## Question

###### Question three The figure below shows a unit step response of a second order system. From...

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 w 5. The transfer function. Hence find the damping ratio ζ and the natural frequency ah-Find also the transfer function of the system.

r 4 02 15 25 35 45 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. 0) The value of the gain K so that the steady state error resulting after a unit step input equals 0.1.

5 CE) s(s2 +3s + 6) 10s s 10 Question Five The figure below shows a unit step response of a control system,fiad: i- The transfer function. i- The rise time. t: 5- 12 12

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 fig below . ure a) Find the values of the constants K and T b) The damped natural frequency od c) The settling time tr (2% error criterion). R(s)+ C(s) s(Ts +1) Sep Rasponse 1.4 1.2 08 0.e 05 152 25 3 2.5 Tme (seconds)

Tutorials a.1 Fig. 1 shows the unit step response of a first order system. Form the response nse find i) the time constant of the system c(t) i) the transfer function. T.F iii) The rise time t C(t) 1.2 rtt) 0.6 t--+--什--· 0.4 + デ + + + +--+ 02 0 10 Fig 1 Ans: T-2 sec,CO =ー, tr = 4.3 sec c(s)- R(S) 2s+1' 1 Q.2 For the control system shown by the block diagram. in Fig-2 le nunerical value of -1 kg-m and B - 1 N-m'(rad'sec). R(s) Y(s) K2 Fig.2 Find the transfer fuction Y(s) R(S). ) Detemine the values of the gain K1 and velocity feedback constant K2 so that the maxiamun overshoot in the unit-step response is 0.2 and peak time is 1 sec. c) With these values of K1 and K2. obtain the nise time and settling time. d) Obtain the response yt) for the unit-step imput rt)

{c(s)=ー KI , K,-12.46, K,-0.1781, tr=0.561 sec, t.-1.864 sec, y(t)-1-1.1236e1,s"sin(3.149t+1.952)) 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)y/R(s). 2- The damping ratio g 3- The natural undamped frequency o 4- The damped natural frequency od 5- The rise time t.. 6- The values of the constants T and K. R(s) C(6)

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