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The most important technique used for stability and the transient response of the system is
- a)Nyquist plot
- b)Root locus
- c)Bode plot
- d)Routh Hurwitz criteria
Correct answer is option 'B'. Can you explain this answer?
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The most important technique used for stability and the transient resp...
Definition:
The root locus plots the poles of the closed-loop transfer function in the complex s-plane as K varies from 0 to ∞
The purpose of Root locus is defined as:
- To find the nature of the system and ‘K’ value for stability.
- To find the relative stability.
- If the root locus branches move towards the right, system is less stable and if they move towards the left then the system is more relative stable.
- It is the best method to find the Relative stability and RH criteria is best to find absolute stability
The relation between the closed-loop and open-loop poles
D(s) = 0 gives open-loop poles and N(s) = 0 gives closed-loop poles
Characteristic equation is D(s) + kN(s) = 0.
Closed-loop poles are nothing but the sum of open-loop poles and zeroes.
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The most important technique used for stability and the transient resp...
Root Locus:
Explanation:
The root locus method is a powerful tool used in control systems engineering to analyze the transient response and stability of a system. It is based on the concept of the poles of the closed-loop transfer function as a parameter, such as the gain of a proportional controller, is varied.
Key Points:
- The root locus technique provides insights into how the poles of the closed-loop system move as a certain parameter is changed.
- By plotting the roots of the characteristic equation in the complex plane as the parameter varies, engineers can determine the stability and transient response of the system.
- The root locus plot helps in designing controllers that meet specific performance criteria such as settling time, overshoot, and steady-state error.
- It is a graphical method that can be used to analyze the effects of adding poles and zeros to the system as well as changing the controller parameters.
- By examining the root locus plot, engineers can determine the range of controller parameters that will result in a stable system with acceptable transient response characteristics.
Conclusion:
In conclusion, the root locus technique is crucial for analyzing the stability and transient response of a control system. By using this method, engineers can design controllers that meet desired performance specifications and ensure the system operates effectively.
Explanation:
The root locus method is a powerful tool used in control systems engineering to analyze the transient response and stability of a system. It is based on the concept of the poles of the closed-loop transfer function as a parameter, such as the gain of a proportional controller, is varied.
Key Points:
- The root locus technique provides insights into how the poles of the closed-loop system move as a certain parameter is changed.
- By plotting the roots of the characteristic equation in the complex plane as the parameter varies, engineers can determine the stability and transient response of the system.
- The root locus plot helps in designing controllers that meet specific performance criteria such as settling time, overshoot, and steady-state error.
- It is a graphical method that can be used to analyze the effects of adding poles and zeros to the system as well as changing the controller parameters.
- By examining the root locus plot, engineers can determine the range of controller parameters that will result in a stable system with acceptable transient response characteristics.
Conclusion:
In conclusion, the root locus technique is crucial for analyzing the stability and transient response of a control system. By using this method, engineers can design controllers that meet desired performance specifications and ensure the system operates effectively.
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