3. Question 3 [25 marks] The digital control system for the positioning of a hard-disk read/write head is shown in Fig.

[answerhappygod]

3 Question 3 25 Marks The Digital Control System For The Positioning Of A Hard Disk Read Write Head Is Shown In Fig 1 (127.14 KiB) Viewed 49 times

3. Question 3 [25 marks] The digital control system for the positioning of a hard-disk read/write head is shown in Fig. 23. The sampling time is T, = 5.10 's The controller is a simple proportional gain K>0. K ZOH 1 104 s(s+102) Sampler Figure Q3 (a) Derive the transfer function Ga(z) representing the discrete-time operation of the plant. Hint: the denominator of Ga(z) should be in the form (z - 1)(z-a). [10 marks) (b) Show that the characteristic polynomial of the closed loop system is p(z) =z? +(0.11K - 1.61)z+0.09K+0.61. [4 marks] (c) Find the range of values of K for which the closed-loop system is stable. [6 marks] (d) It is required that the control system does not exhibit oscillatory behaviour. Hence, the gain K should be chosen in such a way that the closed-loop poles are real. Eval- uate whether K = 1 satisfies the design requirements. (5 marks]