MIT6_01F09_lec05

# MIT6_01F09_lec05 - 6.01: Introduction to EECS 1 Week 5...

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Example: wallFinder System ± ± Approach a wall, stopping a desired distance d i in front of it. d i = desiredFront d o = distanceFront d o K = 0 . 5 t d o K = 1 t d o K = 2 t d o K = 8 t What causes these diﬀerent types of responses? Is there a systematic way to optimize K ? Analysis of wallFinder System: Review Response of system is concisely represented with diﬀerence equation. d i = desiredFront d o = distanceFront proportional controller: v [ n ]= Ke [ n K d i [ n ] d s [ n ] locomotion: d o [ n d o [ n 1] Tv [ n 1] sensor with no delay: d s [ n d o [ n ] The diﬀerence equations provide a concise description of behavior. d o [ n d o [ n 1] [ n 1] = d o [ n 1] TK d i [ n 1] d o [ n 1] However it provides little insight into how to choose the gain K . 6.01: Introduction to EECS 1 Week 5 October 6, 2009 6.01: Introduction to EECS I Designing Control Systems Signals and Systems We have developed multiple representations of systems, each with particular strengths. Diﬀerence equations are mathematically compact. y [ n x [ n ]+ p 0 y [ n 1] Block diagrams illustrate signal ﬂow paths graphically. Delay + p 0 X Y Operators represent systems as polynomials. Y = X + p 0 R Y System Functions represent entire systems as single operations. Y = HX ; H = Y X = 1 1 p 0 R Week 5 October 6, 2009 Feedback, Cyclic Signal Paths, and Poles We have also developed insights in the use of feedback. Feedback produces cyclic signal ﬂow paths. Delay + X Y Cyclic signal ﬂow paths persistent responses to transient inputs. Delay + p 0 X Y We can characterize persistent responses (called modes) with poles. 1 0 1234 n y [ n p n o ; n 0 Designing a Control System Today’s goal: use system theory to design a control system. 1

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6.01: Introduction to EECS 1 Week 5 October 6, 2009 Analysis of wallFinder System: Block Diagram A block diagram for this system reveals two feedback paths. ± d i = desiredFront d o = distanceFront proportional controller: v [ n ]= Ke [ n K d i [ n ] d s [ n ] locomotion: d o [ n d o [ n 1] Tv [ n 1] sensor with no delay: d s [ n d o [ n ] V D i + K D o T + R Analysis of wallFinder System: System Functions Simplify block diagram with R operator and system functions. Start with accumulator. + K T + R D i D o What is the input/output relation for an accumulator?
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## This note was uploaded on 11/07/2011 for the course COMPUTER 6.01 taught by Professor Staff during the Spring '09 term at MIT.

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MIT6_01F09_lec05 - 6.01: Introduction to EECS 1 Week 5...

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