Chapter 5 - wiley.com · ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e 19...

©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e

Chapter 5: Reduction of Multiple Subsystems1

Chapter 5

Reduction of Multiple Subsystems



Figure 5.1The space shuttleconsists of multiplesubsystems. Can you identify those that are control systems, or parts of control systems?

© NASA-Houston.



Figure 5.2Components of a block diagram fora linear, time-invariantsystem



Figure 5.3a. Cascadedsubsystems;b. equivalent transferfunction



Figure 5.4Loading in cascadedsystems



Figure 5.5a. Parallelsubsystems;b. equivalenttransferfunction



Figure 5.6a. Feedback controlsystem;b. simplified model;c. equivalent transferfunction



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



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



Figure 5.9Block diagramfor Example5.1



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)



Figure 5.11Block diagram forExample 5.2



Figure 5.12Steps in the block diagram reduction forExample 5.2



Figure 5.13Block diagram forSkill-AssessmentExercise 5.1



Figure 5.14Second-orderfeedback controlsystem



Figure 5.15Feedback system forExample 5.3



Figure 5.16Feedback system forExample 5.4



Figure 5.17Signal-flow graph components:a. system;b. signal;c. interconnection of systems and signals



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



Figure 5.19Signal-flow graphdevelopment:a. signal nodes;b. signal-flow graph;c. simplified signal-flow graph



Figure 5.20Signal-flow graphfor demonstratingMason’s rule



Figure 5.21Signal-flow graph forExample 5.7



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)



Figure 5.22(continued)e. form dx3 /dt;f. form output



Figure 5.23Representation ofFigure 3.10 system ascascaded first-ordersystems



Figure 5.24a. First-order subsystem;b. signal-flow graph for Figure 5.23 system



Figure 5.25Signal-flowrepresentationof Eq. (5.45)



Figure 5.26Signal-flowrepresentationof Eq. (5.52)



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



Figure 5.28Signal-flow graph for observer canonicalform variables:a. planning;b. implementation



Figure 5.29Feedbackcontrol systemfor Example 5.8



Figure 5.30Creating a signal-flowgraph for theFigure 5.29 system:a. forward transferfunction;b. complete system



Figure 5.31State-space forms forC(s)/R(s) =(s+ 3)/[(s+ 4)(s+ 6)].Note: y = c(t)



Figure 5.32State-spacetransformations



Figure 5.33To be an eigenvector,the transformation Axmust be collinear withx; thus in (a), x is notan eigenvector; in (b),it is.



Figure 5.34Alvin, a mannedsubmersible,explored the wreckage of theTitanic with a tethered robot, Jason Junior.

© Rob Catanach, Woods Hole Oceanographic Institution.



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



Figure 5.36Signal-flow graph forthe antenna azimuthposition controlsystem



Figure 5.37Block diagram ofthe UFSS vehicle’selevator and vehicledynamics, from whicha signal-flow graphcan be drawn



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)



Figure 5.39Block diagram of the headingcontrol system for the UFSSvehicle



Figure P5.1



Figure P5.2



Figure P5.3



Figure P5.4



Figure P5.5



Figure P5.6



Figure P5.7



Figure P5.8



Figure P5.9



Figure P5.10



Figure P5.11



Figure P5.12



Figure P5.13



Figure P5.14



Figure P5.15



Figure P5.16



Figure P5.17



Figure P5.18



Figure P5.19

Chapter 5 - wiley.com · ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e 19...

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