[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-657466-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-657466-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","control-engineering_module-2-block-diagrams-construction-and-reduction","Control-Engineering_Module-2 - Block Diagrams - Construction and Reduction","","Block diagram modeling in control engineering connects system variables through functional blocks, signals, branch points, and summing points. The module explains how differential equations governing rotational and DC motor systems are transformed using Laplace transforms into algebraic forms, then used to construct interconnected block sections that yield overall block diagrams. It further introduces block diagram algebra, including cascade block combination, as a basis for diagram reduction to obtain the system’s overall transfer function without changing input-output behavior.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/control-engineering_module-2-block-diagrams-construction-and-reduction/657466/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/control-engineering_module-2-block-diagrams-construction-and-reduction/657466.png","ImageObject",300,407,{"name":42,"@type":43},"Guten Appetit_Joghurt","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What are the key elements of a block diagram in control engineering?","Question",{"text":63,"@type":64},"A block diagram uses functional blocks, branch points, and summing points. Arrows represent signal flow directions into and out of blocks.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are differential equations used to construct block diagrams?",{"text":68,"@type":64},"Differential equations are converted into algebraic equations by taking Laplace transforms. Inputs and outputs are identified, then block sections are drawn and interconnected to form the overall block diagram.",{"name":70,"@type":61,"acceptedAnswer":71},"Why must quantities combined at summing points have the same dimensions and units?",{"text":72,"@type":64},"The plus or minus signs at arrowheads indicate addition or subtraction only when the quantities match in dimensions and units, ensuring physical consistency.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},657466,1793105717,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,100,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":102,"slug":103},6,50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":55,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":101,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145},1374408768420,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","The electricalanalogous elements forthe elements of mechanical rotational systemare given below.  \nJ₁→C₁  \nJ₂→C₂  \n0₂→V₂  \nJ₃→C₃  \nW₃→V₃  \nThe node basis equations usina Kirchoff's current law for the circuit shown infia9are given below(Refer fig 10,1and 12).  \nIt is observed that the node basis equations(10),(11)and(12)are similarto the differential equations(4),(5)and(6goveming the mechanicalsystem.  \n   \n# 1.11 BLOCK DIAGRAMS\n\n   \nA control system may consist of a number of components.In control engineering to show thefunctions.performed by each component,we commonly use a diagram called the block diagram.A blocldiagram of a system is a pictorial representation of the functions performed by each component and othe flow of signals.Such a diagram depicts the interrelationships that exist among the various componentsThe elements of a block diagram are block,branch point and summing point.  \n# BLOCK\n\n   \nIn a block diagram all system variables are linked to each other through functional blocks.Thefunctional block or simply block is a symbol for the mathematical operation on the input signal to thblock that produces the output.The transfer functions of the components are usually entered in thcorresponding blocks,which are connected by arrows to indicate the direction of the flow of signalsFigure 1.25 shows the block diagram of functional block.  \nThe arrowhead pointing towards the block indicates theinput,and the arrowhead leading away from the block representsthe output.Such arrows are referred to as signals.The outputsignal from the block is given by the product of input signaland transfer function in the block.  \n   \nB₁→1/R,  \nB₂→1/R₂  \nK₃→1/L₃  \n...(10)  \n..(11)  \n....(12)  \nFig 1.25:Functional block.  \nSUMMING POINT  \n   \nSumming points are used to add two or more signals in theystem.Referring to figure 1.26,a circle with a cross is the symbol thatdicates a summing operation.  \nThe plus or minus sign at each arrowhead indicates whether the signalto be added or subtracted,It is important that the quantities being added orsubtracted have the same dimensions and the same units.  \n# BRANCH PQINT\n\n   \nA branch point is a point from which the signal from a blockpes concurrently to other blocks or summing points.  \n# LONSTRUCTING BLOCK DIAGRAM FOR CONTROL SYSTEMS\n\n   \nA control system can be represented diagramatically by block diagram.The differential equationsoverning the system are used to construct the block diagram.By taking Laplace transform the differentialjuations are converted to algebraic equations.The equations will have variables and constants.From thesorking knowledge of the system the input and output variables are identified and the block diagram forich equation can be drawn.Each equation gives one section of block diagram.The output of one sectionill be input for another section.The various sections are interconnected to obtain the overallblockagram of the system.  \n   \nEXAMPLE 1.14  \n   \nConstruct the block diagram of amature controlled dcmotor.  \n# SOLUTION\n\n   \nThe diferential equations govemingthe armature controlled dcmotorare (refersection 1.7),  \nT=Ki  \neb=K,a  \nOn taking Laplace transfomofequation(1)weget,  \nVa(s)=l(s)Ra+Ls1(s)+E(s)  \nInequation(6),V(s)and E(s)are inputs andl(s)is theoutput.Hence theation (6)is rearrangedand the block diagramfor this equation isshown infig 1.  \nVa(s)-E(s)=la(s)[Ra+sLa]  \nOn taking Laplace transform of equation(2)weget,  \nT(s)=K1a(s)  \nIn equation(7);I(s)is the input and T(s)is the output.The block diagram for this equation is shown in fig2.  \nFig 1.26:Summing point.  \nBranch point  \nFig 1.27:Branch point.  \n…(1)  \n..(2)  \n..(3)  \n…(4)  \n.…(5)  \n……(6)  \nFig 1.  \n…(7)  \nFig 2.  \n   \n   \nOn takingLaplace transform ofequation(3)weget,  \n..(8)T(s)=Jso(s)+Bo(s)  \nIn equation(8),T(s)is the inpit ando(s)is the output.Hence the equation(8)is rearranged and the block diagramfthisequation is shown in fig(3).T(s)=(Js+B)w(s)  \nT(s)  \n   \nOn takingLaplace transfom of equation(4)we get,  ","cbCaiiIZTOZFrcgC","https://ap.wps.com/l/cbCaiiIZTOZFrcgC","pdf",2327448,53,"English","# 1.11 BLOCK DIAGRAMS\n## BLOCK\n## SUMMING POINT\n## BRANCH PQINT\n# LONSTRUCTING BLOCK DIAGRAM FOR CONTROL SYSTEMS\n# EXAMPLE 1.14\n## SOLUTION\n# EXAMPLE 1.15\n## SOLUTION\n# OK DIAGRAM REDUCTION\n# RULES OF BLOCK DIAGRAM ALGEBRA\n## Rule-1: Combining the blocks in cascade","[{\"question\":\"What are the key elements of a block diagram in control engineering?\",\"answer\":\"A block diagram uses functional blocks, branch points, and summing points. Arrows represent signal flow directions into and out of blocks.\"},{\"question\":\"How are differential equations used to construct block diagrams?\",\"answer\":\"Differential equations are converted into algebraic equations by taking Laplace transforms. Inputs and outputs are identified, then block sections are drawn and interconnected to form the overall block diagram.\"},{\"question\":\"Why must quantities combined at summing points have the same dimensions and units?\",\"answer\":\"The plus or minus signs at arrowheads indicate addition or subtraction only when the quantities match in dimensions and units, ensuring physical consistency.\"}]","Control-Engineering_Module-2 - Block Diagrams - Construction and Reduction | PDF",1792980391,134]