(Solved): 6. The root locus of a sampled plant system G(z) is shown in Fig. 2, with a sample rate of 50 Hz ...

6. The root locus of a sampled plant system G(z) is shown in Fig. 2, with a sample rate of 50 Hz. Root Locus 0.5 /T 0.7m/T 0.5 0.2 0 -0.2 -0.5 Imaginary Axis 0.8/T System: Gz Gain: 1.91 Pole: -0.999 Damping: 0.000454 Overshoot (%): 99.9 Frequency (rad/s): 157 1-/T 0,97/T 0.8 /T 0.6/T 0.4/T 0.5/T 0 Real Axis 02 0.3 0.4 0.5 0.6 28 obdd 10 000 0.7 0.b.3/T 0.8 0.9 0.2 T 0.1/T 0.1/T/ 0.2/T 0.7 /T 0.3 /T 0.6/T 0.4+/T -1- -0.5 -0.2 0.2 0.5 Fig. 2 a) Estimate the transfer function of the plant, G(z). Leave the system gain as K. [2] b) From Fig.2, find the system gain range of K for a stable system. c) What are the corresponding poles and zeros in the s-plane? [1] [2] d) To meet closed-loop design specifications: w? ? 0.3n/T and ? 0.5, the Poles of the system must be located within certain zones on the z-plane, mark this zone on the attached Q6(d) answer sheet. [2] e) Design a Dead-Beat digital controller for the G(z) system with K=1 to a step input. [3] Imaginary Axis 1 0.5 0.2 O -0.2 -0.5 -1 0.8/T -1 System: Gz Gain: 1.91 Pole: -0.999 Damping: 0.000454 Overshoot (%): 99.9 Frequency (rad/s): 157 17/T 10,9T/T 0.7 T/T 0.8T/T 0:7T/T -0.5 Root Locus 0.5T/T 0.6TT/T 0.6T/T -0.2 Fig. 2 0.5T/T 0 Real Axis 0.4T/T 10:16.37/1 0.2 0.4T/T 0.2 0.3 0.4 0.5 0.6 0.7 -0.8 0.9 456 0.3T/T 0.5 0.2#/T 0.1/T 0.17/T 0.2?/T