optimal control

first of all, what is an "optimal control law" or actually a "control law"? is it the equation that defines your control variable/vector u ?
second of all ... I'm taking "optimal control" right now as a grad course and, while it's too early to tell, for now the course has been mainly math and optimisation. how to find the minimum "something" with some constraints, and variations on this theme.
let's say I solve the problem and find the equations that define my optimal control law, whatever that is... let's say for a multivariable ssytem in state space.
how do I actually make a control system for this? in practical real world terms...
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mr sparkle wrote:

The cynical answer: Chuck the theoretical crap and build a good ol' PID.
The answer you were looking for: You need to carefully model your system, with all of the actuators, sensors, ADCs, DACs and anything else that may impact the transfer function seen by the controller. Then take the controller model that you've designed and implement it in software or hardware, try it, find out it doesn't work, spend several weeks flipping signs only to find out that you failed to model some important parameter and your gain is really much too high, then chuck the theoretical crap and build a good ol' PID.
Oops. That was even _more_ cynical. It can be done, and done well, but there be pitfalls and it can't really be covered by one simple post.
--

Tim Wescott
Wescott Design Services
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Hello, It is good question. I will give some small example for this. Let us take Satellite example while is taking off. At the starting take of velocity sould be more and then once attaince certian altitute becasue of the Gravitaion , the fuel ignition rate will be less. So the Iginitin rate of the Fule should be optimally controlled with time. There the control vector " u" plays a ood role. for this, the non linear dynamical eqautions of the total vehicle system should known and then , then the " Optimal control Law" should be defined and and the optimal control should be find out, finally the corresponding hardware be made with all , DSP, Micro Controllers, PLC and other interfacing devices.
It may be a good example. But you can have some idea having gone thrugh this.
All the best ,
sathish

law"?
constraints,
optimal
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Actually with the case of rockets, the faster you burn the fuel (assuming efficient combustion) the more efficient the whole system. For example, a gun burns all the fuel instantly. The faster you burn the fuel the less distance you have to transport the fuel. The optimal approach here is very simple -- run your engines at their maximum until you reach the required velocity.
Walter.

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