A byte of basic control theory
This paper provides knowledge of the basic control-related concepts required in the following. Given a dynamic system, one may want its output to evolve over time in a certain manner. Most frequently this means desiring that a prescribed trajectory be followed, or that the system motion minimise some cost function depending on output and/or state and possibly input, or any combination thereof, although here it shall restrict the scope to cases in which a reference output trajectory needs following. To achieve the desired goal, the system to be controlled must be conveniently coupled to some other system, devoted to suitably determining its input. The former system is termed the controlled system or - for traditional reasons - the plant, the latter the controller, and the compound of the two the control system. The most typical control problem is to determine the controller given the controlled system and the specifications.
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