Block Diagram in control systemsAny system can be described by a set of differential equations, or it can be represented by the schematic diagram that contains all the components and their connections. However, these methods do not work for complicated systems. The Block diagram representation is a combination of these two methods. A block diagram is a representation of a system using blocks. For representing any system using block diagram, it is necessary to find the transfer function of the system which is the ratio of Laplace of output to Laplace of input. Where Then, the system can be represented as Summing Point: When we want to apply a different input signal to the same block then the resultant input signal is the summation of all the inputs. The summation of an input signal is represented by a crossed circle called summing point which is shown in the figure below. Take off Point: When there is more than one block, and we want to apply the same input to all the blocks, we use a takeoff point. By the use of a takeoff point, the same input propagates to all the blocks without affecting its value. Representation of same input to more than one block is shown in the below diagram. How to draw the block Diagram:Consider a simple RL circuit Apply KVL Now taking laplace transform of Eq.1 and Eq.2 with initial condition zero From eq.3 and eq.4 From fig: Now taking laplace transform of Eq.5, and Eq.6 For the righthand side of eq.5, we will use a summing point. Here the output of summing point is given to the block, and the output of the block is I(s) Now the output I(s) is given to another block containing element SL and the output of this block is V0. By combining the above two figures, we get the required block diagram. Closed loop control system A system in which a feedback path is there is called a closedloop control system. In this system, the output is feedback into the error detector and then it is compared with the input signal. The feedback signal can be negative or positive. For positive feedback And for negative feedback Block diagram reduction rulesRule No.1. Blocks in Cascade When two or more blocks are connected in series, then the resultant block is the product of the individual blocks. Rule No.2 Blocks in parallel When two or more blocks are connected in parallel, then the resultant block is the sum of the individual blocks. Rule No.3 Moving a takeoff point ahead of a block When the takeoff point is moved ahead of a block (before the block), then the same transfer function is introduced in the takeoff point branch. Rule No.4 Moving the takeoff point after the block When the takeoff point is moved after the block, then a block with reciprocal of a transfer function is introduced in the takeoff point branch. Rule No.5 Moving a summing point beyond the block Rule No.6:Moving a summing point ahead of a block Rule No.7:Interchanging two summing points Rule No.8:Moving a takeoff point beyond a summing point Rule No.9:Moving a takeoff point ahead of a summing point Rule No.10:Eliminating a forward loop ExampleFind the transfer function of the following by block reduction technique. SolutionStep 1: There are two internal closed loops. Firstly, we will remove this loop. Step 2: When the two blocks are in a cascade or series we will use rule no.1. Step 3: Now we will solve this loop. Step 4:
Next TopicSignal flow graphs
