Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Computer Science Posted 27 Aug 2017 My Price 9.00

upside-down pendulum

Unstable equations of motion of the form

arise in situations where the motion of an upside-down pendulum (such as a rocket) must be controlled. (a) Let u = –Kx (position feedback alone), and sketch the root locus with respect to the scalar gain K.

(b) Consider a lead compensator of the form

Select a and K so that the system will display a rise time of about 2 sec and no more than 25% overshoot. Sketch the root locus with respect to K.

(c) Sketch the Bode plot (both magnitude and phase) of the uncompensated plant.

(d) Sketch the Bode plot of the compensated design, and estimate the phase margin.

(e) Design state feedback so that the closed-loop poles are at the same locations as those of the design in part (b).

(f) Design an estimator for x and using the measurement of x = y, and select the observer gain L so that the equation for x has characteristic roots with a damping ratio ζ = 0.5 and a natural frequency ω = 8.

(g) Draw a block diagram of your combined estimator and control law, and indicate where and appear. Draw a Bode plot for the closed-loop system, and compare the resulting bandwidth and stability margins with those obtained using the design of part (b).

Answers

Maurice Tutor
(5)
Status NEW Posted 27 Aug 2017 02:08 PM My Price 9.00

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