{"id":1667,"date":"2024-06-06T10:24:03","date_gmt":"2024-06-06T10:24:03","guid":{"rendered":"https:\/\/skygyan.tech\/?p=1667"},"modified":"2024-06-06T10:24:04","modified_gmt":"2024-06-06T10:24:04","slug":"to-study-step-response-of-2nd-order-control-system","status":"publish","type":"post","link":"https:\/\/skygyan.tech\/index.php\/2024\/06\/06\/to-study-step-response-of-2nd-order-control-system\/","title":{"rendered":"To Study Step response of 2nd order control system"},"content":{"rendered":"\n<p><strong>Object<\/strong>: To Study Step response of second order control system.<\/p>\n\n\n\n<p><strong>Apparatus required<\/strong>: Experimental kit<\/p>\n\n\n\n<p><strong>Theory<\/strong>: <\/p>\n\n\n\n<p>The time response has utmost importance for the design and analysis of control systems because these are inherently time domain systems where time is independent variable. During the analysis of response, the variation of output with respect to time can be studied and it is known as time response. To obtain satisfactory performance of the system with respect to time must be within the specified limits. From time response analysis and corresponding results, the stability of system, accuracy of system and complete evaluation can be studied easily. Due to the application of an excitation to a system, the response of the system is known as time response and it is a function of<br>time. The two parts of response of any system: Transient response; Steady-state response.<\/p>\n\n\n\n<p>Time Response Specification Parameters: The transfer function of a 2-nd order system is generally represented by the following transfer function: <\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"204\" height=\"71\" src=\"https:\/\/skygyan.tech\/wp-content\/uploads\/2024\/06\/111.jpg\" alt=\"\" class=\"wp-image-1668\"\/><\/figure>\n\n\n\n<p>The dynamic behavior of the second-order system can then be described in terms of two parameters: the damping ratio and the natural frequency. If the dumping ratio is between 0 and 1, the system poles are complex conjugates and lie in the left-half s plane. The system is then called underdamped, and the transient response is oscillatory. If the damping ratio is equal to 1 the system is called critically damped, and when the damping ratio is larger than 1 we have overdamped system. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"423\" height=\"261\" src=\"https:\/\/skygyan.tech\/wp-content\/uploads\/2024\/06\/22.jpg\" alt=\"\" class=\"wp-image-1669\" srcset=\"https:\/\/skygyan.tech\/wp-content\/uploads\/2024\/06\/22.jpg 423w, https:\/\/skygyan.tech\/wp-content\/uploads\/2024\/06\/22-300x185.jpg 300w\" sizes=\"auto, (max-width: 423px) 100vw, 423px\" \/><\/figure>\n\n\n\n<p><strong>Delay time (td):<\/strong> The delay time is the time required for the response to reach half the final value the very first time.<br><strong>Rise time (tr):<\/strong> The rise time is the time required for the response to rise from 10% to 90%, 5% to 95%, or 0% to 100% of its final value. For underdamped second-order systems, the 0% to 100% rise time is normally used. For overdamped systems, the 10% to 90% rise time is commonly used.<br><strong>Peak time (tp)<\/strong>: The peak time is the time required for the response to reach the first peak of the overshoot.<br><strong>Maximum (percent) overshoot (Mp):<\/strong> The maximum overshoot is the maximum peak value of the response curve measured from unity. If the final steady-state value of the response differs from unity, then it is common to use the maximum percent<br>overshoot. It is defined by-<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"226\" height=\"77\" src=\"https:\/\/skygyan.tech\/wp-content\/uploads\/2024\/06\/333.jpg\" alt=\"\" class=\"wp-image-1670\"\/><\/figure>\n\n\n\n<p><strong>Settling time (ts)<\/strong>: The settling time is the time required for the response curve to reach and stay within a range about the final value of size specified by absolute percentage of the final value (usually 2% or 5%). The settling time is related to the largest time constant of the control system.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Object: To Study Step response of second order control system. Apparatus required: Experimental kit Theory: The time response has utmost importance for the design and analysis of control systems because these are inherently time domain systems where time is independent variable. During the analysis of response, the variation of output with respect to time can [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,8],"tags":[632,622,623,631],"class_list":["post-1667","post","type-post","status-publish","format-standard","hentry","category-blog","category-diploma","tag-controllabpracticalfile","tag-controlsystem","tag-controlsystemlab","tag-controlsystemlabexperiment"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>To Study Step response of 2nd order control system - SkyGyan<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/skygyan.tech\/index.php\/2024\/06\/06\/to-study-step-response-of-2nd-order-control-system\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"To Study Step response of 2nd order control system - SkyGyan\" \/>\n<meta property=\"og:description\" content=\"Object: To Study Step response of second order control system. 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