chapter 5 - wiley.com · ©2000, john wiley & sons, inc. nise/control systems engineering, 3/e...
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©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 5: Reduction of Multiple Subsystems1
Chapter 5
Reduction of Multiple Subsystems
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©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 5: Reduction of Multiple Subsystems2
Figure 5.1The space shuttleconsists of multiplesubsystems. Can you identify those that are control systems, or parts of control systems?
© NASA-Houston.
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Figure 5.2Components of a block diagram fora linear, time-invariantsystem
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Figure 5.3a. Cascadedsubsystems;b. equivalent transferfunction
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Figure 5.4Loading in cascadedsystems
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Figure 5.5a. Parallelsubsystems;b. equivalenttransferfunction
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Figure 5.6a. Feedback controlsystem;b. simplified model;c. equivalent transferfunction
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Figure 5.7Block diagramalgebra for summingjunctions—equivalent forms for moving a blocka. to the left past asumming junction;b. to the right past asumming junction
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Figure 5.8Block diagram algebra for pickoff points—equivalent forms for moving a blocka. to the left past a pickoff point;b. to the right past a pickoffpoint
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Figure 5.9Block diagramfor Example5.1
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Figure 5.10Steps in solvingExample 5.1:a. collapse summingjunctions;b. form equivalentcascaded systemin the forward pathand equivalentparallel system in thefeedback path;c. form equivalentfeedback system andmultiply by cascadedG1(s)
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Figure 5.11Block diagram forExample 5.2
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Figure 5.12Steps in the block diagram reduction forExample 5.2
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Figure 5.13Block diagram forSkill-AssessmentExercise 5.1
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Figure 5.14Second-orderfeedback controlsystem
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Figure 5.15Feedback system forExample 5.3
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Figure 5.16Feedback system forExample 5.4
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Figure 5.17Signal-flow graph components:a. system;b. signal;c. interconnection of systems and signals
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Figure 5.18Building signal-flowgraphs:a. cascaded systemnodes (from Figure 5.3(a));b. cascaded systemsignal-flow graph;c. parallel systemnodes (from Figure 5.5(a));d. parallel systemsignal-flow graph;e. feedback systemnodes (from Figure5.6(b));f. feedback systemsignal-flow graph
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Figure 5.19Signal-flow graphdevelopment:a. signal nodes;b. signal-flow graph;c. simplified signal-flow graph
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Figure 5.20Signal-flow graphfor demonstratingMason’s rule
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Figure 5.21Signal-flow graph forExample 5.7
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Figure 5.22Stages ofdevelopment of asignal-flow graphfor the system ofEqs. 5.36:a. place nodes;b. interconnectstate variables andderivatives;c. form dx1/dt ;d. form dx2/dt(figure continues)
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Figure 5.22(continued)e. form dx3 /dt;f. form output
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Figure 5.23Representation ofFigure 3.10 system ascascaded first-ordersystems
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Figure 5.24a. First-order subsystem;b. signal-flow graph for Figure 5.23 system
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Figure 5.25Signal-flowrepresentationof Eq. (5.45)
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Figure 5.26Signal-flowrepresentationof Eq. (5.52)
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Figure 5.27Signal-flow graphs for obtaining forms forG(s) = C(s)/R(s) = (s2 + 7s + 2)/(s3 + 9s2 + 26s + 24):a. phase-variable form;b. controller canonical form
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Figure 5.28Signal-flow graph for observer canonicalform variables:a. planning;b. implementation
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Figure 5.29Feedbackcontrol systemfor Example 5.8
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Figure 5.30Creating a signal-flowgraph for theFigure 5.29 system:a. forward transferfunction;b. complete system
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Figure 5.31State-space forms forC(s)/R(s) =(s+ 3)/[(s+ 4)(s+ 6)].Note: y = c(t)
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Figure 5.32State-spacetransformations
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Figure 5.33To be an eigenvector,the transformation Axmust be collinear withx; thus in (a), x is notan eigenvector; in (b),it is.
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Figure 5.34Alvin, a mannedsubmersible,explored the wreckage of theTitanic with a tethered robot, Jason Junior.
© Rob Catanach, Woods Hole Oceanographic Institution.
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Figure 5.35Block diagramreduction for theantenna azimuthposition controlsystem:a. original;b. pushing inputpotentiometer tothe right past thesumming junction;c. showing equivalentforward transferfunction;d. final closed-loop transfer function
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Figure 5.36Signal-flow graph forthe antenna azimuthposition controlsystem
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Figure 5.37Block diagram ofthe UFSS vehicle’selevator and vehicledynamics, from whicha signal-flow graphcan be drawn
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Figure 5.38Signal-flow graphrepresentation of theUFSS vehicle’s pitch-control system:a. without position andrate feedback;b. with position andrate feedback(Note: Explicitlyrequired variables are:x1 = θ, x2 = dθ/dt,and x4 =δe)
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Figure 5.39Block diagram of the headingcontrol system for the UFSSvehicle
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Figure P5.1
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Figure P5.2
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Figure P5.3
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Figure P5.4
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Figure P5.5
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Figure P5.6
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Figure P5.7
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Figure P5.8
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Figure P5.9
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Figure P5.10
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Figure P5.19