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Unformatted text preview: and D, as follows 5 A block diagram representation is where Simple example of a second order system The externally applied force f is the input and the output is the displacement d of the mass away from its rest position ( d = 0) 6 diﬀerential equation for this systems is, using ( F = ma ) This is a second order system so we need two states. Choose We need the time derivatives of these two states Thus we can write the vector/matrix equations 7 Also, any nonsingular transformation of the state of a system is also a state of the system. For example, suppose the ( n × n ) matrix T is a nonsingular transformation of the state x to a new state x ± . Then so If we then deﬁne the equations for the new state are 8 Similarly so and hence so the input and output are the same as before but we now have a transformed state x ± . 9...
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.
 Fall '03
 willcox
 Aeronautics

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