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©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space1
Chapter 12
Design via State Space
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space2
Figure 12.1An automaticpharmacy systemshowing a robotpicking up drugsto deposit inboxes for individual patientsat a hospital © Dick Blume--Syracuse Newspapers/ The Image Works.
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space3
Figure 12.2a. State-spacerepresentationof a plant;b. plant with state-feedback
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space4
Figure 12.3a. Phase-variablerepresentation for plant;b. plant with state-variablefeedback
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space5
Figure 12.4a. Phase-variablerepresentationfor plant of Example 12.1;b. plant with state-variable feedback
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space6
Figure 12.5Simulation of closed-loopsystem ofExample 12.1
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space7
Figure 12.6Comparison ofa. controllable andb. uncontrollablesystems
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space8
Figure 12.7System forExample 12.2
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space9
Figure 12.8a. Signal-flowgraph in cascadeform for G(s ) =10/[(s + 1)(s + 2)];b. system with state feedback added
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space10
Figure 12.9Signal-flow graph for plant of Example 12.4
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space11
Figure 12.10Designed systemwith state-variablefeedback forExample 12.4
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space12
Figure 12.11State-feedback designusing an observer toestimate unavailablestate variables:a. open-loop observer;b. closed-loop observer;c. exploded view of aclosed-loop observer,showing feedbackarrangement toreduce state-variableestimation error
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space13
Figure 12.12Third-order observer inobserver canonicalform:a. before the addition of feedback;b. after the addition of feedback
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space14
Figure 12.13a. Signal-flow graph of a system using observer canonical form variables;b. additional feedback to create observer
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space15
Figure 12.14Simulation showingresponse of observer:a. closed-loop;b. open-loop withobserver gainsdisconnected
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space16
Figure 12.15Comparison ofa. observable andb. unobservablesystems
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space17
Figure 12.16System ofExample 12.6
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space18
Figure 12.17System ofExample 12.7
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space19
Figure 12.18Observer design
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space20
Figure 12.19Observer design step response simulation:a. closed-loopobserver;b. open-loop observer with observer gainsdisconnected
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space21
Figure 12.20a. Plant;b. designed observerfor Example 12.9
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space22
Figure 12.21Integral control forsteady-state errordesign
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space23
Figure 12.22Simplified block diagram of antennacontrol system shown on thefront endpapers (Configuration 1)with K = 200
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space24
Figure 12.23Conceptual state-space designconfiguration, showingplant, observer, and controller
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space25
Figure 12.24Signal-flow graph forG(s) = 1325/[ s(s2 + 101.71s + 171)]
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space26
Figure 12.25Plant with state-variable feedback for controller design
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space27
Figure 12.26Completedstate-space design for the antenna azimuthposition controlsystem, showingcontroller andobserver
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space28
Figure 12.27Designed response of antenna azimuthposition control system:a. impulse response—plant and observerwith the same initialconditions, x1(0) = b. portion of impulseresponse—plant andobserver with differentinitial conditions,x1(0) = 0.006 forthe plant,for the observer
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space29
Figure P12.1
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space30
Figure P12.2(figure continues)
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space31
Figure P12.2(continued )
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space32
Figure P12.3
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space33
Figure P12.4
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space34
Figure P12.5
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 12: Design via State Space35
Figure P12.6Block diagram of agas-fired heater
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