Question three The figure below shows a unit step response of a second order system. From the graph of response find: 1- The rise timet,. 2- The peak timet. 3- The maximum overshoot Mp. 4- The damped natural frequency wa 5- The transfer function. Hence find the damping ratio ( and the natural frequency a. Find also the transfer function of the system. 12 08 06 04 92 3ep Response 05 2 25 45 Tew (sec) Question Four For the control system shown in the figure below, find: a) The feedforward transfer function. b) The feedback transfer function. c) The open loop transfer function. d) The overall transfer function. e) The characteristic equation. 1) The value of the gain K so that the steady state error resulting after a unit step input equals 0.1. R(s) K C(=) s(s²+3s+6) 10s S+ 10 Question Five The figure below shows a unit step response of a control system, find: i- The transfer function. ii- The rise time. t: 5.1 12 onday 02 Question Six 6 Consider the control system shown in the figure below. When this system is excited by a unit step input its response will be as shown in the response figure below. a) Find the values of the constants K and T. b) The damped natural frequency wa c) The settling time t, (2% error criterion). R(s) C(s) K Amplitude s(Ts+1) 1.4 Slep Response 12 1 0.8 0.8 0.4 62 02 05 1.5 2 2.5 3.5 Time (seconds) Tutorials Q.1 Fig. 1 shows the unit step response of a first order system. Form the response find: i) the time constant of the system c(t) ii) the transfer function. T.F iii) The rise time tr C(t) 1.2 r(t)₁ 8 0.8 Step response 0.6 0.4 0.2 Fig 1 Ans: T=2 sec, C(s) R(s) 25+1' ty = 4.3 sec Q.2 00 6 For the control system shown by the block diagram. in Fig.2 ie numerical value of 3-1 kg-m² and B- 1 N-m (rad'sec). R(s) Y(s) ΚΙ 1/s Js+B K2+ Fig.2 a) Find the transfer function Y(s) R(s). b) Determine the values of the gain K1 and velocity feedback constant K2 so that the maximum overshoot in the unit-step response is 0.2 and peak time is 1 sec. e) With these values of K1 and K2. obtain the rise time and settling time. d) Obtain the response y(t) for the unit-step input r(t). C³ => s2+(1+K1K2)s+K, K₁=12.46, K,-0.1781, t, =0.561 sec, t,-1.864 sec, y(t)=1-1.1236esin(3.149t+1.952)) R(s) Q.3 Fig. (A) shows the block diagram representation of a control system. When this system is excited with a unit step input, it responds as shown in the graph of Fig. (B). Find, 1- The overall transfer function C(s)/R(s). 2- The damping ratio 5 3- The natural undamped frequency (0," 4- The damped natural frequency () d. 5- The rise time t. 6- The values of the constants T and K. R(s) K C(s) (Ts+1) (A) c(t) 1 /0.22 (B) 8