A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. CHAPTER 6 BLOCK DIAGRAMS 6.1DEFINITIONS Block Diagram is the shorthand, pictorial representation of the cause-and-effect relationship between the input and the output of a physical system. It provides a convenient and useful method for characterizing the functional relationships among the various components of a control system. SystemcomponentsarealternativelycalledElementsofthe System.TheSimplestFormorCanonicalFormofaBlockDiagramisa single block, with one input and one output. The interior of the rectangle representing the Block usually contains the description or name of the element, or the Transfer Function or Transmittance representing the element, or the symbol forthemathematicaloperationtobeperformedontheinputtoyieldtheoutput.TheArrows represent the direction of information or signal flow. Theoperationsofadditionandsubtractionhaveaspecial representation.Theblockbecomesasmallcircle,calledtheSumming Point or Summer, with the appropriate plus or minus sign associated with thearrowsenteringthecircle.Theoutputisthealgebraicsumofthe inputs.Anynumberof inputsmayenterasummingpointbut mustonly have one output. In order to have the same signal or variable be an input to more than one block or summing point, a Takeoff Point or Pickoff Point is used. This permits the signal to proceed unaltered or unchanged along several different paths to several destinations. 6.2CONTROL SYSTEM TERMINOLOGIES PRESENTED IN A BLOCK DIAGRAM PlantorProcess,orControlledSystemisthesystem,subsystem,process,orobject controlled by the feedback control system. ControlledOutputistheoutputvariableofthePlantunderthecontroloftheFeedback Control System. ForwardPathisthetransmissionpathfromthefirstsummingpointtotheControlled Output. A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. Feedforward (Control) Elements are the components of the Forward Path that generate the ControlSignalappliedtotheplant.Note:FeedforwardElementstypicallyincludecontroller(s), compensator(s) or equalization elements, and/or amplifier(s). ControlSignalorManipulatedVariableistheoutputsignaloftheFeedforwardElements applied as an input to the Plant. FeedbackPathisthetransmissionpathfromtheControlledOutputbacktothefirst summing point. Feedback Elements establish the functional relationship between the Controlled Output and the Primary Feedback Signal. Note: Feedback Elements typically include sensor(s) of the controlled output, compensator(s), and/or controller element(s). Reference Input is an external signal applied to the Feedback Control System, usually at the first summing point, in order to command a specified action of the Plant. It usually represents ideal (or desired) plant output behavior. Primary Feedback Signal is a function of the Controlled Output, algebraically summed with the Reference Input to obtain the Actuating (error) Signal. An Open-Loop System has no Primary Feedback Signal. TheActuatingorErrorSignalistheReferenceInputSignalplusorminusthePrimary FeedbackSignal.TheControlActionisgeneratedbytheActuating(Error)SignalinaFeedback Control System. Negative Feedback means the summing point is a subtractor. Positive Feedback means the summing point is an adder. 6.3ADDITIONAL DEFINITIONS A Sampler is a device that converts a Continuous-Time Signal into a Discrete-Time Signal. A Hold or Data Hold Device is one that converts the Discrete-Time Output of a Sampler into a particular kind of Continuous-Time or Analog Signal. An Analog-to-Digital Converter is a device that converts an Analog or Continuous Signal into a Discrete or Digital Signal. ADigital-to-AnalogConverterisadevicethatconvertsaDiscreteorDigitalSignalintoa Continuous or Analog Signal. A Computer-Controlled System includes a computer as the primary control element. A Transducer is a device that converts one energy form to another. TheCommandisaninputsignal,usuallyequaltotheReferenceInput.Whentheenergy formofthecommandisnotthesameasthatoftheprimaryfeedback,aTransducerisrequired between the command and the reference input. WhenthefeedbackelementconsistsofaTransducerandaTransducerisrequiredatthe input, that part of the Control System is called the Error Detector. AStimulusorTestInputisanyexternally(exogenously)introducedinputsignalaffecting the Controlled Output. A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. A Disturbance is an undesired stimulus or input signal affecting the value of the Controlled Output. The Time Response of a system, subsystem, or element is the output as a function of time, usually following application of a prescribed input under specified operating conditions. A Multivariable System is one with more than one input (multi-input), and/or more than one output (multi-output). The term Controller in a Feedback Control System is often associated with the elements of theforwardpath,betweentheActuating(Error)Signalandthecontrolvariable.Itisalso sometimes includes the summing point, the Feedback Elements, or both, and some authors use the term controller and compensator synonymously. Types of Controllers: 1.On-OffController(two-position,binarycontroller)hasonlytwopossiblevaluesatits output, depending on the input to the controller. 2.Proportional (P) Controller has an output proportional to its input. 3.Derivative (D) Controller has an output proportional to the derivative of its input. 4.Integral (I) Controller has an output proportional to the integral of its input. 5.PD,PI,DI,andPIDControllersarecombinationsofproportional(P),derivative(D),and integral (I) controllers. A Servomechanism is a power-amplifying Feedback Control System in which the controlled variable is mechanical position, or a time derivative such as velocity or acceleration. ARegulatororRegulatingSystemisaFeedbackControlSysteminwhichtheReference Inputorcommandisconstantforlongperiodsoftime,oftenfortheentiretimeintervalduring which the system is operational. Such an input is often called a Setpoint. 6.4COMBINATIONS OF BLOCKS BlocksinCascade:Anyfinitenumberofblocksinseriesmaybe algebraicallycombinedbymultiplicationofTransferFunctions.Multiplication of Transfer Functions is commutative. BlocksinTandem:Twoormoreblocksinparallelmaybe algebraicallycombinedtoasinglesumofTransferFunctionsor Transmittances. BlocksinaFeedbackConfiguration:Itisanarrangementof blockswhereoneblockisontheforwardpathhavingaforward transmittanceandtheotherblockisonthefeedbackpathhavinga feedback transmittance. TRANSFORMATION AND/OR REDUCTION OF BLOCKS IN A BLOCK DIAGRAM (BLOCK DIAGRAM ALGEBRA) NoTransformationEquationBlock DiagramEquivalent 1 Combining Blocks in Cascade ( ) X P P Y2 1= A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. 2 Combining Blocks in Tandem or Parallel, or Eliminating Forward Loop X P X P Y2 1 =( ) X P P Y2 1 = 3 Removing a Block from a Forward Path 4 Eliminating a Feedback Loop( ) Y P X P Y2 1 =XP P 1PY2 11||.|

\|= 5 Removing a Block from a Feedback Loop 6 Rearranging Summing Points Y X W Z = 7 Moving a Summing Point Ahead of a Block Y PX Z = 8 Moving a Summing Point Beyond of a Block ( ) Y X P Z = 9 Moving a Takeoff Point Ahead of a Block PX Y = 10 Moving a Takeoff Point Beyond of a Block PX Y = A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. 11 Moving a Takeoff Point Ahead of a Summing Point Y X Z = 12 Moving a Takeoff Point Beyond of a Summing Point Y X Z = 6.5SIMPLIFYING OR REDUCING SINGLE-INPUT, SINGLE-OUTPUT SYSTEMS IN BLOCK DIAGRAMS AND ITS TRANSFER FUNCTIONS Hierarchy of Operations for Combining Blocks: 1.Combine all Blocks in Cascade using transformation or reduction. 2.Combine all Blocks in Parallel or in Tandem using transformation or reduction. Then, check for cascades resulting after the combination. 3.EliminateallMinorFeedbacksorFeedbackLoopsusingtransformationorreduction.Then, check for cascades and blocks in parallel, respectively, resulting after the combination. 4.Shiftsummingpointsorsummerstotheleftandtakeoffpointstotherightofthemajor loopusingtransformationorreduction.Then,checkforcascades,blocksinparallel,and minor feedbacks, respectively, resulting after the shifting. 5.Repeat Steps #1 to #4 until the canonical form has been achieved for a particular input and output. Example:SolvefortheTransferFunctionofthefollowingblockdiagrambytransformationand reduction to its canonical form. Solution: Simplify the diagram and mark the blocks to combine. Assign variables with subscripts or numericalnotationstorepresentthetransmittancesofthecombinedblocks.Solveforthe combined transmittances. 2 s11 1 s11 s1 1 s1 s11 s111 s11 G+=+ +=++ ++=++ += ( ) ( ) 4 s 2 s34 s32 s12 G+ +=++= A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( ) 4 s 2 s3 4 s 2 s4 s 2 s34 s 2 s314 s 2 s33 G+ ++ + ++ +=+ +++ += ( ) ( ) 3 4 s 2 s33 G+ + += ( ) ( ) 3 4 s 2 s33 G) s ( R) s ( Y) s ( T+ + += = = Example:SolvefortheTransferFunctionofthefollowingblockdiagrambytransformationor reduction to its canonical form. Solution: Shift the summing point found after the block whose transmittance is equal to 8 ahead of that particular block.After shifting the summing point, simplify the diagram and mark the blocks to combine. Assign variables to represent the transmittances of the combined blocks.Solve for the combined transmittances. ( ) 1 s 8s 3811 ss 31 G+= +=( )18 s2 s 82 s16 2 s82 s28 182 G++=++ +=|.|

\|+ += ( )( )( ) 1 s 8s 3 1 s 81 s 8s 31 3 G+ +=((

+ =( ) ( )( ) ( ) 10 s s 18 s2 s s 810 s ss18 s2 s 84 G2 2+ + ++=+ +++= A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. ( )( ) ( )( )( ) ( )( )( ) ( )( ) ( ) ( )( ) ( )( )( ) ( ) ( ) 2 s s 8 10 s s 18 s2 s s 810 s s 18 s2 s s 8 10 s s 18 s10 s s 18 s2 s s 810 s s 18 s2 s s 8110 s s 18 s2 s s 85 G222222+ + + + ++=+ + ++ + + + ++ + ++=+ + ++++ + ++= ( )( )( )( ) ( ) ( )( ) ( ) | |( ) ( ) ( ) ( ) | | 2 s s 8 10 s s 18 s 1 ss 3 1 s 8 2 s s2 s s 8 10 s s 18 s2 s s 81 s 8s 3 1 s 86 G2 2+ + + + + + + +=+ + + + +++ += ( ) ( ) | |( ) ( ) ( ) ( ) | | 2 s s 8 10 s s 18 s 1 ss 3 1 s 8 2 s s6 G) s ( R) s ( Y) s ( T2+ + + + + + + += = = Example:SolvefortheTransferFunctionofthefollowingblockdiagrambytransformationor reduction to its canonical form. Solution: Simplify the diagram and mark the blocks to combine. Assign variables to represent the transmittances of the combined blocks.Solve for the combined transmittances. s5s15 1 G = =( )6 s12 s4 2 s2 s142 s112 s12 G+=+ + + +=|.|

\|+++= A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. Thetakeoffpointfoundaftertheblockwhosetransmittanceisequalto(3s/s+4)canbeshifted before the said block.After shifting the takeoff point, simplify the diagram and mark the blocks to combine. Solve for the combined transmittances. 4 s154 ss 3s53 G+=+ =( ) ( )( ) ( ) 3 s 4 s4 s s 3 s 3s3 ss4 ss 34 G+ ++ + +=+++= ( ) ( )( ) ( )( ) ( ) 15 4 s 6 s4 s4 s 6 s15 4 s 6 s6 s14 s15 6 s116 s15 G+ + ++=+ ++ + ++=|.|

\|+|.|

\|+++= ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( ) ( ) | | 15 4 s 6 s 3 s4 s s 3 s 3s3 s 4 s4 s s 3 s 3s15 4 s 6 s4 s6 G+ + + ++ + +=+ ++ + ++ + ++= ( ) ( )( ) ( ) ( ) | | 15 4 s 6 s 3 s4 s s 3 s 3s6 G) s ( R) s ( Y) s ( T+ + + ++ + += = = 6.6SIMPLIFYINGORREDUCINGMULTIPLE-INPUT,MULTIPLE-OUTPUTSYSTEMSIN BLOCK DIAGRAMS AND ITS TRANFER FUNCTIONS BY SUPERPOSITION METHOD TheSuperpositionMethodsolvesfortheTransferFunctionsbytransformingthemultiple-input,multiple-outputsystemintoasimplifiedsingle-input,single-outputsystemwhichwould represent the relationship between a certain input with a particular output. A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. Step 1: Ignore all outputs except the one being considered. Step 2: Set all inputs, except the one being considered, to be equal to zero. Step 3:Draw the resulting single-input, single-output Block Diagram. Step 4:Usingblockdiagramtransformationorreduction,transformtheresultingblock diagram to its canonical form to obtain the Transfer Function. Step 5:Repeat Steps #2 to #4 for each of the remaining inputs. Step 6: When all inputs have been considered, take the next output and repeat Steps #1 to #5. Do this process for each of the remaining outputs. ) s ( R) s ( Y) s ( TJIIJ= Example:SolvefortheTransferFunctionsofthefollowingblockdiagrambytransformationor reduction to its canonical form. Solution:Therearefour inputsandoneoutput.Thereshouldbe fourTransferFunctions forthis multiple-inputsystem.Thereisnoneedtoignoreallotheroutputsbecausethereisonlyone output. Set 0 ) s ( 4 R ) s ( 3 R ) s ( 2 R = = = 2 H 2 G 12 G1 A += 2 H 2 G 12 G 1 G2 H 2 G 12 G1 G 1 A 1 G 2 A+=+ = = 1 H2 H 2 G 12 G 1 G12 H 2 G 12 G 1 G3 A1 H 2 A 12 A3 A |.|

\|+++= += 2 H 2 G 11 H 2 G 1 G 2 H 2 G 12 H 2 G 12 G 1 G3 A+ + ++= 1 H 2 G 1 G 2 H 2 G 12 G 1 G3 A+ += 1 H 2 G 1 G 2 H 2 G 12 G 1 G3 A) s ( R) s ( Y) s ( T111+ += = = A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. Set 0 ) s ( 4 R ) s ( 3 R ) s ( 1 R = = = 2 H 2 G 12 G1 A += ( ) 1 H 1 G 1 G 1 H 4 A = = ( ) 1 H 1 G2 H 2 G 12 G12 H 2 G 12 G5 A4 A 1 A 11 A5 A |.|

\|++= = 1 H 2 G 1 G 2 H 2 G 12 G5 A2 H 2 G 11 H 2 G 1 G 2 H 2 G 12 H 2 G 12 G5 A+ +=+ + ++= 1 H 2 G 1 G 2 H 2 G 12 G5 A) s ( R) s ( Y) s ( T212+ += = = Set 0 ) s ( 4 R ) s ( 2 R ) s ( 1 R = = = 2 H 2 G 12 G1 A += 1 H 1 G 4 A = 1 H 2 G 1 G 2 H 2 G 12 G5 A+ += 1 H 2 G 1 G 2 H 2 G 12 G5 A) s ( R) s ( Y) s ( T313+ += = = Set 0 ) s ( 3 R ) s ( 2 R ) s ( 1 R = = = 2 H 2 G 12 G1 A+= 1 H 1 G 4 A = ( )2 H 2 G 11 H 2 G 1 G6 A1 H 1 G2 H 2 G 12 G1 A 4 A 6 A+= += = A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. 12 H 2 G 11 H 2 G 1 G12 H 2 G 11 H 2 G 1 G1 6 A 16 A7 A|.|

\|++= = 2 H 2 G 11 H 2 G 1 G 2 H 2 G 12 H 2 G 11 H 2 G 1 G7 A+ + ++= 1 H 2 G 1 G 2 H 2 G 11 H 2 G 1 G7 A+ += 1 H 2 G 1 G 2 H 2 G 11 H 2 G 1 G7 A) s ( R) s ( Y) s ( T414+ += = = The Response: ) s ( R ) s ( T ) s ( R ) s ( T ) s ( R ) s ( T ) s ( R ) s ( T ) s ( Y4 14 3 13 2 12 1 11 + + + = 1 H 2 G 1 G 2 H 2 G 1) s ( R 1 H 2 G 1 G1 H 2 G 1 G 2 H 2 G 1) s ( R 2 G1 H 2 G 1 G 2 H 2 G 1) s ( R 2 G1 H 2 G 1 G 2 H 2 G 1) s ( R 2 G 1 G) s ( Y4 3 2 1+ ++ ++ +++ +=1 H 2 G 1 G 2 H 2 G 1) s ( R 1 H 2 G 1 G ) s ( R 2 G ) s ( R 2 G ) s ( R 2 G 1 G) s ( Y4 3 2 1+ + + = Example:SolvefortheTransferFunctionsofthefollowingblockdiagrambytransformationor reduction to its canonical form. Solution: There are two inputs and two outputs.There should be four Transfer Functions for this multiple-input, multiple-output system. Ignore ) s ( Y2and set 0 ) s ( R2= ( ) 4 G 3 G 2 G 2 G 4 G 3 G 1 A = = ( ) 4 G 3 G 2 G 1 G 11 G1 A 1 G 11 G2 A += += 4 G 3 G 2 G 1 G 11 G2 A= 4 G 3 G 2 G 1 G 11 G2 A) s ( R) s ( Y) s ( T1111= = = Ignore ) s ( Y2and set 0 ) s ( R1= ( ) 4 G 3 G 1 G 1 G 3 G 4 G 3 A = =A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. ( )4 G 3 G 2 G 1 G 14 G 3 G 1 G4 A2 G 4 G 3 G 1 G 14 G 3 G 1 G2 G 3 A 13 A4 A= += += 4 G 3 G 2 G 1 G 14 G 3 G 1 G4 A) s ( R) s ( Y) s ( T2112= = = Ignore ) s ( Y1and set 0 ) s ( R2= ( ) 4 G 2 G 1 G 4 G 2 G 1 G 5 A = = ( )4 G 3 G 2 G 1 G 14 G 2 G 1 G6 A3 G 4 G 2 G 1 G 14 G 2 G 1 G3 G 5 A 15 A6 A= += += 4 G 3 G 2 G 1 G 14 G 2 G 1 G6 A) s ( R) s ( Y) s ( T1221= = = Ignore ) s ( Y1and set 0 ) s ( R1= ( ) 3 G 2 G 1 G 3 G 1 G 2 G 7 A = = ( )4 G 3 G 2 G 1 G 14 G8 A3 G 2 G 1 G 4 G 14 G7 A 4 G 14 G8 A= += += 4 G 3 G 2 G 1 G 14 G8 A) s ( R) s ( Y) s ( T2222= = = The Responses: 4 G 3 G 2 G 1 G 1) s ( R 4 G 3 G 1 G4 G 3 G 2 G 1 G 1) s ( R 1 G) s ( R ) s ( T ) s ( R ) s ( T ) s ( Y2 12 12 1 11 1= + =4 G 3 G 2 G 1 G 1) s ( R 4 G4 G 3 G 2 G 1 G 1) s ( R 4 G 2 G 1 G) s ( R ) s ( T ) s ( R ) s ( T ) s ( Y2 12 22 1 21 2+ = + = 6.7BLOCK DIAGRAM CONSTRUCTION: ELECTRICAL NETWORK TO BLOCK DIAGRAM EQUIVALENT Recall: ) t ( i R ) t ( vR R=R) t ( v) t ( iRR=A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. Then:) s ( RI ) s ( VR R=R) s ( V) s ( IRR=Recall:) t ( idtdL ) t ( vL L==t0L Ldt ) t ( vL1) t ( iThen:) s ( LsI ) s ( VL L=Ls) s ( V) s ( ILL=Recall: =t0C Cdt ) t ( iC1) t ( v ) t ( vdtdC ) t ( iC C=Then: Cs) s ( I) s ( VCC= ) s ( V Cs ) s ( IC C=Recall:R) s ( I) s ( VRR= Ls) s ( I) s ( VLL=Cs1) s ( I) s ( VCC= Example:SolvetheTransferFunctionoftheelectricalnetworkshownbyblockdiagram transformation and reduction. Solution:Toconverttheelectrical networktoitsequivalentblockdiagram,redrawandassignall thecurrents,voltages,andimpedances,expressingeverythingintheirequivalentLaplace Transforms.If 0 ) s ( IL= , then,0 ) s ( VL= ,) s ( V ) s ( VO C= ,) s ( I ) s ( I ) s ( IC R= = . RCs1Cs1R11 B = = 1 RCs1RCS11RCs11 B 11 B2 B+=+=+= 1 RCs12 B) s ( Vi) s ( Vo) s ( T+= = = Example:SolvetheTransferFunctionoftheelectricalnetworkshownbyblockdiagram transformation and reduction. A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. Solution:If0 ) s ( I2 R= , then,0 ) s ( V2 R= ,) s ( Vo ) s ( Vb = ,) s ( Ib ) s ( IL= . The diagram above can be more clearly shown by removing the guide signals. Simultaneouslyshiftthesummingpointfoundaftertheblockwhosetransmittanceis1/R1to ahead of that block, and shift the takeoff point found after the block whose transmittance is 1/Ls to beyond the block whose transmittance is 1/C2s. s 1 C 1 R1s 1 C11 R11 A = = 2s 2 LC1s 2 C1Ls12 A = = s 2 C 1 R s 2 C 1 R 3 A = = s 1 C 1 R11s 1 C 1 R11 1 A 11 A4 A+= += 1 s 1 C 1 R1s 1 C 1 R1 s 1 C 1 Rs 1 C 1 R14 A+=+= A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. 1 s 2 LC1s 2 LC1 s 2 LCs 2 LC15 As 2 LC11s 2 LC11 2 A 12 A5 A222222+=+=+= += 1 s 2 LC11 s 1 C 1 R15 A 4 A 6 A2++= = ( ) ( ) 1 s 2 LC 1 s 1 C 1 R16 A2+ += 3 A 6 A 16 A7 A +=( ) ( )( ) ( )| | s 2 C 1 R1 s 2 LC 1 s 1 C 1 R111 s 2 LC 1 s 1 C 1 R17 A22((

+ +++ +=( ) ( )( ) ( )( ) ( )( ) ( ) s 2 C 1 R 1 s 2 LC 1 s 1 C 1 R17 A1 s 2 LC 1 s 1 C 1 Rs 2 C 1 R 1 s 2 LC 1 s 1 C 1 R1 s 2 LC 1 s 1 C 1 R17 A2222+ + +=+ ++ + ++ += ( ) ( ) s 2 C 1 R 1 s 2 LC 1 s 1 C 1 R1) s ( T7 A) s ( Vi) s ( Vo) s ( T2+ + +== = 6.8PROBLEM SETS 6.8.1SINGLE-INPUT, SINGLE-OUTPUT BLOCK DIAGRAMS A. B. A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. C. D. 6.8.2MULTIPLE-INPUT, MULTIPLE-OUTPUT BLOCK DIAGRAMS A. B. 6.8.3TRANSFORMATIONFROMELECTRICALNETWORKTOITSEQUIVALENT BLOCK DIAGRAM Instruction: Transform the given electrical circuit to its equivalent Block Diagram; then,solvetheTransferFunctionusingBlockDiagramTransformationor Reduction. A COMPILATION OF LECTURE NOTES IN CONTROL SYSTEMCHAPTER 6 CATADMAN, LIZETTE IVY G. SOURCES/ REFERENCES Distefano, Joseph III J., Allen R. Stubberub, and Ivan J. Williams.Schaums Outlines: Feedback and Control Systems, Second Edition. USA: McGraw-Hill Companies, Inc., 1995. Hostetter, Gene H., Clement J. Savant Jr., and Raymond T. Stefani. Design of Feedback Control Systems, 2nd Edition. USA: Saunders College Publishing, 1989.