2 Step Input Optimal Control.

Cuthbert Nyack
This applet shows the response to a modified step input. With K fixed ht and wid are adjusted to give an acceptable step response. Then wid is varied to get a minimum J. Some cases are given below:-

(3.0, 1.0, 1.0, 1.92, 0.72) 1.279267
(4.0, 1.0, 1.0, 1.64, 0.69) 1.303315
(5.0, 1.0, 1.0, 1.46, 0.68) 1.361515
(6.0, 1.0, 1.0, 1.34, 0.66) 1.394961
(6.0, 0.5, 1.0, 0.96, 0.72) 1.625266
(6.0, 1.5, 1.0, 1.62, 0.63) 1.326888

Varying K, wid and ht to obtain a minimum J yields an unsatisfactory step response eg (4.1, 1.0, 1.0, 1.6, 0.59) 1.228032

Varying K, wid and ht to obtain a minimum J yields an unsatisfactory step response eg (4.1, 1.0, 1.0, 1.6, 0.59) 1.228032

Reducing m does a little better eg (22.0, 1.0, 0.1, 0.7, 0.56) 0.411087





Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.