Maurice Tutor

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Teaching Since: May 2017
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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 11.00

scaled equations

The normalized, scaled equations of a cart as drawn in Fig. 5.66 of mass mc holding an inverted uniform pendulum of mass mp and length l with no friction are

Where  is a mass ratio bounded by 0 . The cart motion y is measured in units of pendulum length as  and the input is force normalized by the system weight . These equations can be used to compute the transfer functions

In this problem you are to design a control for the system by first closing a loop around the pendulum, Eq. (5.96), and then, with this loop closed, closing a second loop around the cart plus pendulum, Eq. (5.97). For this problem, let the mass ratio be mc = 5mp .

(a) Draw a block diagram for the system with V input and both Y and Θ as outputs.

(b) Design a lead compensation  for the Θ loop to cancel the pole at s = – 1 and place the two remaining poles at –4 ± j4. The new control is U(s), where the force is V (s) = U(s) + D(s)Θ(s). Draw the root locus of the angle loop.

(c) Compute the transfer function of the new plant from U to Y with D(s) in place.

(d) Design a controller Dc(s) for the cart position with the pendulum loop closed. Draw the root locus with respect to the gain of Dc(s).

(e) Use MATLAB to plot the control, cart position, and pendulum position for a unit step change in cart position.

Answers

Maurice Tutor
(5)
Status NEW Posted 27 Aug 2017 02:08 PM My Price 11.00

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