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FAQs on Root Locus (Control Systems)

1. What is the root locus in control systems?

Ans. The root locus is a graphical representation that shows how the roots of a characteristic equation vary with respect to a specific parameter, typically a gain or controller parameter, in a control system. It helps in analyzing the stability and transient response of the system.

2. How is the root locus plotted?

Ans. The root locus is plotted by determining the poles and zeros of the open-loop transfer function of the control system. Then, by varying the value of the parameter of interest, the roots of the characteristic equation are found. By repeating this process for different values of the parameter, the root locus is obtained.

3. What information can be obtained from the root locus plot?

Ans. The root locus plot provides valuable information about the stability and performance of a control system. It can determine the range of parameter values for which the system is stable, identify the locations of poles and zeros, and reveal the transient response characteristics such as settling time and damping ratio.

4. How can the root locus be used to design a controller?

Ans. The root locus can be used for controller design by selecting a desired closed-loop pole location on the plot. By adjusting the controller parameter, the desired pole location can be achieved. This allows for the design of a controller that meets specific performance requirements such as stability, transient response, and steady-state accuracy.

5. What are the limitations of the root locus technique?

Ans. The root locus technique assumes that the control system is linear and time-invariant. It also assumes that the open-loop transfer function of the system is known and that there are no uncertainties or disturbances. Additionally, the root locus may not provide accurate results for systems with significant time delays or non-linearities.

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Nov 09, 2024 Last updated

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