Answer Happy

5-5. The characteristic equation of a second-order system is 5* + 0.68 + 9 = 0 * 9 Find (a). The natural frequency on (b) The damping ratios (c) The damped natural frequency wd (d) The time constant (envelope time constant) (e) The percentage peak overshoot 5-10. The response of a second-order servo to a step input is shown in Fig. P5-10. Find the values of , T (time constant), wn, and are 5.11. The parameters of a second-order servo are K, = 57 V/rad K = 1.82 x 10-4 lb-ft/V F.= 4 x 10-4 lb. ft. F:-0.= 4 x 10-6 slug . ft? Ji = 8.64 x 10- slug .ft N 1 h = feedback gear ratio = N, 12 N 1 a = gear ratio from motor to load = 12 Ti = extraneous load torque = 20.88 N- 1.6 1.4 1.2 The input command is 0, 0.1 rad. (a) Draw the block diagram of the system. (b) Find the value of the amplifier gain K, required to yield a steady-state error E of 0.174 rad. (5 (c) Determine w, and 1.0 1 0.8 Settling time 7.5s- 0.6 0.4 0.2 0 1 2 3 4 6 7 8 1,5 Fig. P5.10