Digital Control of Electrical Drives S Vukosavic Springer.pdf

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Digital Control of Electrical Drives

Power Electronics and Power Systems Series Editors: M. A. Pai Alex Stankovic University of Illinois at Urbana-Champaign Northeastern University Urbana, Illinois Boston, Massachusetts Digital Control of Electrical Drives Slobodan N. Vukosavić ISBN 978-0-387-48598-0 Three-Phase Diode Rectifiers with Low Harmonics Predrag Pejović ISBN 978-0-387-29310-3 Computational Techniques for Voltage Stability Assessment and Control Venkataramana Ajjarapu ISBN 978-0-387-26080-8 Real-Time Stability in Power Systems: Techniques for Early Detection of the Risk of Blackout Savu C. Savulesco, ed. ISBN 978-0-387-25626-9 Robust Control in Power Systems Bikash Pal and Balarko Chaudhuri ISBN 978-0-387-25949-9 Applied Mathematics for Restructured Electric Power Systems: Optimization, Control, and Computational Intelligence Joe H. Chow, Felix F. Wu, and James A. Momoh, eds. ISBN 978-0-387-23470-0 HVDC and FACTS Controllers: Applications of Static Converters in Power Systems Vijay K. Sood ISBN 978-1-4020-7890-3 Power Quality Enhancement Using Custom Power Devices Arindam Ghosh and Gerard Ledwich ISBN 978-1-4020-7180-5 Computational Methods for Large Sparse Power Systems Analysis: An Object Oriented Approach S.A. Soman, S.A. Khaparde, and Shubha Pandit ISBN 978-0-7923-7591-3 Operation of Restructured Power Systems Kankar Bhattacharya, Math H.J. Bollen, Jaap E. Daalder ISBN 978-0-7923-7397-1 Transient Stability of Power Systems: A Unified Approach to Assessment and Control Mania Pavella, Damien Ernst, and Daniel Ruiz-Vega ISBN 978-0-7923-7963-8 Maintenance Scheduling in Restructured Power Systems M. Shahidehpour and M. Marwali ISBN 978-0-7923-7872-3 Continued after index

Digital Control of Electrical Drives Slobodan N. Vukosavić The University of Belgrade

Slobodan N. Vukosavić University of Belgrade Faculty of Electrical Engineering Bulevar Kralja Aleksandra 73 11120 Belgrade Serbia Series Editors: M. A. Pai, Professor Emeritus Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801 Alex M. Stankovic, Professor Dept. of Electrical & Computer Engineering, 440DA Northeastern University 360 Huntington Ave. Boston, MA 02115 e-ISBN 978-0-387-48598-0 Library of Congress Control Number: 2006935130 ISBN 978-0-387-25985-7 Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com

Contents Preface .......................................................................................................ix 1 Speed Control..........................................................................................1 1.1 Basic structure of the speed-controlled system.................................1 Problems .................................................................................................5 2 Basic Structure of the Speed Controller ..............................................7 2.1 Proportional control action ...............................................................7 2.1.1 Open-loop and closed-loop transfer functions...........................8 2.1.2 Load rejection of the proportional speed controller ................12 2.1.3 Proportional speed controller with variable reference.............13 2.1.4 Proportional speed controller with frictional load ...................15 2.2 The speed controller with proportional and integral action............16 2.2.1 Transfer functions of the system with a PI controller..............17 2.2.2 Load rejection with the PI speed controller.............................18 2.2.3 Step response with the PI speed controller ..............................19 2.2.4 The PI speed controller with relocated proportional action...................................................................26 2.2.5 Parameter setting and the closed-loop bandwidth ...................28 2.2.6 Variable reference tracking .....................................................30 2.3 Suppression of load disturbances and tracking errors ....................31 2.3.1 The proper controller structure for the given reference profile......................................................................32 2.3.2 Internal Model Principle (IMP) ...............................................37 2.4 Feedforward compensation.............................................................40 Problems ...............................................................................................47 3 Parameter Setting of Analog Speed Controllers ................................51 3.1 Delays in torque actuation ..............................................................51 3.1.1 The DC drive power amplifiers ...............................................52 3.1.2 Current controllers...................................................................56 3.1.3 Torque actuation in voltage-controlled DC drives ..................58

vi Contents 3.2 The impact of secondary dynamics on speed-controlled DC drives....................................................................................... 59 3.3 Double ratios and the absolute value optimum............................... 61 3.4 Double ratios with proportional speed controllers.......................... 66 3.5 Tuning of the PI controller according to double ratios................... 69 3.6 Symmetrical optimum .................................................................... 72 Problems ............................................................................................... 77 4 Digital Speed Control ........................................................................... 79 4.1 Discrete-time implementation of speed controllers ........................ 80 4.2 Analysis of the system with a PI discrete-time speed controller .... 86 4.2.1 The system with an idealized torque actuator and inertial load ...................................................................... 87 4.2.2 The z-transform and the pulse transfer function ...................... 91 4.2.3 The transfer function of the mechanical subsystem ................ 96 4.2.4 The transfer function of the speed-measuring subsystem........ 98 4.3 High-frequency disturbances and the sampling process............... 100 4.4 The closed-loop system pulse transfer function ........................... 103 4.5 Closed-loop poles and the effects of closed-loop zeros................ 108 4.6 Relocation of proportional gain .................................................... 112 4.7 Parameter setting of discrete-time speed controllers .................... 113 4.7.1 Strictly aperiodic response..................................................... 113 4.7.2 Formulation of criterion function .......................................... 117 4.7.3 Calculation of the optimized values for normalized gains .... 119 4.8 Performance evaluation by means of computer simulation.......... 124 4.9 Response to large disturbances and the wind-up phenomenon.................................................................................. 129 4.10 Anti-Wind-Up mechanism ......................................................... 135 4.11 Experimental verification of the discrete-time speed controller..................................................................................... 140 Problems ............................................................................................. 143 5 Digital Position Control...................................................................... 147 5.1 The role and desired performance of single-axis positioners ....... 148 5.2 The pulse transfer function of the control object.......................... 151 5.3 The structure of position controllers............................................. 157 5.3.1 Derivative action in position controllers ............................... 157 5.3.2 Relocation of derivative action into the feedback path ......... 160 5.3.3 The position controller with a minor speed loop ................... 161 5.3.4 Stiffness of the position-controlled system ........................... 163

Contents vii 5.4 The discrete-time PD position controller...................................... 165 5.5 Optimized parameter setting......................................................... 174 5.6 Computer simulation of the system with a PD controller............. 178 5.7 Operation of the PD position controller with large disturbances .................................................................................. 181 5.8 The nonlinear position controller.................................................. 184 5.8.1 The speed-limit dependence on the remaining path .............. 184 5.8.2 Enhancing the PD controller.................................................. 185 5.8.3 The error of the minor-loop speed controller ........................ 190 5.9 Computer simulation of the system with a nonlinear PD controller................................................................................ 191 5.10 Experimental evaluation of performances .................................. 195 Problems ............................................................................................. 203 6 The Position Controller with Integral Action ..................................205 6.1 The operation in linear mode and the pulse transfer functions ...................................................................................... 208 6.2 Parameter setting of PID position controllers.............................. 214 6.3 The step response and bandwidth of the PD and PID controller .. 218 6.4 Computer simulation of the input step and load step response..... 220 6.5 Large step response with a linear PID position controller............ 225 6.6 The nonlinear PID position controller .......................................... 230 6.6.1 The maximum speed in linear operating mode...................... 232 6.6.2 Enhancing the PID controller with nonlinear action ............. 235 6.6.3 Evaluation of the nonlinear PID controller........................... 240 6.7 Experimental verification of the nonlinear PID controller ........... 246 Problems ............................................................................................. 250 7 Trajectory Generation and Tracking................................................253 7.1 Tracking of ramp profiles with the PID position controller ......... 253 7.1.1 The steady-state error in tracking the ramp profile ............... 254 7.2 Computer simulation of the ramp-tracking PID controller........... 257 7.3 Generation of reference profiles ................................................... 264 7.3.1 Coordinated motion in multiaxis systems ............................. 265 7.3.2 Trajectories with trapezoidal speed change........................... 268 7.3.3 Abrupt torque changes and mechanical resonance problems ................................................................................. 269 7.3.4 ‘S’ curves ............................................................................... 270 7.4 Spline interpolation of coarse reference profiles .......................... 273 Problems ............................................................................................. 279

viii Contents 8 Torsional Oscillations and the Antiresonant Controller................. 281 8.1 Control object with mechanical resonance ................................... 282 8.2 Closed-loop response of the system with torsional resonance ..... 286 8.3 The ratio between the motor and load inertia ............................... 291 8.4 Active resonance compensation methods..................................... 294 8.5 Passive resonance compensation methods................................... 295 8.6 Series antiresonant compensator with a notch filter ..................... 296 8.6.1 The notch filter attenuation and width................................... 297 8.6.2 Effects of the notch filter on the closed-loop poles and zeros ..................................................................... 300 8.6.3 Implementation aspects of the notch antiresonant filters ...... 305 8.7 Series antiresonant compensator with the FIR filter..................... 308 8.7.1 IIR and FIR filters ................................................................. 309 8.7.2 FIR antiresonant compensator ............................................... 310 8.7.3 Implementation aspects of FIR antiresonant compensators ......................................................................... 313 8.8 Computer simulation of antiresonant compensators..................... 314 8.9 Experimental evaluation ............................................................... 319 8.10 Sustained torsional oscillations................................................... 325 Problems ............................................................................................. 325 Appendices.............................................................................................. 329 C-code for the PD position controller...................................... 329 ASM-code for the PID position controller............................... 333 Time functions and their Laplace and z-transforms................. 337 Properties of the Laplace transform......................................... 339 Properties of the z-transform ................................................... 341 Relevant variables and their units............................................ 343 A B C D E F References............................................................................................... 345 Index ....................................................................................................... 347

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