Hello everyone, I am trying to develop a control model for trolleybus (or car ) travel time.
According to the optimal control theory.
First, I must determine the dynamic equation for a trolleybus that moves from stop A and arrives at stop B, for which I made use of Newton's laws, with which I obtained
Fn=Fa-fr-F_air, where Fn is the net force, Fa is the force due to the acceleration of the trolleybus, fr is the kinectic friction force and F_air is the aerodynamic drag. (Is correct?)
Or how do you think that would be the correct dynamic for this problem?
Second, remember that the trolleybus moves in an exclusive way and that during the trip you can find another trolleybus later or there is another trolleybus behind, with this consideration, how can I obtain a dynamic equation that relates the movement of the trolleybus according to whether there is another unit forward or backward ?.
I thought that this dynamic comes from the law of universal gravitation.
Third, according to the optimal control theory, it must have a cost function or a performance index, and this is where I have my biggest drawback, since in the usual theory it is shown that this performance index is (see the image) But my colleagues tell me that I should have a cost functional where the control variable is reflected (the acceleration due to the accelerator), that is, But my colleagues tell me that I should have a cost function that reflects the control variable (acceleration due to the accelerator), that is, a function f that depends on the distance and the control variable. min T(u)= ∫ f(x,x',u)
You can help me clarify these ideas and thus be able to develop a minimum time control model.
check this links the article maybe help you
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.459.7417&rep=rep1&type=pdf
Thanks for your quick response but it's not what I'm looking for. Although the topic of traffic flow is interesting .
Dear Alex,
I suggest you to see links and attached files in topic.
-Energy recovery effectiveness in trolleybus transport
www.ceec.uitp.org/sites/.../1-s2.0-S0378779614000716-main.pdf
-Transportation Planning Handbook
https://books.google.dz/books?isbn=1118762355
Best regards
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