MIT2_017JF09_p05

# MIT2_017JF09_p05 - 5 LTI MACHINE 5 8 LTI Machine If you put...

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Unformatted text preview: 5 LTI MACHINE? 5 8 LTI Machine? If you put a sequence of ﬁve numbers into a certain machine, it responds with a ﬁve-number sequence; this exchange constitutes one experiment. For each possible machine characteris­ tic below, give enough sets of input-output sequences (that is, ”experiments”) that would demonstrate it: 1. Linear, time-invariant A solution: [1,1,1,1,1] → [3,2,2,1,0] and [0,2,2,2,2] → [0,6,4,4,2]. 2. Linear, time-varying A solution: [1,1,0,0,0] → [0,3,2,1,0] and [0,2,2,0,0] → [0,6,4,2,0]. 3. Nonlinear, time-invariant A solution: [1,2,3,0,0] → [5,4,3,0,0] and [0,2,4,6,0] → [0,4,3,2,0]. Note this is a static mapping; a dynamic system would take more trials to determine that it was both nonlinear and time-invariant. 4. Nonlinear, time-varying A solution: [2,3,4,0,0] → [1,1,0,1,1] and [0,4,6,8,0] → [0,0,3,0,3]. A time-varying system cannot be a static map, so we have to have dynamics. However, similarly to the above case, there is a limit to what can be deduced with only two trials. MIT OpenCourseWare http://ocw.mit.edu 2.017J Design of Electromechanical Robotic Systems Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . ...
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MIT2_017JF09_p05 - 5 LTI MACHINE 5 8 LTI Machine If you put...

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