Nyquist; Bode Plot; Root Locus

a) Analyse the closed loop stability of the system with open loop transfer function {see attachment}
  i)Make a sketch of the Bode diagram and hence the full Nyquist diagram, showing all relavent details
  ii) If the system is unstable, state the number of closed loop right hand plane poles and comment on how you might stabilise it. If the system is stable, give the gain and phase margins and show these on the Nyquist diagram
  iii) Without calculating break-away points, jw crossings etc, make a rough sketch of the root-locus of the above system to confirm your answer in (ii) above.

b) Given an open loop stable L(s), show by making sketches on the Nyquist diagram and the inverse Nichols chart (attached) that for closed loop stability, L(jw) cannot go over the {see attachment} point on the inverse Nichols chart.

*Please see attachments for chart and proper citation of symbols.

Attached file(s):

P6.jpg  View File

inverseNicholschart.jpg  View File