lecture_18 - MIT OpenCourseWare http://ocw.mit.edu 2.004...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . T T T T 1 2 3 4 a ) U n i t p u l s e s o f d i f f e r e n t e x t e n t s b ) T h e i m p u l s e f u n c t i o n 1 / T 1 1 / T 2 1 / T 3 1 / T 4 t @ ( t ) t @ Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 Dynamics and Control II Spring Term 2008 Lecture 18 1 Reading: Nise: Sec. 1.5 1 Common Inputs Used in Control System Design and Analysis Two classes of inputs commonly used to characterize the performance of feedback control systems are: (a) The Singularity Functions: These functions have a discontinuity at time t = 0: (i) The Dirac Delta (Impulse) Function: The delta function is used to charac- terize the response of a system to brief, intense inputs. In the figure below, (a) shows some unit pulses (pulses with unit area so that if the duration of the pulse is T , its amplitude is 1 /T . The Dirac delta function ( t ) is the limiting case of such pulses as T 0. Notice that this implies that the amplitude 1 /T . The strict definition of ( t ) is ( t ) = 0 , for t = 0 ( t ) is undefined at t = (lim ( t ) = ) t + ( t ) dt = 1 (ii)...
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lecture_18 - MIT OpenCourseWare http://ocw.mit.edu 2.004...

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