Salman Bin Abdulaziz University EE3511: Automatic Control Systems Block Diagram Dr. Ahmed Nassef EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Learning Objective To understand the concept of Block diagrams and their assumptions To be able to reduce complex block diagrams to a simple (one block) diagram EE3511_L8 Salman Bin Abdulaziz University

Block Diagram of Electrical Communication System channel Input signal Transmitter Receiver Output signal The block diagram illustrates the functional parts of the communication system but many details are hidden More details can be added by drawing detailed block diagram for each the shown subsystems. EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Block Diagrams X Y G G H A block diagram is pictorial representation of systems. It shows different components (subsystems) that make a system and shows their interactions. Each rectangular block represents a subsystem. Inputs are represented by arrows entering the block. Outputs are represented by arrows leaving the block. EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Block diagrams A block diagram is used to represent linear relationship between the input and the output of a subsystem. Let the input and the output be U and Y, the relationship between U and Y is represented by a rectangular block having a transfer function G G U Y = G U EE3511_L8 Salman Bin Abdulaziz University

Block Diagram Notation Transfer function block V=GX Summing point The output of the sum point is the algebraic sum of the entering signals E=V-W X V Y E G P Pickoff point Variables connected at pickoff point have identical values Y=Z Z W H The signal entering the sum point is multiplied by -1 EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Voltage Divider Input Output EE3511_L8 Salman Bin Abdulaziz University

Two-input-two-output systems inputs outputs EE3511_L8 Salman Bin Abdulaziz University

Main Objective of This Lesson Given a block diagram with input X and output Y, find a single block that represent the transfer function between X and Y X Y G P H X T=? Y EE3511_L8 Salman Bin Abdulaziz University

Rules of Block Diagram Manipulation Blocks in Series G H H G G Blocks in parallel H + G H Blocks in Feedback G G . 1+H G _ H X Moving a sum point X G Y Y G G X Moving a pickoff point X Y G G V V Y G EE3511_L8 Salman Bin Abdulaziz University

Block Diagram Manipulation Blocks in Cascade (Series) Y X HG Y X V G H Two blocks in cascade are replaced by a single block whose transfer function is the product of transfer functions EE3511_L8 Salman Bin Abdulaziz University

Block Diagram Manipulations Parallel Combination Y X G Y G+H X H Two blocks that are in parallel can be replaced by a single block whose transfer function is the sum of transfer functions EE3511_L8 Salman Bin Abdulaziz University

Block Diagram Manipulations Moving a pickoff point (#1) Z=V G Z=V G V Y G Y V You can move a pickoff point behind a block (Backward movement). EE3511_L8 Salman Bin Abdulaziz University

Block Diagram Manipulations Moving a pickoff point (#2) Z=X Z=X G─1 X G Y G Y X You can move a pickoff point ahead of a block (Forward movement). EE3511_L8 Salman Bin Abdulaziz University

Block Diagram Manipulations Moving a summing point (#1) Y X X Y G G G─1 U U You can move a summing point behind a block (Backward movement). EE3511_L8 Salman Bin Abdulaziz University

Block Diagram Manipulations Moving a summing point (#2) Y X X G G Y U U G You can move a summing point ahead of a block (Forward movement). EE3511_L8 Salman Bin Abdulaziz University

Block Diagram Manipulations Eliminating a Feedback Loop X Y G X Y H The feedback loop is replaced by the ratio of: forward path gain over (1 - the loop gain) EE3511_L8 Salman Bin Abdulaziz University

Example 1 Pressure Measurement System The pressure measurement system consists of A pressure sensor Signal conditioner Pressure Sensor Generates electric current proportional to the pressure G=0.1 mA/Pa Signal Conditioner (Amplifier) K=20 U Y EE3511_L8 Salman Bin Abdulaziz University

Example 1(solution) Pressure Measurement System Pressure Sensor Generates electric current proportional to the pressure G=0.1 mA/Pa Signal Conditioner (Amplifier) K=20 P V T.F=20*0.1= 2 mA/Pa V P EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Example 2 Find the transfer function of the following system G H K ? EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Example 2(solution) Find the transfer function of the following system U V W Y G H K Y = KW = K (HV) = K H (GU) = KHG U KHG The transfer function of three blocks in series is the product of the three transfer functions EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University More Rules G G H H K K L L EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Example 3 Find the transfer function of the following system G H K ? EE3511_L8 Salman Bin Abdulaziz University

Example 3 (solution) Find the transfer function of the following system Replace by a single block GH G H K EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Example 4 Reduce the block diagram to a single block F X Y A B D E C ? Y X EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Example 4 Reduce the block diagram to a single block F X Y A B D E C Loop replaced by AB/(1-ABC) Parallel paths D+E F X AB . 1-ABC Y D+E EE3511_L8 Salman Bin Abdulaziz University

Example 4 Reduce the block diagram to a single block X Y X X Y F AB . 1-ABC Y D+E Two processes in series F X AB (D+E) 1-ABC X AB(D+E) . 1-ABC+FAB(D+E) Y EE3511_L8 Salman Bin Abdulaziz University

Example 5 Alternative way to solve Example 4 Reduce the block diagram to a single block F X Y A B D E C This is the same block diagram in Example 4 ? Y X EE3511_L8 Salman Bin Abdulaziz University

Example 5 Alternative way to solve Example 4 Reduce the block diagram to a single block F X Y A B D E C Replacing the parallel blocks F X Y A B D+E Move the pickoff point in front of D+E block C EE3511_L8 Salman Bin Abdulaziz University

Example 5 Reduce the block diagram to a single block X Y X Y F A B D+E Replacing the cascade blocks . 1 . D+E C F X Y AB(D+E) . C . D+E Replacing the parallel blocks EE3511_L8 Salman Bin Abdulaziz University

Example 5 Reduce the block diagram to a single block X Y X Y AB(D+E) ─ F Replacing the cascade blocks then the feedback loop X AB(D+E) . 1-ABC+FAB(D+E) Y EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Homework Find the transfer function relating X and Y K X Y G M H EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Summary Block diagrams are for linear systems Apply the rules of block manipulation to simplify the block diagrams Alternative approaches can be done in reduction EE3511_L8 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Keywords Summing point Pickoff point Transfer function Cascade combination Parallel combination Feedback combination Block diagram Block diagram reduction EE3511_L8 Salman Bin Abdulaziz University