[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-656258-105":59,"doc-detail-656258-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","section-2-block-diagrams-signal-flow-graphs-ese-430-feedback-control-systems","Section 2 - Block Diagrams & Signal Flow Graphs - ESE 430 - Feedback Control Systems","","SECTION 2 explains how block diagrams represent feedback control systems. It defines blocks as subsystems modeled with transfer functions and signals as inputs/outputs with arrow directions. Summing junctions are described for algebraic summation, including subtraction using a negative sign. It then derives single-block equivalents for interconnections in cascade, parallel, and feedback, giving the corresponding relationships and closed-loop transfer function forms, including negative-feedback and notes on positive-feedback loop gain.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/section-2-block-diagrams-signal-flow-graphs-ese-430-feedback-control-systems/656258/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/section-2-block-diagrams-signal-flow-graphs-ese-430-feedback-control-systems/656258.png","ImageObject",300,407,{"name":92,"@type":93},"cryingin4k","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-25",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What do blocks, signals, and summing junctions represent in a block diagram?","Question",{"text":112,"@type":113},"Blocks represent subsystems and are typically labeled with transfer functions. Signals represent inputs and outputs, with direction indicated by arrows. Summing junctions algebraically combine signals, with subtraction shown using a negative sign.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the equivalent transfer function for cascade-connected blocks obtained?",{"text":117,"@type":113},"For cascade connections, the equivalent transfer function equals the product of the individual transfer functions of the blocks.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the closed-loop transfer function for a feedback system and how do negative feedback and loop gain relate?",{"text":121,"@type":113},"For the feedback form, the closed-loop transfer function is the forward-path gain divided by 1 plus the product of forward path gain and feedback-path gain. The denominator’s feedback factor corresponds to the loop gain (open-loop transfer function). Negative feedback uses the plus sign in the denominator, while positive feedback uses the corresponding opposite sign as shown in the notes.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},656258,1793051497,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},137458181193,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","SECTION 2: BLOCK DIAGRAMS & SIGNAL FLOW GRAPHS  \nESE 430 – Feedback Control Systems  \n2 Block Diagrams  \nK. Webb ESE 430  \n3  \n􀂅 In the introductory section we saw examples of block diagrams  \nto represent systems, e.g.:  \n􀂅 Block diagrams consist of  \n􀂆 Blocks – these represent subsystems – typically modeled by, and labeled with, a transfer function  \n􀂆 Signals – inputs and outputs of blocks – signal direction indicated by arrows – could be voltage, velocity, force, etc .  \n􀂆 Summing junctions – points were signals are algebraically summed – subtraction indicated by a negative sign near where the signal joins the summing junction  \nK. Webb ESE 430  \n4  \n􀂅 The basic input/output relationship for a single block is:  \n􀜻 􀝏 = 􀜷 􀝏 ⋅ 􀜩 􀝏  \n􀂅 Block diagram blocks can be connected in three basic forms:  \n􀂆 Cascade  \n􀂆 Parallel  \n􀂆 Feedback  \n􀂅 We’ll next look at each of these forms and derive a singleblock equivalent for each  \nK. Webb ESE 430  \n5  \n􀂅 Blocks connected in cascade:  \n􀜺1 􀝏 = 􀜷 􀝏 ⋅ 􀜩 1 􀝏 , 􀜺2 􀝏 = 􀜺1 􀝏 ⋅ 􀜩 2 􀝏  \n􀜻 􀝏 = 􀜺2 􀝏 ⋅ 􀜩 3 􀝏 = 􀜺1 􀝏 ⋅ 􀜩 2 􀝏 ⋅ 􀜩 3 􀝏  \n􀜻  = 􀜷  ⋅ 􀜩 1  ⋅ 􀜩 2  ⋅ 􀜩 3  = 􀜷  ⋅ 􀜩􀯘􀯤   \n􀜩􀯘􀯤  = 􀜩 1  ⋅ 􀜩 2  ⋅ 􀜩 3   \n􀂅 The equivalent transfer function of cascaded blocks is the product of the individual transfer functions  \nK. Webb  \nESE 430  \n6  \n􀂅 Blocks connected in parallel:  \n􀜺1 􀝏 = 􀜷 􀝏 ⋅ 􀜩 1 􀝏  \n􀜺2 􀝏 = 􀜷 􀝏 ⋅ 􀜩 2 􀝏  \n􀜺3 􀝏 = 􀜷 􀝏 ⋅ 􀜩 3 􀝏  \n􀜻 􀝏 = 􀜺1 􀝏 ± 􀜺2 􀝏 ± 􀜺3 􀝏  \n􀜻 􀝏 = 􀜷 􀝏 ⋅ 􀜩 1 􀝏 ± 􀜷 􀝏 ⋅ 􀜩 2 􀝏 ± 􀜷 􀝏 ⋅ 􀜩 3 􀝏  \n􀜻  = 􀜷  􀜩 1  ± 􀜩 2  ± 􀜩 3   = 􀜷  ⋅ 􀜩􀯘􀯤   \n􀜩􀯘􀯤  = 􀜩 1  ± 􀜩 2  ± 􀜩 3   \n􀂅 The equivalent transfer function is the sum of the individual transfer functions:  \nK. Webb ESE 430  \n7  \n􀂅 Of obvious interest to us, is the feedback form:  \n􀜻 􀝏 = 􀜧 􀝏 􀜩 􀝏  \n􀜻 􀝏 =  􀜴 􀝏 − 􀜺 􀝏  􀜩 􀝏  \n􀜻 􀝏 =  􀜴 􀝏 − 􀜻 􀝏 􀜪 􀝏  􀜩 􀝏  \n􀜻 􀝏  1 + 􀜩 􀝏 􀜪 􀝏  = 􀜴 􀝏 􀜩 􀝏  \n􀜻  = 􀜴  ⋅  􀜩    \n1 + 􀜩 􀝏 􀜪 􀝏  \n􀂅 The closed-loop transfer function, 􀜶 􀝏 , is  \n􀜻 􀝏 􀜩 􀝏  \n􀜶 􀝏 = ~~ ~~ = ~~ ~~  \n􀜴 􀝏 1 + 􀜩 􀝏 􀜪 􀝏  \nK. Webb ESE 430  \n8  \n􀜶 􀝏 =  \n􀂅 Note that this is negative feedback, for positive feedback:  \n􀜶  =  􀜩    \n1 − 􀜩 􀝏 􀜪 􀝏  \n􀂅 The 􀜩 􀝏 􀜪 􀝏 factor in the denominator is the loop gain or open-loop transfer function  \n􀂅 The gain from input to output with the feedback path broken is the forward path gain – here, 􀜩 􀝏  \n􀂅 In general:  \n􀜶  = fo~~ ~~rw1rldopoapth~~ ~~gagainin  \nK. Webb ESE 430  \n9  \n􀂅 Calculate the closed-loop transfer function  \n􀂅 􀜦 􀝏 and 􀜩 􀝏 are in cascade  \n􀂅 􀜪1 􀝏 is in cascade with the feedback system consisting of 􀜦 􀝏 ,􀜩 􀝏 , and 􀜪2 􀝏  \n􀜶  = 􀜪1  ⋅  􀜦  􀜩    \n1 + 􀜦 􀝏 􀜩 􀝏 􀜪2 􀝏  \n􀜪1 􀝏 􀜦 􀝏 􀜩 􀝏  \n􀜶 􀝏 = ~~ ~~  \n1 + 􀜦 􀝏 􀜩 􀝏 􀜪2 􀝏  \nK. Webb ESE 430  \n10  \n􀂅 We’re often interested in unity-feedback systems  \n􀂅 Feedback path gain is unity  \n􀂆 Can always reconfigure a system to unity-feedback form  \n􀂅 Closed-loop transfer function is:  \nK. Webb ESE 430","cbCaitiW6xWhE4IA","https://ap.wps.com/l/cbCaitiW6xWhE4IA","pdf",1363050,63,"English","# 2 Block Diagrams\n## Blocks and signals in block diagrams\n## Input/output relationship for a single block\n## Interconnection forms: cascade, parallel, feedback\n## Cascade equivalent transfer function\n## Parallel equivalent transfer function\n## Feedback form and closed-loop transfer function\n## Negative vs positive feedback and loop gain","[{\"question\":\"What do blocks, signals, and summing junctions represent in a block diagram?\",\"answer\":\"Blocks represent subsystems and are typically labeled with transfer functions. Signals represent inputs and outputs, with direction indicated by arrows. Summing junctions algebraically combine signals, with subtraction shown using a negative sign.\"},{\"question\":\"How is the equivalent transfer function for cascade-connected blocks obtained?\",\"answer\":\"For cascade connections, the equivalent transfer function equals the product of the individual transfer functions of the blocks.\"},{\"question\":\"What is the closed-loop transfer function for a feedback system and how do negative feedback and loop gain relate?\",\"answer\":\"For the feedback form, the closed-loop transfer function is the forward-path gain divided by 1 plus the product of forward path gain and feedback-path gain. The denominator’s feedback factor corresponds to the loop gain (open-loop transfer function). Negative feedback uses the plus sign in the denominator, while positive feedback uses the corresponding opposite sign as shown in the notes.\"}]","Section 2 - Block Diagrams & Signal Flow Graphs - ESE 430 - Feedback Control Systems | PDF",1792967243,159]