Numerical Optimization of Regulators for Automatic Control System (200,00 руб.)

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UDC 621.375.087.9:681.515/516 (075.8) Z 62 Reviewers: Novosibirsk State Technical University, Novosibirsk, Russia Dr. of Technical Sciences, Prof. G.A. Frantsuzova, Dr. of Physics and Mathematical Sciences, Corresponding member of RAN, Prof. A.V. Taichenachev, Institute of Laser Physics, Novosibirsk, Russia Z 62 Zhmud Vadim A. Numerical Optimization of Regulators for Automatic Control ISBN 978-5-7782-3802-2 The book is intended for students and PhD students in the field of auSystem: Textbook for higher education / Vadim A. Zhmud, Lubomir V. Dimitrov, Jaroslav Nosek. – Novosibirsk: NSTU Publisher, 2019. – 296 p. tomatics, mechatronics, robotics, digital or analog feedback control. Particullary, in NSTU (Novosibirsk, Russia) it is intended for the students enrolled in the educational field 27.03.04 “Control in Technical Systems” in the course “Computer-aided design tools and control systems” (for Bachelors in their 4th year). It includes training materials and guidelines for selfassessment (questions for self-testing). The basic knowledge of previously studied mathematical disciplines is required for successful study of this course. The book is prepared due to the financial support from the European Foundation Erasmus+, projects KA-107A and SmartCity. UDC 621.375.087.9:681.515/516 (075.8) ISBN 978-5-7782-3802-2 © Vadim A. Zhmud, Lubomir V. Dimitrov, Jaroslav Nosek, 2019 © Novosibirsk State Technical University, 2019

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Content Introductory words .................................................................................................... 7 1. Introduction ......................................................................................................... 8 1.1. The subject of study: locked dynamical control systems ............................... 8 1.2. Feature of ACS: negative feedback .............................................................. 10 1.3. The task of regulator calculation .................................................................. 15 1.4. Questions for self-control ............................................................................. 18 2. Terminology and mathematical tools of TAC ................................................ 20 2.1. Basic requirements and mathematical tools for the system.......................... 20 2.2. Requirements for the possibility of the physical realization of the model ............................................................................................................ 22 2.3. The choice of the regulator structure ........................................................... 24 2.4. Regulator with fixed coefficients ................................................................. 25 2.5. Regulators with a non-integer integration and differentiation ..................... 27 2.6. Classification of developing direction of methods of the designing of ACS.......................................................................................................... 28 2.7. Adaptive and self-tuning regulators ............................................................. 30 2.8. Adaptive regulators and prospects of this approach ..................................... 31 2.9. Self-tuning regulators ................................................................................... 34 2.10. Robust regulators ....................................................................................... 35 2.11. Advantages of digital regulators ................................................................ 40 2.12. The two kind of tasks of regulator numerical optimization ....................... 42 2.13. Objectives and tasks for the further research ............................................. 43 3. Visual simulation of unlocked stuctutres ........................................................ 45 3.1. The window of the software VisSim ............................................................ 45 3.2. Start of the working in the software ............................................................. 49 3.3. Tuning of the parameters of the simulation and optimization ...................... 51 3.4. Choice of the time sampling step ................................................................. 54 3

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3.5. Choice of the integrating method ................................................................. 56 3.6. Tuning of the parameters of simulation and optimization ............................ 60 3.7. Simulation of the response of the linear link ................................................ 61 3.8. Simulation of the response of non-linear links ............................................. 64 4. Visual simulation of the locked structures ...................................................... 66 4.1. Simulation of the locked linear system ........................................................ 66 4.2. The differences between theoretical analysis, simulation and practical results ........................................................................................................... 73 5. Statement of the task of optimization of locked structures and tools for its resolving .................................................................................................. 76 5.1. Demands to the locked loops of the model for simulation ........................... 76 5.1.1. Demands for the possibility of simulation ................................................ 76 5.1.2. Demands to the feedback loop from the point of view of the adequacy of the regulators to their tasks ................................................. 77 5.1.3. Demands to the cost function .............................................................. 81 5.1.3. Additional demands to the locked systems .......................................... 83 5.2. Structure for the regulator optimization ....................................................... 84 5.3. Tools of the cost functions ........................................................................... 86 5.4. An example of the system quality analysis based on the cost function ........ 91 5.5. Grounds for choosing of weight coefficients in complex cost functions ........ 93 6. Numerical optimization of the locked structures ........................................... 96 6.1. Procedure for the automatic optimization of regulators ............................... 96 6.2. Fixing of the coefficients ........................................................................... 104 6.3. Optimization of the ensemble of systems for the robust control ................ 105 6.4. The validity of the model for optimizing of the regulator .......................... 108 6.5. Forced limitation of the regulator coefficients ........................................... 111 6.6. Forced limitation of the frequency range of the model used in optimizing of the regulator ................................................................................... 114 7. Dividing of the motion: the use of multiple drives (MISO) ......................... 117 7.1. Justification for an excessive number of the influencing actions on the object .......................................................................................................... 117 7.2. Combining of the advantages of the different drives ................................. 117 8. Dividing of motions: using of multiple sensors (SIMO) ............................... 126 8.1. Combining of the advantages of the different sensors ............................... 126 8.2. Simultaneous combing of the advantages of the different sensors and different drives ........................................................................................... 133 4

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9. Modification of the cost functions .................................................................. 133 9.1. Providing of the power saving ................................................................... 134 9.2. The detector of the error growth ................................................................ 139 9.3. Optimization with the use of etalon transient response .............................. 142 10. New structures for single channel objects (SISO) ...................................... 147 10.1. Robust power saving two-channel regulator with single output .............. 148 10.2. Robust power saving two-channel regulator with single output object, prone to oscillations ..................................................................... 154 10.3. Regulator with separation of “right” and “wrong” movements ............... 158 10.4. The use of bypass channel for feedback control of an oscillating object ........................................................................................................ 164 11. Feedback systems with pseudo local loops .................................................. 172 11.1. About local and pseudo local loops ......................................................... 172 11.2. The control of objects with two integrators ............................................. 173 11.3. The control of objects with two integrators and non-linear positive feedback ................................................................................................... 175 11.4. The control of objects with three integrators and non-linear positive feedback ................................................................................................... 178 12. Design of a piecewise adaptive regulator .................................................... 189 12.1. Robust system as a prototype of the adaptive system .............................. 189 12.2. An example of splitting a set of object parameters into subsets ............... 191 12.3. Identifying the belonging of the object model to a given subset .............. 192 13. Optimization of the regulator for multichannel objects (MIMO) ............ 194 13.1. The task of control of multichannel object ............................................... 194 13.2. The statement of the problem and the solvability conditions ................... 197 13.3. Methods for solving the problem ............................................................. 199 13.4. The efficiency of the completeness of a PID-regulator when controlling a multi-channel object ....................................................................... 200 13.5. The idea of Smith multichannel predictor ................................................ 209 13.6. Numerical optimization of the regulator for an object of dimension 3 Ч 3 ......................................................................................................... 232 14. Investigation of the numerical optimization toolkit for control of an oscillatory unstable object ................................................................... 252 14.1. Statement of the problem ......................................................................... 253 14.2. Methods for solving the problem, theory and practical results ................ 254 14.2.1. Optimizing the PID-regulator .......................................................... 254 5

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14.2.2. The optimization of PIDD-regulator ............................................... 256 14.2.3. Bypass channel application ............................................................. 257 14.2.4. Using pseudo-local links and an open object model........................ 259 14.2.5. The danger of obtaining non-robust solution ................................... 265 14.3. The proposed modification of the known methods .................................. 267 14.4. Discussion ................................................................................................ 271 14.5. Conclusions for the chapter ...................................................................... 272 15. Practical recearch and laboratory works in the field of feedback control in technical universities of Liberec and Sofia ...................................... 272 16. Questions for control at exams .................................................................... 284 Concluslion ........................................................................................................... 287 Acknowledgments ................................................................................................ 288 References ............................................................................................................. 289 Apendix ................................................................................................................. 293 6

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