I have the solution to this question but I could not get the phase margin and ga

Question

I have the solution to this question but I could not get the phase margin and gain margin.

So that what is the phase margin and gain margin for this solution.

Also, I want to understand how we drew the Nyquist Criterion

Show that the system is stable and the final answer is Z-N+P-2-2-0, which means the system stable. Also, make sure to find Gain margin (GM) and Phase margin (PM) Digital Compensator Plant R(s) C(s) Sensor For standard system as shown bellow, the open loop frequency response is as shown on the flowing page. Use the Nyquist Criterion to determine whether or not system is stable. Determine any applicable stability margins.Be sure to solve the problem step by step, including the direction of travel on the Nyquist diagram, and any calculations however sample that are required to determine stability Where: G(s) H(s) = 1 , D (z) = , (s-0.2)(s + 5)

Explanation / Answer

Gain Margin can be calculated from Bode plot by seeing how much much gain is required to reach gain 0dB  at the frequency where the open-loop system's phase equals -180 degrees.

From your data

Closest value ( to -1800) is -178.732 at 1.057758 rad/sec frequency. So, I will assume it as phase cross over frequency.

So, Gain Margin ( GM) = 0 - 4.432647

= - 4.432647 dB

Phase Margin can be calculated from Bode plot by seeing how much amount of phase lag is required to reach -180 degrees at the frequency where the open-loop system's magnitude is 0 dB.

From your data

Closest value ( to 0dB) is 4.5133379E-01 at 1.242281E-01 rad/sec frequency. So, I will assume it as gain cross over frequency.

So, Phase margin (PM) = -180 - 123.593500

= -303.5935o

I think you must have drawn Bode Plot so you can get more accurate data using exact value at those cross over frequencies.

Nyquist Plot is drawn on Real axis & imaginary axis instead of what you had drawn on angles axis. And even your Nyquist criteria is wrong although you got correct answer just because both P & Z are equal. So, I will correct and explain the criteria.

Although you got Nyquist criteria right.

As per Nyquist Criteria number of closed loop pole in right half of plane is given by,

N = Z - P

N is no of zeroes on RHP or encirclements in RHP

P is number of poles

Z is number of zeroes.

N = 2-2

= 0

So, the system don't have any zeroes on RHP so system is stable.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---