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It explains open-loop versus closed-loop (feedback) control, then introduces block diagrams as a versatile tool for depicting system composition and interconnections. The course defines transfer functions as input-output relationships and details simplifying rules for series, parallel, and feedback block structures. Worked examples derive closed-loop transfer functions, and extensions cover systems with two inputs using superposition and characteristic equations.",{"@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/automatic-control-systems-part-i-block-diagrams-and-transfer-functions/657431/",{"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/automatic-control-systems-part-i-block-diagrams-and-transfer-functions/657431.png","ImageObject",300,407,{"name":92,"@type":93},"404brain","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the difference between open-loop and closed-loop control systems?","Question",{"text":112,"@type":113},"Open-loop systems (non-feedback) cannot automatically ensure the actual output matches the desired value. Closed-loop systems (feedback) use a mechanism to keep the actual output close to the desired value.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What are block diagrams used for in control system analysis?",{"text":117,"@type":113},"Block diagrams describe how system components are composed and interconnected. They can also be used together with transfer functions to express cause-and-effect relationships across the system.",{"name":119,"@type":110,"acceptedAnswer":120},"How are simplifying rules applied to block diagrams?",{"text":121,"@type":113},"The course presents rules for series connections, parallel connections, and feedback control systems. These rules convert complex block structures into equivalent forms, enabling derivation of transfer functions.","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},657431,1793010053,{"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":24,"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},1099529839291,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","|  |\n| --- |\n| |\n| PDHonline Course E138 (4 PDH)\u003Cbr>Automatic Control Systems-Part I: Block Diagrams and Transfer Functions\u003Cbr>Instructor: Shih-Min Hsu, Ph.D., P.E.\u003Cbr>2026\u003Cbr>PDH Online • PDH Central\u003Cbr>9820 Bucklow Hill Dr\u003Cbr>Orlando, FL 32832-7126\u003Cbr>[info@PDHonline.com](info@PDHonline.com)\u003Cbr>[PDHonline.com](PDHonline.com)\u003Cbr>[PDHonline.org](PDHonline.org)\u003Cbr>An Approved Continuing Education Provider |\n\nAutomatic Control Systems  \nPart I:  \nBlock Diagrams and Transfer Functions  \nBy Shih-Min Hsu, Ph.D., P.E.  \nI. Introduction:  \nIn recent years, control systems have gained an increasingly importance in the development and advancement of the modern civilization and technology. Figure 1-1 shows the basic components of a control system. Disregard the complexity of the system, it consists of an input (objective), the control system and its output (result) . Practically our day-to-day activities are affected by some type of control systems. There are two main branches of control systems: 1) Open-loop systems and 2) Closed-loop systems.  \nInput/Objective  \nOutput/Result  \nFig. 1-1. Basic components ofa control system.  \nOpen-loop systems:  \nThe open-loop system is also called the non-feedback system. This is the simpler of the two systems. A simple example is illustrated by the speed control of an automobile as shown in Figure 1-2. In this open-loop system, there is no way to ensure the actual speed is close to the desired speed automatically. The actual speed might be way off the desired speed because of the wind speed and/or road conditions, such as up hill or down hill etc.  \nDesired speed  \n| Controller |  | Engine |\n| --- | --- | --- |\n|  |  |  |\n\nActual speed  \nFig. 1-2. Basic open-loop system.  \nClosed-loop systems:  \nThe closed-loop system is also called the feedback system. A simple closed-system is shown in Figure 1-3. It has a mechanism to ensure the actual speed is close to the desired speed automatically.  \nDesired speed  \n+   \nFig. 1-3. Basic closed-loop system.  \nActual speed  \nBlock Diagrams:  \nBecause of their simplicity and versatility, block diagrams are often used by control engineers to describe all types of systems. A block diagram can be used simply to represent the composition and interconnection of a system. Also, it can be used, together with transfer functions, to represent the cause-and-effect relationships throughout the system. Transfer Function is defined as the relationship between an input signal and an output signal to a device.  \nThree most basic simplifying rules are described in detail as follows.  \nSeries Connection –  \nR(s)  \nC(s)  \nC(s) = G 1 (s)G 2 (s)R (s)  \n􀂠  \nR(s)  \nG 1(s)G2(s)  \nC(s)  \nC(s) = G (s)G (s)  \nR (s) 1 2  \nParallel Connection –  \nC(s) = 􀀾G 1 (s)+ G2 (s)􀁀R (s)  \n􀂠  \nR(s)  \nG 1(s)+G2(s)  \nC(s)  \nCR((ss)) = G 1 (s)+ G2 (s)  \nFeedback Control Systems –  \nC(s) = G (s)E (s) E(s) = R (s)− H(s)C(s) (Error) C(s) = G (s)􀀾R (s)− H(s)C(s)􀁀  \nC(s) =  G (s)  R (s) 1+ G(s)H (s)  \n􀂠  \nC(s) G (s)  \n~~ ~~ = ~~ ~~ (1-1) R (s) 1 + G(s)H (s)  \nSome basic rules of simplifying block diagrams are tabulated in Table 1-1.  \nTable 1-1. Rules of simplifying block diagrams.  \n\n| Case | Original Structure | Equivalent Structure |\n| --- | --- | --- |\n| 1 | R(s)\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>C(s)\u003Cbr>\u003Cbr>\u003Cbr>| R(s)\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>G 1(s)G2(s)\u003Cbr>C(s)\u003Cbr>\u003Cbr>\u003Cbr>|\n| 2 | R(s) \u003Cbr>| R(s)\u003Cbr>G 1(s)±G2(s)\u003Cbr>C(s) |\n| 3 | | R(s)\u003Cbr>G 1 (s) 1 􀀣 G1 (s)G 2 (s)\u003Cbr>C(s) |\n| 4 | \u003Cbr>X\u003Cbr>\u003Cbr>Y | \u003Cbr>\u003Cbr>X |\n| 5 | \u003Cbr>Y\u003Cbr>| \u003Cbr>|\n| 6 | X\u003Cbr>\u003Cbr>G\u003Cbr>Z\u003Cbr>\u003Cbr>Y\u003Cbr>| \u003Cbr>|\n| 7 | \u003Cbr>| \u003Cbr>|\n| 8 | \u003Cbr>| \u003Cbr>|\n\nExample 1-1: Find the transfer function of the closed-loop system below.  \n4  \ns +1  \nR(s) +  \n-  \nC(s)  \n1 s  \nSolution:  \nUse case 1 to combine the two series blocks  \n4  \ns(s +1)  \nR(s) +  \n-  \nC(s)  \nUse case 3 to obtain the transfer function as follows  \n 4   \nC(s)  s(s +1)   4   \n= =  \nR (s) 1 + s(s~~ ~~1) 􀂘1 s 2 + s + 4  \n􀁩  \nExample 1-2: Find the transfer function of the closed-loop system below.  \nR(s) +  \nG 1(s)-  \n","cbCaibeFom0ieXrF","https://ap.wps.com/l/cbCaibeFom0ieXrF","pdf",463715,22,"English","# Introduction\n## Open-loop systems\n## Closed-loop systems\n# Block Diagrams\n## Transfer functions\n## Simplifying rules\n### Series connection\n### Parallel connection\n### Feedback control systems\n# Examples: Deriving transfer functions\n# Systems with two inputs\n## Superposition components\n## Characteristic equation","[{\"question\":\"What is the difference between open-loop and closed-loop control systems?\",\"answer\":\"Open-loop systems (non-feedback) cannot automatically ensure the actual output matches the desired value. Closed-loop systems (feedback) use a mechanism to keep the actual output close to the desired value.\"},{\"question\":\"What are block diagrams used for in control system analysis?\",\"answer\":\"Block diagrams describe how system components are composed and interconnected. They can also be used together with transfer functions to express cause-and-effect relationships across the system.\"},{\"question\":\"How are simplifying rules applied to block diagrams?\",\"answer\":\"The course presents rules for series connections, parallel connections, and feedback control systems. These rules convert complex block structures into equivalent forms, enabling derivation of transfer functions.\"}]","Automatic Control Systems - Part I - Block Diagrams and Transfer Functions | PDF",1792979035,55]