6.01 Lecture Notes - Lecture 1: Harmonic Oscillator, Step Response

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Operator representations are compact and preserve ow information. Combine best features of difference equations and block diagrams. Provide a convenient way to reason out a system. Operator expressions are commutative and associative, and multiplication distributes over addition. Equivalent polynomials > equivalent systems (when started at rest) We can represent an entire system by its operator representation, which we call the system function. Functionals for systems without feedback are polynomials in r. A system can be represented by a delay or gain or the combination of the two systems using a cascade or feedforwardadd or feedbackadd. Any of the rules of composition can be added to any two systems to generate a new type of system. Difference between the two: the change of sign g. The second form is useful in most control applications where the goal is to make y and x converse. Assume that f and g can be represented by polynomials in r.

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