What is a real work problem in control theory when a system becomes unstable?
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Hunting (too much movement to locate a stable operating point) and hysteresis (lost motion in mechanisms or even electronics) require practical and theoretical solutions.
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A control system is a device or set of devices that manage the behavior of other devices.A control system is an interconnection of components connected or related in such a manner as to command, direct, or regulate itself or another system.\n\nThere are two common types of controllers, with many variations and combinations: logic controls, and feedback or linear controls. There is also fuzzy logic, which attempts to combine the easy design of logic with the real-world utility of feedback controls.
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I am terribly afraid of the equilibrium problem.. the first one on the free response!!! well, good luck!
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use conservation of angular momentum in these kind of problems\nNOT energy conservation\nif you dont know how to use the conservation equation, better read up on examples
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Assume dc/dz is constant, n(t=T)=-DA(dc/dz) T\nBut in reality dc/dz often changes.  Normally dc/dz should decrease with time.  If it is a close system, it will reach the equilibrium state.
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In transfer function analysis of a typical closed loop control system, the transducer (sensor) is modeled as the block that is on the feedback path.  This block measures and sometimes modifies the output signal and sends the signal back to be compared with the reference signal.
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A difficulty in turbulence theory caused by more unknowns than equations.\n\nThe closure problem of turbulence is alternately described as the requirement for an infinite number of equations, which would also be impossible to solve. This problem is apparently associated with the nonlinear nature of turbulence, and the traditional analytical approach of Reynolds averaging the governing equations to eliminate linear terms while retaining the nonlinear terms as statistical correlations of various orders (i.e., consisting of the product of multiple dependent variables). The closure problem is a long-standing unsolved problem of classical (Newtonian) physics. While no exact solution has been found to date, approximations called closure assumptions can be made to allow approximate solution of the equations for practical applications.
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the first link explains system boundary and the second is an explanation of computer simulations in the context of "conceptualizing a system".  hope this helps
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It is knovn as "inertia". It is mathematicaly explained by the first Newton's law (Law of inertia). Both cases are closely connected to the act of the outer force - in the first case, there hasn't been any force around to make resistance to the object's motion (to change it's direction or to slow it down). In the second case, outer forces have made so big resistance to the object's motion that it has to stop because of the loss of kinetic energy, which has been lost in object's attempt to stay in constant motion.
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The loop response time is the key requirement. How fast must the feedback loop correct for a loop input error? Make a model of the complete feedback loop characterizing the time delay of each of it's functional blocks. If the microcomputer is actually within the loop rather than external to it, you'll need to have a repeatable input to output response time. Of course the theory of feedback or servo loops is addressed in electrical engineering courses on "feedback control loops". A "real time operating system" may be required for the microcomputer hardware and software if the response time is critical.
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Possibly working for a robotics supplier?  Lots of application of control theory in the control of a 6-axis robot arm.
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I like the system mechanic. unfortunately it isn't free.\n\nYou can download a demo here:\nhttp://www.systemmechanic.com/\n\nCynthia
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Formulate stability of the system as a function of its energy. Now, one has to show that minimum energy translates into max stability on finding the derivatives.
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Practically, the output isn't always driven to the reference value.  If the output is affected by very large disturbances, the system simply cannot always compensate.  eg: a car's cruise control trying to get the car to top speed up a very steep incline.  Also, it depends on what input reference signal is given.  eg: you try to get the car to follow some crazy speed profile like a sine wave and it may not follow the input well.\n\nAnyway, feedback control systems are usually designed to have zero steady state error at the output for a constant step input.  How is this done?  \n\nThe output is fed back and compared with the reference signal and then the difference is fed to a engineer-designed compensator block.  The compensator then leads to the plant block (the system we are trying to control).\n\nThe compensator is one of the key things here.  It is designed using some special control techniques such as root locus or Bode plot design or simply guess and check with a design program like Matlab.  Basically, the compensator acts on the difference between the output and the input reference in such a way as to create an appropriate signal to the plant.  Depending on whether you go with digital or analog control, the hardware designed to do all this varies.
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Can you post the actual problem here, so we can give you specific help?
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Perhaps something like this that can't be automatically dealt with needs to be changed. Finish your work right away and then spend the rest of your time relaxing. It really helps!
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because it has unstable .dlls