copyright ©2011 by pearson education, inc. all rights reserved. modern control systems, twelfth...

Copyright ©2011 by Pearson Education, Inc.All rights reserved.

Modern Control Systems, Twelfth EditionRichard C. Dorf and Robert H. Bishop

Figure 5.1 Two performance measures versus parameter p.



Figure 5.2 Test input signals: (a) step, (b) ramp, and (c) parabolic.



Figure 5.3 Open-loop control system.



Figure 5.4 Second-order closed-loop control system.



Figure 5.5 (a) Transient response of a second-order system (Equation 5.9) for a step input. (b) The transient response of a second-order system (Equation 5.9) for a step input as a function of ζ and ωnt. (Courtesy of Professor R.Jacquot, University of Wyoming.)



Figure 5.6 Response of a second-order system for an impulse function input.



Figure 5.7 Step response of a control system (Equation 5.9).



Figure 5.8 Percent overshoot and normalized peak time versus damping ratio ζ for a second-order system (Equation 5.8).



Figure 5.9 Normalized rise time, Tr1, versus ζ for a second-order system.



Figure 5.10 The step response for ζ = 0.2 for ωn = 1 and ωn = 10.



Figure 5.11 The step response for ωn = 5 with ζ = 0.7 and ζ = 1.



Figure 5.12 An s-plane diagram of a third-order system.



Figure 5.13 (a) Percent overshoot as a function of ζ and ωn when a second-order transfer function contains a zero. Redrawn with permission from R. N. Clark, Introduction to Automatic Control Systems (New York: Wiley, 1962). (b) The response for the second-order transfer function with a zero for four values of the ratio a/ζωn: A = 5, B = 2, C = 1, and D = 0.5 when ζ = 0.45.



Figure 5.14 Single-loop feedback control system.



Figure 5.15 Specifications and root locations on the s-plane.



Figure 5.16 The poles and zeros on the s-plane for a third-order system.



Figure 5.17 Impulse response for various root locations in the s-plane. (The conjugate root is not shown.)



Figure 5.18 Closed-loop control system with unity feedback.



Figure 5.19 Block diagram of steering control system for a mobile robot.



Figure 5.20 Triangular wave response.



Figure 5.21 A nonunity feedback system.



Figure 5.22 A speed control system.



Figure 5.23 The speed control system of Figure 5.22 with K1 = K2.



Figure 5.24 A system with a feedback H(s).



Figure 5.25 The calculation of the integral squared error.



Figure 5.26 Single-loop feedback control system. (a) Signal-flow graph. (b) Block diagram model.



Figure 5.27 Three performance criteria for a second-order system.



Figure 5.28 A space telescope pointing control system. (a) Block diagram. (b) Signal-flow graph.



Figure 5.29 The performance indices of the telescope control system versus K3.



Figure 5.30 Step responses of a normalized transfer function using optimum coefficients for (a) ISE, (b) IAE.



Figure 5.30 (continued) Step responses of a normalized transfer function using optimum coefficients for (c) ITAE. The response is for normalized time, ωnt.



Figure 5.31 The foreground camera, which may be either a film or video camera, is trained on the blue cyclorama stage. The electronic servocontrol installation permits the slaving, by means of electronic servodevices, of the two cameras. The background camera reaches into the miniature set with a periscope lens and instantaneously reproduces all movements of the foreground camera in the scale of the miniature. The video control installation allows the composite image to be monitored and recorded live. (Part (a) reprinted with permission from Electronic Design 24, 11, May 24, 1976. Copyright © Hayden Publishing Co., Inc., 1976.)



Figure 5.32 The closed-loop roots of a minimum ITAE system.



Figure 5.33 An upper-torso humanoid robot named Domo helps researchers investigate robot manipulation in unstructured environments. (Photo courtesy of Aaron Edsinger, MIT Humanoid Robotics Group.)



Figure 5.34 (a) The Hubble telescope pointing system, (b) reduced block diagram, (c) system design, and (d) systemresponse to a unit step input command and a unit step disturbance input.



Figure 5.35 Control of the bank angle of an airplane using differential deflections of the ailerons.



Figure 5.36 Elements of the control system design process emphasized in the airplane attitude control example.



Figure 5.37 Bank angle control autopilot.



Figure 5.38 Step response comparison of third-order aircraft model versus second-order approximation.



Figure 5.39 Step response of the 3rd-order aircraft model with K = 0.10, 0.16, and 0.20 showing that, as predicted, as K decreases percent overshoot decreases while the time-to-peak increases.



Figure 5.40 The impulse function.



Figure 5.41 (a) Response of a second-order system to a step input. (b) m-file script.



Figure 5.42 (a) Response of a second-order system to an impulse function input. (b) m-file script.



Figure 5.43 The Isim function.



Figure 5.44 (a) Transient response of the mobile robot steering control system to a ramp input. (b) m-file script.



Figure 5.45 (a) Step response comparison for an approximate transfer function versus the actual transfer function.(b) m-file script.



Figure 5.46 Control system model with a second-order model of the motor and load.



Figure 5.47 Response of the system to a unit step input, r(t) = 1, t > 0. (a) m-file script. (b) Response for Ka = 30 and 60.



Figure 5.48 Response of the system to a unit step disturbance, Td(s) = 1/s. (a) m-file script. (b) Response for Ka = 30 and 60.



Figure 5.49 The response of a feedback system to a ramp input with K = 1, 2, and 8 when G(s) = K/[s(s + 1)(s + 3)]. The steady-state error is reduced as K is increased, but the response becomes oscillatory at K = 8.



Figure 5.50 Block diagram for the Skills Check.



Figure 5.51 Feedback system with integral controller and derivative measurement.



Figure E5.2 Racing car speed control.



Figure E5.3 Levitated train control.



Figure E5.5 Feedback system with proportional controller Gc(s) = K.



Figure E5.6 Block diagram with position and velocity feedback.



Figure E5.7 Blood-sugar level control.



Figure E5.11 Unity feedback system.



Figure E5.12 Speed control of a Ferris wheel.



Figure E5.14 Feedback system.



Figure E5.18 Feedback system with prefilter.



Figure E5.20 Nonunity closed-loop feedback control system with parameter Ka.



Figure P5.1 Camera wobble control.



Figure P5.3 Laser beam control.



Figure P5.5 (a) The space telescope. (b) The space telescope pointing control system.



Figure P5.6 Robot path control.



Figure P5.7 (a) Astronaut Bruce McCandless II is shown a few meters away from the earth-orbiting space shuttle. Heused a nitrogen-propelled hand-controlled device called the manned maneuvering unit. (Courtesy of National Aeronautics and Space Administration.) (b) Block diagram of controller.



Figure P5.8 Solar cell control.



Figure P5.9 A model of the antenna for the Telstar System at Andover, Maine. (Photo courtesy of Bell Telephone Laboratories, Inc.)



Figure P5.16 Feedback amplifier.



Figure P5.17 Heart pacemaker.



Figure P5.20 System with pregain, K1.



Figure P5.21 Closed-loop system with parameters k and a.



Figure P5.22 Nonunity closed-loop feedback control system.



Figure AP5.2 System with a variable zero.



Figure AP5.3 System with a variable pole in the process.



Figure AP5.4 Speed control.



Figure AP5.5 System with control parameter α.



Figure AP5.6 DC motor control.



Figure AP5.7 Closed-loop system with unity feedback.



Figure AP5.9 Feedback control system with a proportional plus integral controller.



Figure DP5.1 Roll angle control.



Figure DP5.2 Welding tip position control.



Figure DP5.3 Active suspension system.



Figure DP5.4 Control of a space satellite.



Figure DP5.5 Deburring robot.



Figure DP5.6 Position control robot.



Figure DP5.7 (a) Three-dimensional cam and (b) x-axis control system.



Figure DP5.8 Spray-paint robot.



Figure CP5.3 A simple second-order system.



Figure CP5.4 A negative feedback control system.



Figure CP5.5 Feedback control system with controller and prefilter.



Figure CP5.7 An aircraft autopilot block diagram.



Figure CP5.8 A missile rate loop autopilot.



Figure CP5.9 Nonunity feedback system.



Figure CP5.10 Closed-loop system for m-file.



Figure CP5.11 A single loop unity feedback system. (a) Signal flow graph. (b) Block diagram.

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