Control Systems ME 451
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This 4 page Class Notes was uploaded by Princess Rolfson on Saturday September 19, 2015. The Class Notes belongs to ME 451 at Michigan State University taught by Jay Pil Choi in Fall. Since its upload, it has received 42 views. For similar materials see /class/207526/me-451-michigan-state-university in Mechanical Engineering at Michigan State University.
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Date Created: 09/19/15
ME451 SO7 Output Signal of a Linear System I Input signal unfit f ii TJEIT Output signal mo Hut1 U H y H Tjd 39 1 mm v LWMTJHHE TJMT 4 Superposition f EL39LZTh a def impulse response 1 M15 ii M195 def convolution E quotiii5 T li dT r TiiT4 vr 4 def causality ME451 07 14 Impulse Response h7 H67 1 a u76t 739 ME451 07 15 ME451 SO7 Causal Linear Time Invariant LTI System A causal system a physical or nonanticipative system is a system where the output yt only depends on the input values uriltgtoltrt Thus the current output yt can be generated by the causal system with the current and past input values Causal LTI impulse response 00 Thus we have yf 7Lt Th7 d7 To a 2 ut Th739d739 JO ME451 07 15 Causal System Physically Realizable a my E333 Efuture System PaSt future current current ME451 07 17 ME451 SO7 Causal System Derivative operator input position output velocity Integral operator input velocity output position xt ME451 07 18 Complex Numbers Ordered pair of two real numbers 3 I mijCWhereayE7Zj V l Conjugate g 3 I 17 Addition 81 131 jy132 582 l39 jy2 31 82 1 2 9011 y2 Multiplication 8182 1 jy12 jy2 5512 31192 jlt912 192 88lsl22y2 ME451 07 19 ME451 SO7 Complex Numbers Euler s identity 970 1 cos 9 sin 6 Ej 7le Er quot u E 956 2 w 3 5m 5quot 2 n 2 E 399 1m Polarform Magnitude 7 132 y2 Phase 6 tan 1yx 6 51 T163961 32 r269 2 8152 T1T2 j9192 ME451 07 20 633 sin 13 C0551 2 271 1 n0 ME451 07 21
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