Control Systems

Please refer to the attached file. It is difficult to answer this non-assignment question. Please help to work out the detailed step-by-step answers to this non-assignment question. The detailed step-by-step answers will be helpful for understanding the context of the subject.

Control Systems (Unity Feedback Loop; Nyquist Contour; Routh-Hurwitz Analysis)

A process has a transfer function: {see attached} and is included in a unity feedback loop with a proportional controller Kp in a feedforward branch of the control loop. (a) Sketch a Nyquist contour for this system (b) Apply the Nyquist stability criterion to find a suitable range of K for stable closed loop system behaviour. (c) Verify the above stability result using a Routh-Hurwitz analysis. (d) From the Nyquist contour, estimate the phase margin, and briefly describe how it relates to the stability of the system.

Bode Plot; Root Locus; Nyquist

(a) By drawing a Bode plot (with reasonable accuracy at frequencies of interest) and then using a rough sketch of the (full) Nyquist diagram, assess the stability of the following system in a unity gain, negative feedback configuation {see attached} (b)What would your conclusion in (Q4a) have been if the feedback loop had positive instead of negative feedback? (c)Without any calculations, make a rough sketch of the root locus {see attached} for a positive and negative gain to explain the answer in b and c (You do not need to calculate angels of departure, break-away points etc. but you sketch must make sense.)

Nyquist; Bode Plot

Consider a unity negative feedback system with {see attached} (a) Sketch the open loop Nyquist diagram {see attached} using rough Bode magnitude and phase plots with reasonable accuracy for {see attached}. Show the diagram for {see attached} (using symmetry) with a dotted line. (b)Use the Nyquist diagram in question (a) to estimate the relative closed loop stability (gain and phase margins) of the system for positive and negative k.

Bode; Nyquist; Root Locus

Roughly sketch the Bode diagram, and hence the complete Nyquist diagram for: {see attached} Proportional control of the plant {see attached} in a standard negative feedback 2DOF structure (with an ideal sensor) is to be investigated {see attachment for questions}