 Hello, I am Malkha Jagle working as assistant professor in Department of Mechanical Engineering Volchon Institute of Technology, Solapur. Today we are going to study about Introduction to Block Diagrams. So, let us see learning outcome. At the end of the session students will be able to understand the basics of block diagrams in the control systems. So, these are the contents. What is block diagram, why block diagram is used, block diagram fundamentals, canonical form or standard feedback form of a control system, advantages of block diagram, disadvantages of block diagram and references. So, coming for the question, what is block diagram? Block diagram is a pictorial representation of the system. Any system can be represented in a sequence of operations which are organized by the interconnecting the blocks. The block diagram represents the relationship between input and output of a system. The complicated systems can be completely represented by connecting different blocks. The question arises why block diagrams are used or where we use this block diagrams. So, can you please think about where these block diagrams are used? Let us see. In most of the practical systems, it is very difficult to analyze the entire system. So, there is a need to break the system in small parts. So, when the system is break or it is broken into small parts, then it can be analyzed very easily. So, to analyze such complicated systems, block diagrams are used. The blocks in the systems represent the physical system. Every block is known as a functional block. So, the blocks are arranged according to the sequence of the operations to be performed in the control system. So, I hope it is clear where the block diagrams are used and why they are used. So, let us see block diagram fundamentals. So, before going further, so I just want to focus on what are the elements which are present in the block diagrams. So, let us see. First is block diagram. As I have already said before, it is pictorial representation of cause and effect relationship between input and output of a system. Here, figure 1 shows the block diagram. So, it is a block which represents the physical system. Input signal is given to the system and the processing is done and the output is given here. So, this is nothing but a block. Second is output. The value of output is multiplied to the value of block gain to get the output. So, let us see what is the formula for this. Output is equal to gain into input. So, what is this gain? Gain is nothing but the value which is present over here, that is value which is present in the system. So, that is nothing but gain. That gain multiplied by input is nothing but output. So, we will see in the further slides what actually gain means. Now, next is summing point. Summing point, the name itself indicates it is a summing point where more than one signal can be added or subtracted, that point is known as a summing point. If you see here in figure number 3, it shows a summing point where there are three signals are present coming from here that is positive signal, this is negative and this is one more signal. So, in this, at this location of the summing point, two or three or more signals can be added or subtracted which are going outside of the block. Now, next is take off point. Take off means we are taking the point. In this reference it means we need to take the signal from the system and we need to give it back or we need to give that signal to some point else. Now, if you see the definition of take off point, the point from which a signal is taken for the feedback purpose is called as take off point. So, you see here black dot in figure number 4 is a take off point. So, this is output, this is signal from the input side and this is take off point. This take off point is shifted according to the requirement of the block diagram construction. The main aim of block diagram reduction is to convert a complicated system into simple or single block so that we can analyze it very easily. Next, forward path. Forward path is nothing but the direction of flow of signal is from input to output. This is input R of s is input and C of s is output. The direction of flow of signal from input to output that is from R of s to C of s. The signal R of s goes to block G1 and that gain is given to then G2 and then this is the output. The signal flow from R of s to C of s is known as a forward path as shown in figure number 5. Next, feedback path. Feedback means we are taking the signal and giving it back to the input that is through summing point. As I told here signals can be added or subtracted according to our requirement. So, in this the signal from the output is feedback to the input so as to get a correct output. So, this is the feedback path. Next, types of feedback. Just now we have seen forward path and feedback path. Now there are types of feedback that is positive feedback and negative feedback. What is this positive feedback means? Positive feedback is a feedback with a positive sign. The signal is added. Here you see the plus sign is there. The signal is taken from output and it is given at this point. This is nothing but positive feedback. If you see in this diagram, you see the feedback is negative. That signal from C of s is taken and then given back to input that is at summing point it is given back and then it forwarded to the G block. So, this is the negative feedback. I hope these are clear. Now next, any feedback system or any control system can be simplified and it can be solved. For that you need to convert a complicated block diagram in a simple canonical form. What is simple canonical form or simple form or canonical form? It is nothing but a loop which consists one forward path, one feedback path, one summing point and one takeoff point. It completes a loop. So, this is what a canonical form is known as. A system is given with n number of blocks when these blocks are reduced to a single block which consists one feedback, one forward, one summing and one takeoff. If these four terms are there then that is known as canonical form, control system or feedback control system. So, if you see this is a summing point, if you this is a summing point, this is G block, this is H block, this is a takeoff point, feedback is given here both I have given this is just take it as plus or minus that is positive or negative. This is error signal, this is feedback, E of s is error signal, B of s is feedback signal R of s reference signal and C of s output signal. If you see in the next slide, these canonical form is converted into simple block. This feedback system can be converted into single block that is this one, G of s H of s can be converted into single block that is G of s upon 1 plus or minus G of s H of s. Now, the positive sign should be taken if there is a negative feedback and negative sign should be taken if there is a positive feedback. So, if you see from the this derivation, so it is proved that if there is a negative feedback we need to take positive sign while solving here and if there is a positive feedback we need to take negative sign. So, this is the overall derivation that is to how to simplify a canonical form. I repeat it is nothing but one summing, one takeoff, one G block that is feedback path and one forward path. Okay, now what are advantages of control system? As a very simple to construct complicated systems, function of individual element can be visualized from block diagram. It gives information of individual as well as performance of the system by using transfer function shown in the block diagram. Disadvantages of block diagram, block diagram for given systems are non-unique, source of energy in the system is not given in the diagram. In the procedure of reduction of block diagram, some important functions may be omitted or hidden there is no check for it. The block diagram does not give any information about the physical construction. These are the disadvantages of block diagram. These are the references. Thank you.