System Dynamics& Control
System Dynamics& Control AE 3515
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This 0 page Class Notes was uploaded by Demond Hoppe on Monday November 2, 2015. The Class Notes belongs to AE 3515 at Georgia Institute of Technology - Main Campus taught by Amy Pritchett in Fall. Since its upload, it has received 12 views. For similar materials see /class/234299/ae-3515-georgia-institute-of-technology-main-campus in Aerospace Engineering at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
AE35 5 Lecture Notes 09 Mar 202 Overview Closedloop openloop Block diagrams Feedback P I D controllers PID design Openloop Systems RS I CS 0 Plant is supplied an input and responds with an output 0 Cannot compensate for disturbances 0 Examples massspring wconstant force toaster speakers Section 3 Fuday which 9 lt2 Closedloop Systems Desueti r3131 4E Xcmul on m r 011m mm j mu H 23 Controller H t l 1 ti Actuator gtP1 iceltlt i if k I L J 0 Add feedback to close the loop 0 Can compensate for disturbances 0 Greater accuracy but more complex 4 Section 3 Friday March 9 12 Block Diagram Algebra n Blocks in series Blocks in parallel with their outputs added 1 391 I 1 Us H 391 Jv o 0 z 0 0 1 r 3 g I Y Y U2S GlGZ S G1 02 15 US Can recluce complex systems into single transfer functions 5 Section 52 Friday March 9 12 Original Block Diagram TABLE 341 Some of the Block Diagram Reduction Manipulations Manipulation Modi ed Block Diagram LC Cascaded elements R Addition or subtraction eliminating auxiliary L forward path R C R Shifting of pickoff point ahead of blOCk R C Shifting of pickoff point behind block R E Shifting summing oint ahead of block C TC 9 e R E R E Shifting summing oint behind block C c p R C Removing H from feedback path Eliminating Rgt L C feedback path 1 GH S 5 2 6 e Ctl O n Friday March 9 12 Negative Feed back Plant and contrailsr Input 0 Ges is closed oop transfer Feedback fu n CtiO n 0 GsHs is the openloop transfer function Section 52 Fuday which 9 12 Example 4 lt a Figure 0226 Copyright 2008 Pearson Prentice Hall Inc Reduces to Glczlcg cJ quot 539 klu l 8 Section 52 Friday March 9 12 Unity Feedback contrciler piam Rs 65 reference commued inpui feedback path The actual output is used to generate the error signal 9 Section 53 Fuday which 9 12 Unity Feedback 0 The closedloop transfer function becomes 05 Gc5G25 7 Rs 7 1 GCSGIS 0 Notice that the characteristic equation for the above system becomes GAS I Gcscps o 0 The controller has an effect on the system s poles 0 Section 53 Fuday which 9 12 P I D Controllers Proportional controllers pure gain or attenuation Integral controllers integrate error Derivative controllers differentiate error Chapter 9 Friday March 9 12 Proportional Controller uer 0 Controller input is error reference output 0 Controller output is control signal 0 P controller involves only a proportional gain or attenuation Integral Controller UKifECIt 0 Integral of error with a constant gain 0 Increase system type by I In nity steadystate gain Eliminate steadystate error for a unit step input Derivative Control 0 Differentiation of error with a constant gain 0 Reduce overshoot and oscillation 0 Do not affect steadystate response 0 Sensitive to noise Fuday which 9 12 Controller Structure 0 Single controller P controller I controller D controller 0 Combination of controllers PI controller PD controller PID controller PID Controller 0 PI controller K uerKifedt UsK 39EY 0 PD controller de M er K E Um KP deEs 0 PID controller de M erKifedtKdT K d Us Kn 19mm Fuday Wmh 9 12 PID Controller Us KP g KusEs s ms gt Fuday Mamh 9 lt2 P Controller 1 G s 7 A szs1 Us KPEs K 0LTF s s1 K CLTF quot s2s1Kp IS Fuday Mamh 9 2 Friday March 9 12 P Controller Increase in gain upgrade both steadystate and transient responses reduce steadystate error reduce stability P Controller o 39 KP 10 g F KP S 5 r K 2 2 quot p KP 1 Tim SW may W quot 912 P Controller high gain
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