Differential Equations Solutions 126

Differential Equations Solutions 126 - case the parameter...

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136 Chapter 22. Solutions: Case Study: Robot Control: Swinging Like a Pendulum 0 2 4 6 8 10 12 14 16 18 20 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 time (t) θ (t) Dampled Driven Pendulum with Optimal Control Parameter Figure 22.3. The path of the robot arm with optimal control. CHALLENGE 22.6. See the program problem6.m on the website. The energy function returns the energy as speciFed above plus a large positive penalty term in
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Unformatted text preview: case the parameter is unsuccessful; the penalty keeps the minimizer from choosing an unsuccessful parameter. ±or b = − 1 . 7859, the total energy consumed is about 43.14 Joules. The motion of the pendulum is shown in ±igure 22.3. Note that it is always a good idea to sketch the function to be minimized to see if the reported solution is reasonable....
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