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Formula Sheet 1

Formula Sheet 1 - a'3 IR c “H” 7 shynv «Mann-gamma c a...

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(fix 6:?“ 3‘70 : R 6:55.73} X 5 F1;-%- 5:1TEES 2“; LA) — yo fiw:-£:[-j «— " CA Eff" élfléf’e V 3 : ya I-Ef/l) "' 2 ya ‘- 56A)- ?” fi. Eagflfli FEM-B ‘ (540.) h 1) '7/ I; .1 \ I V f / ,t ,0; (q A») 43 fizz." " i Ll [ {A} ow~~+~ h“ k j -\\ ; «1—H ‘ ‘r \ VF? 1% i “w a ' - “ C _. b~a ‘ 4’“. Moran”) Problem 1 (15 pts): Draw the component block diagram of a feedback control system. Problem 2 (10 pts): What is the purpose of feedback? Problem 3 (10 pts): Find the Laplace transform of function f(t) = 2 + 4t2 + 36(t) + «2‘3t + cos(8t). Problem 4 Consider a system with transfer function H (s) = 3+1). Suppose the input of the system is u(t)=A[1(t)-1(t-T)i H/ 33 z Where A and T are constants. I [,5 I (5-a) (15'pts): Determine the system output iy(t). (5—b) (10 pts): Assume that p is positive. Show that, for arbitrarily small A > 0 and T > O, the output y(t) tends to infinity as time t tends to infinity. Problem 5 (15 pts): Model the mechanical system shown in Figure 1. Find the transfer function H (s) := %(%%% where F(t) is a force and y(t) is the displacement of the mass with respect to t e position Where the spring is unstretched and uncompressed. Suppose that the friction force is proportional to the velocity With friction coefficient constant = r at Spring l L Q/——' r ‘f’. U( S) 3 2 7 if CF 5f!” T ‘i y f“ f I 3 friction c (\2 p {’ coefficient = C, J , J :5;— t b ‘ X) (f a r ‘ —L—-—- ‘ A /Q J 1: P 5 _ l‘ g( (- igure r0 em A 5‘: 3’?) S J Problem 6 (25 pts): Find the transfer function H := %(§3)1 of the circuit shown in H co 1 = I "Siam F” ya) - e c He Figure 2: Problem 6 ...
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