From: "Claude Tydtgat" Subject: Re: Control Theory Newsgroups: sci.math Date: Mon, 22 Jun 1998 13:19:46 +0200 Hi, Control theory is much used in electronic systems. The purpose is to control a physical quantity, like temperature in a room, speed of a motor. For example suppose a drilling machine which runs a 2000 rotations per minute. If the drill will enter a metal, the speed will decrease because of the friction. However, an appropriate control system can in that case increase the applied voltage to the drilling machine so that the speed remains constant. Essentialy control theory tries to describe all blocks in a control system with a transfer function, which is a mathematical function in the laplace parameter s. Once all transfer functions of all blocks are known ( which is the hardest part of it ), one can calculate if the complete system is stable, what is its dynamical behaviour, ... Other examples are phase locked loops, stabilising rockets, ... fran and matthew b. wrote in article <358DD897.5@rconnect.com>... > Hi! > .... > Can anyone tell me briefly some basics of control theory (i.e. > historical background, mathematical basis, practical purposes) or > perhaps suggest some basic texts that get across the overall import of > the topic (withoput going necessarily into all of the high level > details?) ============================================================================== From: Anna Kryswiez Newsgroups: sci.math Subject: Re: Control Theory Date: Mon, 22 Jun 1998 13:16:58 +0100 Fran B asks: > [...] Can anyone tell me briefly some basics of control theory? [...] to which Claude Tydtgat replies: > [.. good stuff...] Essentially control theory tries to describe all blocks in a control > system with a transfer function. [...more good stuff...] to which I add: Fine, but there are other branches of Control Theory. The one above is the "classical" one of "linear control theory" which leads to differential equations, Laplace transforms, Fourier transforms, Nyquist stability criteria and suchlike. Don't forget the other totally different approach of "Optimal Control Theory" and "Discrete Control Theory". Optimal Control Theory gives you a different approach and solution. For example, suppose you have to move a heavy weight (e.g. a radio telescope) from position A to position B as fast as possible given that you have a motor of variable torque but limited to some maximum torque T. Then optimal control theory will give you results like "put the motor on full forward, and accelerate the weight as fast as possible. When you get halfway to the new position, slam the motor into full reverse. The weight will come to rest at precisely the right position. Or you might have an industrial process that you want to change with least expenditure of money. Linear control theory will give you answers like varying the torque according to a linear function of position and velocity, leading to critically damped exponential approach to the new position. Discrete Control theory works well with computer-based systems which sample the status data periodically and then compute the new inputs to feed into the system. It could be linear, in which case you are dealing with things like Discrete Fourier Transforms, and Fast Fourier Transforms. It is in practice often combined with optimal control theory. For example, in the above example of the heavy weight, the computer might sample the position and speed every second and re-compute the best setting for the motor, or the best time at which to slam it into reverse. Be aware that Linear Control Theory provides a rich source of exam questions with mathematics, whereas Optimal Control Theory good for real-life situations but difficult to set exam questions on! Roy Everett ============================================================================== From: Roy Everett Newsgroups: sci.math Subject: Re: Control Theory Date: Mon, 22 Jun 1998 13:32:39 +0100 My previous posting was ended and sent prematurely... Fran B asks: > [...] Can anyone tell me briefly some basics of control theory? [...] to which Claude Tydtgat replies: > [.. good stuff...] Essentially control theory tries to describe all blocks in a control > system with a transfer function. [...more good stuff...] There was a lot of work done by Russian mathematicians in this area in the 1960s. I don't have access to my old lecture notes in this, but the name "Lyupanov" comes to mind. Roy Everett e-mail: purpose@compuserve.com Organisation: Kira IT. (Apologies for spurious reference to UEA and a "Anna Kryswiez" in my previous posting: configuration error.)