Question

5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency, wd the damping ratio, and the damped 7. For the feedback system shown in Figure 1, find the closed loop transfer function, the characteristic polynomial, and where appropriate, the time constants, damping ratio and natural frequency, if (a) G(s)T (b) G (s) = 14 +14s+12 (c) G (s) +68+29 Ris) C(s) Gis) Figure 1 n Dynamics & Control Engineering KM3473 Syste Tutorial 1 May 7, 2019 1. The transfer function of a dynamic system is given by G (s) It is subjected to a unt step input. Determine (a) the time constant. T (b) the steady state value. (c) the time taken for the response to reach 95% of the steady state value 2. Given G suming that al initial conditions are 0. Also, find the value of y as t → x. Determine the system poles and zeros and comment on the stability of each plant solve the following for y(t) given u (t) 3, as- (b) G(s) 2s+10 (d) G (s)= 3. For each G (s) in Question 2, where appropriate, determine the time constant and sketch the response y (t) against t. Indicate the time at which y(t) reaches 98% of the steady state value 4. Given G(s) -,solve te following for y (t) given u(t) -15 assuming that initial conditions are 0. Also, find the value of y as t → oo and comment on the stability of each plant (a) G2

Answer 1

& =上Jac ys S 3

Tofi EC

Input interpretation: plot -0.5 exp(-2t)exp(-3t) t 01 3 Plot: 0.15 0.10 0.05 2.0 1.0 0.5 1.5 2.5 3.0 Arc length of curve: