Figure 13 1 A block diagram of a
Figure 13. 1 A block diagram of a computer control system, including the signal converters. The signal is indicated as digital or analog. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 2 The development of INTEL microprocessors measured in millions of transistors. (Source: INTEL. ) Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 3 The flight deck of the Boeing 757 and 767 features digital control electronics, including an engine indicating system and a crew alerting system. All systems controls are within reach of either pilot. The system includes an inertial reference system making use of laser gyroscopes and an electronic attitude director indicator. A flightmanagement computer system integrates navigation, guidance, and performance data functions. When coupled with the automatic flight control system (automatic pilot), the flight-management system provides accurate engine thrust settings and flight-path guidance during all phases of flight from immediately after takeoff to final approach and landing. The system can predict the speeds and altitudes that will result in the best fuel economy and command the airplane to follow the most fuel-efficient or the “least time” flight paths. (Courtesy of Boeing Airplane Co. ) Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 4 A digital control system. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 5 An ideal sampler with an input r(t). Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 6 (a) An input signal r(t). (b) The sampled signal The vertical arrow represents an impulse. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 7 A sampler and zero-order hold circuit. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 8 The response of a zero-order hold to an impulse input r(k. T), which equals unity when k = 0 and equals zero when k ≠ 0, so that r*(t) = r(0)Ϭ (t). Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 9 The response of a sampler and zero-order hold for a ramp input r(t ) = t. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 10 The response of a sampler and zero-order hold to an input r(t ) = e-t for two values of sampling period T. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 11 An open-loop, sampled-data system (without feedback). Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 12 System with sampled output. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 13 The z-transform transfer function in block diagram form. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 14 Feedback control system with unity feedback. G(z) is the z-transform corresponding to G(s), which represents the process and the zero-order hold. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 15 (a) Aibo is a sophisticated entertainment robot. Aibo looks like a Chihuahua and wags its tail, does tricks, and goes for walks. Aibo depends on a wide range of sensors, including touch, color CCD camera, range finder, and velocity sensors. A 64 -bit RISC microprocessor and 16 MB of memory are built in. It has 18 joints powered by 18 motors. Photo courtesy of Sony Electronics Inc. (b) Feedback control system with a digital controller. (c) Block diagram model. Note that G(z ) = Z{G 0(s)Gp(s)}. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 16 A closed-loop, sampled-data system. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 17 The response of a second-order system: (a) continuous (T = 0), not sampled; (b) sampled system, T = 1 s. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 18 A closed-loop sampled system. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 19 The maximum overshoot │y│or a second-order sampled system for a unit step input. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 20 The loci of integral squared error for a second-order sampled system for constant values of I. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 21 The steady-state error of a second-order sampled system for a unit ramp input r(t ) = t, t > 0. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 22 The response of a sampled-data second-order system to a unit step input. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 23 The continuous system model of a sampled system. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 24 Closed-loop system with a digital controller. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 25 Root locus for Example 13. 8. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 26 Root locus for Example 13. 9. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 27 Curves of constant ζ on the z-plane. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 28 A table motion control system: (a) actuator and table; (b) block diagram. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 29 Model of the wheel control for a work table. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 30 (a) Fly-by-wire aircraft control surface system and (b) block diagram. The sampling period is 0. 1 second. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 31 Elements of the control system design process emphasized in this fly-by-wire aircraft control surface example. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 32 Root locus for D(z) = K. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 33 Root locus for D(z) = K with the stability and performance regions shown. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 34 Compensated root locus. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 35 Closed-loop system step response. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 36 (a) The tf function. (b) The c 2 d function. (c) The d 2 c function. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 37 Using the c 2 d function to convert G(s) = G 0(s)Gp(s) to G(z). Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 38 The step function generates the output y(k. T) for a step input. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 39 The impulse function generates the output y(k. T) for an impulse input. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 40 The Isim function generates the output y(k. T) for an arbitrary input. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 41 The discrete response, y(k. T), of a sampled second-order system to a unit step. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 42 The continuous response y(t) to a unit step for the system of Figure 13. 16. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 43 The rlocus function for sampled data systems. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 44 Feedback control system with a digital controller. Note that G(z ) =Z[G 0(s)Gp(s)]. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure 13. 45 Root locus. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure E 13. 5 (a) Space shuttle and robotic arm. (b) Astronaut control of the arm. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure E 13. 6 Automobile spray paint system. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure E 13. 15 An open-loop sampled-data system with sampling time T = 1 s. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure E 13. 16 An open-loop sampled-data system with sampling time T = 0. 5 s. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure P 13. 3 Sampling system. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure P 13. 9 Mobile camera for football field. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure AP 13. 2 A glue control system Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure AP 13. 5 A closed-loop sampled-data system with sampling time T = 0. 1 s. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure DP 13. 3 Vehicle fraction control system. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure DP 13. 5 Control system for an extruder. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure DP 13. 6 A closed-loop sampled-data system with sampling time T = 1 s. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Figure CP 13. 5 Control system with a digital controller. Modern Control Systems, Eleventh Edition Richard C. Dorf and Robert H. Bishop Copyright © 2008 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
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