them then the position of summing point can be changed. If you see here in figure number 5 a here it is a b 1 summing point and b 2 summing point. The output of this is R of s minus b 1 minus b 2 and if you see in figure number 5 b you see that b 2 is interchanged and b 1 is interchanged according to the law of associative law. If you see here figure number b b 2 and b 1 are interchanged but the output remains same that is R of s minus b 1 and b 2. So, this equation and this equation both are same it states that summing points can be changed. So, what is the need of summing point? Why we need to change the position of summing point? Because when complicated block diagram is given to you when a complicated system with many blocks then the main motto or the main focus is to reduce the block diagram to a single block. So, in that case according to the condition according to the you need to judge whether the system how system can be simplified. We can there are many rules like shifting takeoff point shifting summing point we are going to see in the further videos but for time being this is the law which states summing points can be interchanged. There is no change in the output if summing points are interchanged. So, these are the references. Thank you.