# Bode Plot, Nyquist & Root Locus

See attached file for full problem description.

Consider the system with the loop transfer function shown in the attached.

a) Sketch the Bode plot and calculate (tabulate) L(jw) at w = [0, 1, 5, 10, 40, infinity] rad/s. Hence sketch the full Nyquist diagram.

b) Analyse the closed loop system stability If the closed loop system iss table, state the gain and phase margins. if the closed loop system is unstable, state the number of right hand plane closed loop poles and calculate the gain values that could be used to stabilise it.

c) Without calculations, sketch the positive gain root locus for kL(s) above to confirm that your answer in (a) is reasonable. (Identify real-axis branches that should have break-away points but do not attempt to calculate their locations.)

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#### Solution Summary

The posting considers a loop transfer functions and calculates and sketches the full Nyquist diagram. Along with this it also analyzes the gain and phase margins of the closed loop system as well as sketches the positive gain root locus.