Problem 2.Consider the inverted pendulum on a cart given in Figure 1.mg sinemeFigure 1. Inverted pendulum schematic.The state variables for this system can be defined to be: x, (t) = 0(t), x, (t) = 0(t). Assume that theequation of motion for the pendulum can be written as follows:x2cos (x,)g sin (x,)m cos (x,)m_+m44(x),m cos3m. +mm. +m where g=9.8 m/s, mc is the cart's mass, m is the mass of the pole, I is the half length of the pole, and u isthe applied force.a)b)Find a linearized state equation if the desired equilibrium value for each state is zero.Find a linearized state equation if it is desired to position the pendulum at a 45°.

Answered: Image /qna-images/answer/6ef426f9-c341-4e0d-a05f-3749bcf4058e.jpg

where g=9.8 m/s, mc is the cart's mass, m is the mass of the pole, I is the half length of the pole, and u is the applied force. a) b) Find a linearized state equation if the desired equilibrium value for each state is zero. Find a linearized state equation if it is desired to position the pendulum at a 45°.

where g=9.8 m/s, mc is the cart's mass, m is the mass of the pole, I is the half length of the pole, and u is the applied force. a) b) Find a linearized state equation if the desired equilibrium value for each state is zero. Find a linearized state equation if it is desired to position the pendulum at a 45°.

Electric Motor Control

10th Edition

ISBN:9781133702818

Author:Herman

Publisher:Herman

Chapter3: Magnetic Starters

Section: Chapter Questions

Problem 30SQ

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