Sketch the complete Nyquist plot for the following open loop transfer ...
Open Loop Transfer Function:
The given open loop transfer function is denoted by G(s). The Nyquist plot can be obtained by plotting the complex values of the transfer function G(s) along the imaginary axis (jω axis) as ω ranges from -∞ to +∞.
Nyquist Plot:
The Nyquist plot represents the frequency response and stability of a system. It consists of two plots - the real part and the imaginary part.
Stability Analysis:
To analyze the stability of a system using the Nyquist plot, we need to check the encirclement of the (-1, 0) point. The number of encirclements of the (-1, 0) point in the Nyquist plot indicates the number of poles of the closed-loop system in the right half of the s-plane.
Steps to Sketch the Nyquist Plot:
1. Determine the poles and zeros of the open loop transfer function G(s).
2. Plot the complex values of G(s) for different frequencies (ω) along the imaginary axis.
3. Identify the encirclements of the (-1, 0) point in the Nyquist plot.
Number of Poles in the Right Half of s-plane:
1. If the Nyquist plot encircles the (-1, 0) point in the clockwise direction, it indicates the presence of poles in the right half of the s-plane.
2. The number of encirclements of the (-1, 0) point indicates the number of poles in the right half of the s-plane.
Explanation:
To determine the number of poles in the right half of the s-plane based on the Nyquist plot, follow these steps:
1. Sketch the Nyquist plot by plotting the complex values of the open loop transfer function G(s) along the imaginary axis (jω axis) for different frequencies (ω).
2. Identify the encirclement of the (-1, 0) point by the Nyquist plot. If the Nyquist plot encircles the (-1, 0) point in the clockwise direction, it indicates the presence of poles in the right half of the s-plane.
3. Count the number of encirclements of the (-1, 0) point in the Nyquist plot. This will give the total number of poles in the right half of the s-plane.
Conclusion:
Based on the Nyquist plot, if the system is unstable, the number of poles of the closed-loop system in the right half of the s-plane can be determined by counting the encirclements of the (-1, 0) point. The Nyquist plot provides a graphical representation of the frequency response and stability of the system.