{"id":557755,"date":"2024-11-05T18:19:00","date_gmt":"2024-11-05T18:19:00","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/esdu-690052009\/"},"modified":"2024-11-05T18:19:00","modified_gmt":"2024-11-05T18:19:00","slug":"esdu-690052009","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/esdu\/esdu-690052009\/","title":{"rendered":"ESDU 69005:2009"},"content":{"rendered":"

INTRODUCTION<\/strong><\/p>\n

This Item presents sets of normalised response curves for simple
\nfirst- and second-order systems.<\/p>\n

The data are restricted to certain basic forms of input, which
\nare presented in Figure 1, and to systems that can be described by
\na linear differential equation with constant coefficients. The
\ncharacteristic equation, and also the denominator of the
\ncorresponding transfer function, is therefore a first or second
\ndegree polynomial.<\/p>\n

The response curves for first- and second-order systems are
\npresented in Figures 2 (2a, 2b, 2c, 2d, 2e, 2f, 2g and 2h) and
\nFigures 3 (3a, 3b, 3c, 3d, 3e, 3f, 3g and 3h) respectively, and
\nmaxima in response to some of the input functions are given in
\nFigure 4 and Figures 5 (5a, 5b, 5c, 5d and 5e).<\/p>\n

A step input, its time integral (ramp input) and its derivative
\n(impulsive or "Delta function" input), are considered independently
\nalthough the responses to any two of these inputs can be deduced
\nfrom the response to the third. Similarly the responses to related
\ninputs of ramp-step and triangular form are given, although these
\ncould be deduced by superposition of the responses to suitably
\nchosen ramp inputs. Brief mention is made of the convolution
\nintegral (Duhamel integral) method for determining the response to
\nan arbitrary input when the response to an impulse is known.<\/p>\n

Data for the simple frequency response, i.e.<\/i> the
\nultimate steady state of a stable system subjected to a sinusoidal
\ninput, are presented in Figures 6 (6a and 6b) and Figures 7 (7a and
\n7b). In this case the diagrams give the ratio of the amplitudes and
\nthe difference in phase of the response variable and the input.<\/p>\n

Finally Appendix A considers the response of a system having a
\nmodified form of transfer function for one of the inputs used, the
\nramp-step input.<\/p>\n","protected":false},"excerpt":{"rendered":"

The Response of First- and Second-Order Systems<\/b><\/p>\n\n\n\n\n
Published By<\/td>\nPublication Date<\/td>\nNumber of Pages<\/td>\n<\/tr>\n
ESDU<\/b><\/a><\/td>\n2009-11<\/td>\n35<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":557759,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2675],"product_tag":[],"class_list":{"0":"post-557755","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-esdu","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/557755","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/557759"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=557755"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=557755"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=557755"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}