Bài tập chương 2 1) For each of the following transfer functions, write, by inspection, the general form of the step response: 400 s 12s 400 900 b) G ( s ) 2 s 90s 900 225 c) G( s) 2 s 30s 225 625 d ) G(s) 2 s 625 a ) G( s) 2 ANSWERS : a ) c(t ) A Be 6t cos(19.08t ) b) c(t ) A Be 78.54 t Ce 11.46t a ) c(t ) A Be 15t Cte 15t a ) c(t ) A B cos(25t ) 2) Find ; n; Ts; Tp; Tr, and %OS for a system whose transfer function is: G( s) 361 s 16s 361 2 ANSWERS : 0.421; n 19; Ts 0.5s; T p 0.182s; Tr 0.079s; %OS 23.3% 3) The following figure shows a mechanical vibratory system.When 2 lb of force (step input) is applied to the system, the mass oscillates, as shown in the figure. Determine m, b, and k of the system from this response curve.The displacement x is measured from the equilibrium position. ANSWERS : k 20lb f / ft; m 167lb; b 12.2lb f / ft / sec 4) Determine the unit-step response c(t) of the following higher-order system: (Obtain the partial-fraction expansion with MATLAB’s residue command) C ( s) 3s 3 25s 2 72s 80 4 R( s ) s 8s 3 40s 2 96s 80 ANSWERS : c(t ) 0.5626e 2 t cos 4t 0.3438e 2 t sin 4t 0.4375e 2 t 0.375te 2 t 1 5) Consider a higher-order system defined by: C ( s) 6.3223s 2 18s 12.811 4 R( s ) s 6s 3 11.3223s 2 18s 12.811 Using MATLAB, plot the unit-step response curve of this system. Using MATLAB, obtain the rise time, peak time, maximum overshoot, and settling time. ANSWERS : tt 0.58; t p 1.66; M p 0.6182; t s 10.02