Question

please show methods and calculations

1. Using measured open-loop frequency response values as presented in Table 1, the plant transfer function in the system of Figure 1 has been estimated as 48 Gp (s)- (S+2)(s +4.8s +16) 3.0 0.4 -j 0.7 o (rad/s) 0.8 5.1 6.7 2 j01.1-j 0.8 - 0.34 +j0 -0.14 +j0.07 Table 1 To improve the accuracy of the frequency response plot, use the transfer function to estimate the open-loop frequency response Gp(G1.6) at the additional frequency value Co 1.6 rad/s (a) [3 marks] (b) Using mm graph paper, (i) sketch the open-loop data of Table 1 on a polar plot, including the new test point calculated in part (a), and (ii) use your polar plot to calculate the system gain margin and phase margin [7 marks] If a delay of 0.3 s is introduced into the plant it is found that the frequency response at ω-5.1 rad/s is changed to GoG5.le of a 0.3 s delay at frequencies of 1.6 and 3.0 rad/s (c) )e-j5.1(03) 0.01 +j 0.34. Calculate the effect [6 marks] (d) Using the results of part (c), sketch how the system polar is changed by the introduction of a 0.3 s delay, and calculate new values for the system gain and phase margins [4 marks] R(s)+ C(s) Gp(s) Figure 1

Answer 1