(BQ) Part 1 book "Automatic control systems" has contents: Introduction, mathematical foundation, block diagrams and signal flow graphs, theoretical foundation and background material - Modeling of dynamic systems, time-domain analysis of control systems, the control lab | Ninth Edition Farid Golnaraghi • Benjamin C. Kuo Laplace Transform Table Laplace Transform F(s) Time Function f(t) 1 Unit-impulse function 8{t) 1 s Unit-step function Us{i) 1 Unit-ramp function t f(n = positive integer) 1 „-«' e i' + Q! 1 fa—at te (s + a)2 n\ (s + a)" + 1 1 (s + a)(s + p) s (s + a)(s + p) t"e~°"(n = positive integer) 1 (r-M {S-cSC 1 fi-o 1 s(s + a) 5(5 + a ) 2 i ( l - e~at or 1 s2 (s + a) 1 2 s (s + a) s (s + a)2 pe-P-ae-*)^® a 1 2 r~Pl\{n=Lt0 ){a J * C + e-m) L{ca-\ or 1 a2 a (1 ate'0") \ ct/ -at)e-°" CO,, 2 s + col s s +co2 2 sin co„t IWWfll Laplace Transform Table (cont.) Time Function /(7) Laplace Transform F(s) 2 4 1 — cos cont 2 s{s +co ) con J a2 + OJ2 sin(6>„/ + 9) where 6 = t a n - ' (con/a) W " r-°" 1 * nnf/.t t s2 + 2£co„s + co2 r"to"'nnfa) \/l » wherefl = cos~ l £ s2(s2 + 2^cons + co2) (?2 f2 f O j- 1 1 ^ a - £con , (*<1) . t - ^ + r ? ' - * * s m ( w „ \ / l - <2 / + 0) v 7 «h tony/I-^ _l 2 where# = c o s ( 2 £ - l ) (f
