Polar Nyquist [PDF]

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NATIONAL INSTITUTE OF TECHNOLOGY, TIRUCHIRAPPALLI TAMILNADU- 620 015. ELECTRICAL AND ELECTRONICS ENGINEERING. B.Tech. DEGREE , V SEMESTER EE303 - CONTROL SYSTEMS Assignment questions on Polar and Nyquist plot 1. Sketch the polar plots of the open-loop transfer function G(s)H(s) =



K(Ta s + 1)(Tb s + 1) s2 (T s + 1)



Where Ta > T > 0 and Tb > T > 0 2. Sketch the polar plots of the open-loop transfer function G(s)H(s) =



K(Ta s + 1)(Tb s + 1) s2 (T s + 1)



Where T > Ta > 0 and T > Tb > 0 3. A system with the open-loop transfer function K s2 (T1 s + 1)



G(s)H(s) =



is inherently unstable.This system can be stabilized by adding derivative control. Sketch the polar plots for the open-loop transfer function with and without derivative control. 4. Draw a Nyquist locus for the unity-feedback control system with the open-loop transfer function G(s)H(s) =



K(1 − s) s+1



Using the Nyquist stability criterion, determine the stability of the closed-loop system. 5. Consider the closed-loop system with the following open-loop transfer function: G(s)H(s) =



10K(s + 0.5) s2 (s + 2)(s + 10)



Plot both the direct and inverse polar plots of G(s)H(s) with K=1 and K=10. Apply the Nyquist stability criterion to the plots, and determine the stability of the system with these values of K. 6. Draw a Nyquist plot of the following G(s): G(s) =



s(s2



1 + 0.8s + 1)



7. Consider a unity-feedback control system with the following open-loop transfer function: G(s) =



s3



1 + 0.2s2 + s + 1



Draw a Nyquist plot of G(s) and examine the stability of the system. 8. Consider a unity-feedback control system with the following open-loop transfer function: G(s) =



s2 + 2s + 1 s3 + 0.2s2 + s + 1



Draw a Nyquist plot of G(s) and examine the stability of the closed-loop system. 9. Consider the unity-feedback control system with the following open-loop transfer function G(s): G(s) =



K(s + 2) s(s + 1)(s + 10)



Plot Nyquist diagrams of G(s) for K=1, 10, and 100. 10. Consider a negative-feedback system with the following open-loop transfer function: G(s) =



2 s(s + 1)(s + 2)



Plot the Nyquist diagram of G(s). If the system were a positive- feedback one with the same open-loop transfer function G(s), what would the Nyquist diagram look like?