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# Lanif

**Final**

This Final covers Week 5-8. Show all required calculations, MATLAB code and MATLAB plots for full credit.

- A u nity feedback control system has a loop transfer function:

Gc(s)G(s) = K / ((1 + s/4)(1 + s)(1 + s/20)(1 + s/80))

where K = 10. Use MATLAB to obtain the Bode diagram of this system.

- A closed-loop system has a loop transfer function:

L(s) = Gc(s)G(s) = K / (s(s + 8)(s + 12))

- Determine the gain K so that the phase margin is 60 degree.
- For the gain K selected in part (a) determine the gain margin of the system.

- An uncompensated control system with unity feedback has a plant transfer function:

G(s) = K / (s(s/2 + 1)(s/6 + 1))

We want to have a velocity error constant of Kv = 20. We also want to have a phase margin of approximately 45 degrees and a closed-loop bandwidth greater than ω = 4 rad/s. Use two identical cascaded phase-lead networks to compensate the system.

- The transfer function of a plant and a zero-order system shown below is

G(z) = K(z + 0.5) / (z(z – 1))

- Use MATLAB to plot the root locus.
- Determine the rang e of gain K for a stable system.