Power Systems Muhammad Ali Masood Cheema John Edward Fletcher Advanced Direct Thrust Force Control of Linear Permanent Magnet Synchronous Motor Power Systems Electrical power has been the technological foundation of industrial societies for many years Although the systems designed to provide and apply electrical energy have reached a high degree of maturity, unforeseen problems are constantly encountered, necessitating the design of more efficient and reliable systems based on novel technologies The book series Power Systems is aimed at providing detailed, accurate and sound technical information about these new developments in electrical power engineering It includes topics on power generation, storage and transmission as well as electrical machines The monographs and advanced textbooks in this series address researchers, lecturers, industrial engineers and senior students in electrical engineering ** Power Systems is indexed in Scopus** More information about this series at http://www.springer.com/series/4622 Muhammad Ali Masood Cheema John Edward Fletcher • Advanced Direct Thrust Force Control of Linear Permanent Magnet Synchronous Motor 123 Muhammad Ali Masood Cheema Research and Special Design Northern Transformer Corporation Maple, ON, Canada John Edward Fletcher The University of New South Wales Sydney, NSW, Australia ISSN 1612-1287 ISSN 1860-4676 (electronic) Power Systems ISBN 978-3-030-40324-9 ISBN 978-3-030-40325-6 (eBook) https://doi.org/10.1007/978-3-030-40325-6 © Springer Nature Switzerland AG 2020 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland To “My Old Man” Muhammad Masood Cheema “Baba! we did it together It is your immense love and spiritual bond I have with you that enabled me to accomplish this great achievement.” To Dr Farrukh Humayun Cheema “For your selfless love that always gave me strength.” Dr Muhammad Ali Masood Cheema To “To those who walked before me for making this research possible, and for those who will follow for their dedication and pursuit of understanding.” Dr John Edward Fletcher Preface The application areas for linear permanent magnet synchronous motors (linear PMSMs) include, but not limited to, servo-mechanisms, automation of manufacturing processes, transportation, renewable energy devices and pumping machinery The broadening scope of the linear PMSMs implies the importance of developing robust, simple and fast control mechanisms for the linear drives to suit the essential needs of these emerging industries This book is focused on the direct thrust force control (DTFC) of tubular surface-mount linear PMSMs The concept of DTFC is derived from direct torque control scheme which was first introduced in the 1980s initially for rotational induction machines, and in later studies this scheme was also applied to rotational permanent magnet synchronous motors (PMSMs) The simple structure of the direct torque control scheme provides it with inherent robustness to parameter variation and a fast transient response These attributes make this control scheme a prime candidate when robustness and fast transient response are of vital significance In recent years, direct torque control scheme has also been extended to linear PMSMs as DTFC; however, a little is published so far in this regard The DTFC scheme is analogous to direct torque control and has a similar switching table-based control structure in conjunction with two multilevel hysteresis comparators to regulate stator flux and thrust force These hysteresis comparators are simplest form of a scaled relay controller with unity gain and are robust to parameter variation; therefore, DTFC is variable structure control scheme in nature However, the main disadvantage of DTFC, due to the variable structure nature of the control scheme, is the presence of ripple in the stator flux and thrust force and a variable switching frequency The implementation of DTFC for linear PMSMs is substantially challenging compared to direct torque control of rotational PMSMs In general, most of the linear PMSMs have a low value of stator inductance due to their larger air gap compared to rotational PMSMs Also, due to the linear motion, the pole pitch of the linear PMSMs also affects the thrust force regulation Therefore, classical switching table-based DTFC-controlled linear PMSMs with low inductance and short pole pitch exhibit large thrust force ripple which is typically beyond acceptable limits vii viii Preface This book aims at in-depth formulation of nonlinear dynamic models for linear permanent magnet synchronous motors from a control system perspective and subsequently utilizes these models to develop several advanced DTFC schemes based on optimal control and sliding mode control approaches A detailed chapter is also dedicated to formulation of sliding mode stator flux observer for sensorless speed estimation of linear PMSM It is worth mentioning that extensive experimental results based on a laboratory prototype for validation of the presented control schemes along with exhaustive discussions are included in the text as well Chapters and of the book are based on a detailed literature review and comprehensive mathematical modelling of linear PMSMs in various reference frames The conventional switching table-based DTFC is analysed at length in Chap In order to reduce the ripple and steady-state error in the stator flux and thrust force response of the linear PMSM, a duty ratio control-based control is proposed and studied to adapt switching table-based DTFC as provided in Chap of the book Another approach to effectively reduce steady-state thrust force ripple is to use space vector pulse-width modulation approach In Chaps 4–7, several advanced DTFC schemes utilizing space vector pulse-width modulation are proposed and analysed Finally, a stator flux observer for sensorless speed estimation comprising a linear state observer and an improved sliding mode component is also proposed in Chap The key feature of this book is formulation of a nonlinear second-order state-space model of the linear PMSM in a synchronously rotating stator flux vector xy-reference frame for combined dynamics of speed and thrust force as system states The proposed nonlinear model is used to formulate the sliding mode control law with space vector pulse-width modulation for combined control of speed and thrust force In view of this fact that this text is written in way that the development of advanced concepts stems from a detailed mathematical foundation of the subject matter, this book is a suitable choice to be used as textbook or reference for undergraduate/graduate students for the subject of advanced electrical drives It is important to note that, although this book is set in the context of linear PMSMs, however the concepts and mathematical formulations presented here can conveniently be adapted or generalized for direct torque control for rotational multiphase PMSMs with or without saliency This can be of great help for graduate research students and professional engineers in the field of electrical drives to expand their understanding of advanced nonlinear dynamics and control schemes for linear/rotational PMSMs Maple, Canada Sydney, Australia Muhammad Ali Masood Cheema John Edward Fletcher Acknowledgements The core of this book is based on my doctoral and postdoctoral research under the supervision of Prof John Edward Fletcher and co-supervision of Prof Muhammad Fazlur Rahman First and foremost, I want to express my gratitude to my supervisors, Prof John Edward Fletcher and Prof Muhammad Fazlur Rahman of the Energy Systems Research Group at the University of New South Wales, for their guidance and support throughout the course of my research for this book I will always cherish my time that I spent under supervision of Prof John Edward Fletcher who has always been kind to me and provided me the opportunity for this research I also thank the University of New South Wales and the Faculty of Engineering for providing the scholarship that enabled the research for this book and also for conferring on me the title of adjunct lecturer that allowed me to further advance the research for this book I also wish to acknowledge valuable support and financial assistance from the management of Northern Transformer Corporation (NTC) who facilitated me in writing this manuscript I wish to express my gratitude to Alexei Miecznikowski, CEO of NTC, who has been very supportive throughout the course of this book and encouraged me to push the envelope in research I would also like to thank the technical staff in the energy system research group of UNSW for their support in logistics Special thanks to Dr Dan Xiao and Mr Gamini Liyadipitiya for their assistance in the experimental work vital to conclude this book I would also like to thank Mr Merlin Chai, Mr Kazi Ahsanullah and Mr David Tan for their insightful discussion and suggestions I wish to pay special thanks to my friend Dr Mohammad Farashadnia for his valuable support throughout the duration of this research I am also grateful to my brother Muhammad Ammar Masood Cheema for his love and support during my studies and always being my strength to fight my forward in the life I am greatly indebted to my parents and sister for their endless love, continuous encouragement, spiritual and financial support during my studies leading to this book My father Engr Muhammad Masood Cheema and mother Dr Fozia have ix x Acknowledgements played a pivotal role throughout in my life, and it is their immense love and faith in myself that enabled me to accomplish this task and made me the person I am today I am very fortunate to have Dr Farrukh Humayun Cheema and Najma Farrukh also as my parents who selflessly loved me, supported me and stood strong by me throughout my life; without them, this book would have been a far-fetched dream I wish to express my love and gratitude to my wife Sunbal for standing by my side during my Ph.D studies Wify! you have always been there for me Lastly, I wish to express love for my sons Muhammad Ali Murtaza and Muhammad Ali Mujtaba who have always been a source of great motivation and joy in my life Dr Muhammad Ali Masood Cheema Chapter Conclusions and Future Work 8.1 Conclusions This book primarily focuses on the DTFC of tubular surface-mount linear PMSMs It is important to note that key features of tubular surface-mount linear PMSMs include high acceleration, wide speed range and high precision, making them a prime candidate for industrial automation and servo-mechanisms Therefore, development of high-performance control schemes for these linear PMSMs is of prime importance This book proposes and rigorously analyses a number of novel DTFC schemes and experimentally validates these for a prototype tubular surface-mount linear PMSM In addition, a combined sliding mode adaptive flux observer for sensorless speed estimation of the surface-mount linear PMSM is also proposed and experimentally validated The mathematical analysis of surface-mount linear PMSMs demonstrates that these machines have a low value of stator inductance compared to their rotational counterparts due to a relatively larger air gap Another important feature of the linear PMSMs that plays a pivotal role in thrust force regulation is a short polepitch Consequently, linear PMSMs tend to exhibit higher ripple in thrust force under conventional direct thrust force control which is typically beyond acceptable limits The duty ratio based DTFC (DTFC1 of Chap 3) proposed in this book significantly reduces the ripple in thrust force and stator flux In addition, DTFC1 ensures an improved transient and steady-state performance of thrust force and stator flux under various operating conditions when compared to the state of the art As the duty ratio calculation is based on the knowledge of machine parameters, therefore the DTFC1 is most suitable when machines parameters are known and a fast transient response is desired However, parameter variation or a long sampling period may deteriorate the performance of the controller The variable switching frequency is another limitation of this approach caused by the selection of the inverter voltage vector by the hysteresis based thrust force and stator flux controllers © Springer Nature Switzerland AG 2020 M A M Cheema and J E Fletcher, Advanced Direct Thrust Force Control of Linear Permanent Magnet Synchronous Motor, Power Systems, https://doi.org/10.1007/978-3-030-40325-6_8 209 210 Conclusions and Future Work The PI-DTFC is a SV-PWM based control scheme The transient and steady-state response of the stator flux and thrust force can be shaped by appropriate tuning of the gains for PI controllers A detailed methodology is presented to compute these gains for a desired control performance of the PI controllers PI-DTFC allows computation of the PI controllers’ gains to achieve any specified damping ratio and phase margin A high value of integral gain for the thrust force PI controller results in a smaller rise time but due to low inductance of the linear PMSM, the overshoot in the transient response and steady-state ripple in thrust force increase Therefore, under PI-DTFC the gains of PI controller are tuned to achieve a compromise between the transient and steady-state performance indicators such as steady-state error, overshoot and transient response However it is important to note that the transient response of the thrust force under PI-DTFC may not be the fastest due to the above compromise An improvement to PI-DTFC is realised in form of the Optimal-DTFC1 The control law under the Optimal-DTFC1 is formulated using the linear quadratic regulator approach and the state feedback gains are computed to achieve the optimal control performance in terms of transient response with no overshoot It is observed that under Optimal-DTFC1 a significantly faster transient response of thrust force with no overshoot is achieved when compared to PI-DTFC However, it is important to note that under both PI-DTFC, and Optimal-DTFC1 the speed control loop is closed by another PI controller to generate the required thrust force reference The two methods are also suitable for the applications where independent thrust force reference is required to be tracked The need of an additional PI controller for the speed control loop is eliminated in Optimal-DTFC2 (Chap 5), SM-DTFC1 (Chap 6) Optimal-DTFC2 provides a combined control of speed and thrust force based on the linear quadratic regulator approach It is important to note that under Optimal-DTFC2 the thrust force is intrinsically controlled according to maximum force per ampere trajectory (MFPA) and no external thrust force reference is required The control law in SM-DTFC1 is based on sliding mode control theory and the integral action is augmented by modification of the reachability condition This control law provides robustness to electrical and mechanical parameter variation of the machine It should be noted that under both the Optimal-DTFC2 and SM-DTFC1 a transient and steady-state speed response comparable to that of PI-DTFC and Optimal-DTFC2 can be achieved without any additional speed PI controller The stator flux and sensorless speed estimation which is essential for the implementation of the abovementioned control schemes is performed by proposing an adaptive flux observer based on a linear state observer combined with a modified sliding mode observer The modified sliding mode observer adds robustness in the overall flux and speed estimation schemes and also improves the observer’s performance during the speed reversal as validated by the experimental result In this research this observer is implemented with the SM-DTFC2 control scheme SMDTFC2 is similar to SM-DTFC1, however in SM-DTFC2 the sliding surface are defined in terms of the integral of tracking errors in speed and flux Moreover the integral action is added by including the sliding surface corresponding to the speed error in the speed control law In SM-DTFC2, this sliding surface adds a PID effect 8.1 Conclusions 211 in the control law which reduces the overshoot and steady-state ripple, however the transient response may become slower compared to SM-STFC1 SM-DTFC1 is a natural choice where faster transient response is desired 8.2 Main Contributions of the Book The key contributions of this book: Detailed analysis of conventional DTFC for linear PMSM (Chap 3) A rigorous analysis and experimental evaluation of switching table based conventional DTFC for the prototype linear PMSM is presented The Lyapunov stability analysis of the switching table based conventional DTFC for the linear PMSM is performed The effect of various inverter voltage vectors on the variations in stator flux and thrust force under different operating conditions is evaluated This analysis concludes that due to the low stator inductance and short pole pitch of the prototype linear PMSM, whenever a voltage vector is applied to the machine for the whole duration of the sampling period the change in the thrust force is much higher than the required change Therefore, significantly larger ripple in the stator flux and thrust force response under the conventional DTFC is observed for the machine under study Despite the proven stability of conventional-DTFC for the surface-mount linear PMSMs, the quality of control performance in terms of thrust force and stator flux ripple is critically dependent on the stator inductance and pole pitch of the machine and necessitates the reduction in duty ratio of the applied voltage vector to reduce the ripple in thrust force A duty-ratio calculation method to reduce thrust force and stator flux ripple in conventional DTFC (Chap 3) A novel approach for the calculation of duty ratio for DTFC that reduces the ripple and steady-state error in the flux and thrust force response of the linear PMSM drive utilizing switching table based DTFC is proposed Analytical expressions for determination of the duty ratio, considering the machine parameters and the mover’s speed, are derived Experimental results, including start-up performance, speed reversal, and force transients, clearly indicate that the novel technique exhibits excellent control of flux and thrust force with lower ripple, faster transient response and reduced steady-state error when compared to the prior duty-ratio based DTFC technique A comprehensive procedure for tuning of PI controllers for SV-PWM based PI-DTFC schemes (Chap 4) An analysis and detailed experimental evaluation of PI controller based DTFC (PIDTFC) utilizing SV-PWM is provided A detailed approach for the design of the stator flux and thrust force PI controllers is also presented In addition, analytical expressions to compute the gains for stator flux and thrust force PI controllers are derived and experimentally validated The PI-DTFC scheme is also set as a benchmark for comparison with other SV-PWM control schemes proposed in the book 212 Conclusions and Future Work Linear Quadratic Regulator based direct thrust force control of linear PMSM (Chap 4) An optimal DTFC scheme referred to as Optimal-DTFC1 is proposed For this purpose, a novel multiple-input multiple-output (MIMO) state space model for the linear PMSM, comprising the stator flux and thrust force as states, is formulated which subsequently allows an optimal linear state feedback control law for DTFC to be synthesized using the optimal linear quadratic regulator approach Integral action is incorporated in the control scheme by state augmentation of the proposed model to reduce the steady-state error Experimental results clearly indicate that Optimal-DTFC1 exhibits improved control of stator flux and thrust force with faster transient response and reduced steady-state error when compared to PI-DTFC Combined speed and direct thrust force control based on the linear quadratic regulator based technique (Chap 5) An optimal combined speed and direct thrust force control scheme referred to as Optimal-DTFC2 is proposed and experimentally validated A 3rd order MIMO state space model for the linear PMSM, with the stator flux, thrust force and mover’s speed as states, is formulated Importantly, the state transition matrix for the proposed state space model is independent of the mover’s speed and therefore, controllable over the whole speed range of the linear PMSM An optimal linear state feedback law for combined speed and direct thrust force control is synthesized in terms of stator flux, thrust force, and mover’s speed using the optimal linear quadratic regulator approach Integral action is incorporated in the control scheme by state augmentation of the optimal state space model to reduce the steady-state error The optimal state feedback gains being independent of mover’s speed can achieve optimal combined speed and direct thrust force control of the linear PMSM for the whole speed range Sliding mode based combined speed and direct thrust force control (Chap 6) A sliding mode control scheme (referred to as SM-DTFC1) that achieves the combined speed and direct thrust force control for linear PMSM is proposed The combined dynamics of thrust force and speed are described by a general 2nd order non-linear state space model with y-axis voltage as input and thrust force and speed as system states In order to eliminate the steady-state error and to ensure a fast transient response, the control law is augmented with integral action by using a modified reaching condition The stability analysis of the proposed controller is discussed in detail The SM-DTFC1 is experimentally validated and improvements in the transient and steady-state response are observed when compared with PI-DTFC A combined sliding mode based adaptive flux observer for sensorless speed estimation of linear PMSM (Chap 7) A stator flux and speed observer comprising a linear state observer and an improved sliding mode component to ensure accuracy and robustness is proposed and experimentally validated The proposed observer provides an effective method for speed 8.2 Main Contributions of the Book 213 Table 8.1 Comparison of transient performance in terms of rise time of PI-DTFC, optimal-DTFC1, optimal-DTFC2, and SM-DTFC1 using IAE index Type of transient phenomena Rise time (ms) for speed response during the transient PI-DTFC Optimal-DTFC1 Optimal-DTFC2 SM-DTFC1 Start-up (0 to 200 mm/s) 35.2 30.1 31.0 30.0 Speed reversal (−600 to 600 mm/s) 66.8 59.6 61.0 59.9 Table 8.2 Comparison of steady-state performance of PI-DTFC, optimal-DTFC1, optimal-DTFC2 and SM-DTFC1 600 mm/s, 52 N PI-DTFC Optimal-DTFC1 Optimal-DTFC2 SM-DTFC1 λrip (%) 0.34 0.238 0.21 0.19 F rip (%) 10.48 6.21 5.83 5.91 vrip (%) 1.92 1.13 1.11 1.08 estimation of the surface mount linear PMSM as a conventional signal injection based method cannot be employed for a surface-mount linear PMSM Moreover, an integral sliding mode control (SM-DTFC2) to achieve combined speed and direct thrust force control of the linear PMSM is derived and experimentally validated The sliding surfaces are formulated in terms of the integral of the tracking errors in the stator flux and speed The comparison of transient response in terms of the rise time during start up and speed reversal for various control schemes proposed in this book is summarised in Table 8.1 The steady state performance comparison for these proposed control techniques is provided in Table 8.2 8.3 Future Work In this book several novel control schemes for direct thrust force control of linear PMSMs are proposed However these control schemes are only tested for the surfacemount linear PMSM As future research, the application of these control schemes can be extended to interior permanent magnet linear motors As discussed in Chap 4, the linearization co-efficient is constant for the prototype surface-mount linear PMSM due to low stator inductance and short pole-pitch However, in case of interior permanent magnet linear motors with larger saliency ratios, the linearization co-efficient may not be constant and will vary as a nonlinear function of operating thrust force and therefore one set of gains for thrust force PI in PI-DTFC will no longer be able to control the machine for the whole operational range of thrust force It is important to perform gain scheduling of the thrust force PI 214 Conclusions and Future Work controller using the analytical expression derived in Chap for interior permanent magnet linear motors and this should be validated experimentally One of the key features of interior permanent magnet linear motors is wide speed operation under field-weakening control due to their saliency Therefore, it is also of interest to evaluate control schemes proposed in the book for field-weakening control of interior permanent magnet linear motors For this purpose the reference flux for the DTFC schemes needs be calculated under field-weakening control trajectory instead of maximum force per ampere as discussed in this book It is important to note that the dynamic modelling of linear PMSM performed in this book does not consider the core loss resistance; therefore future studies may include the core loss resistance in the dynamic modelling of linear PMSM The novel duty ratio calculation method proposed in Chap is parameter dependent and a parameter mismatch may deteriorate the performance of the proposed technique Therefore, a parameter adaption algorithm can be added with duty ratio based DTFC to ensure the robustness of the control scheme Although the novel DTFC schemes presented in this book are validated for the linear PMSM, these schemes are general in the sense that they can also be extended to rotational PMSMs It is worth mentioning that, due to its inherent robustness, the sliding mode based combined speed, and direct thrust force control (Chap 6) can be of great interest for field-weakening control of concentrated wound IPM machines where machines parameters depend on the operating conditions of the machines Appendix A Description of the Experimental Setup A.1 Description of the Prototype Tubular Surface-Mount Linear PMSM The prototype tubular surface-mount linear PMSM used in this research is Model No STA 2504S manufactured by Dunker Motor Advanced Motion Solutions and is categorised as servo tube by the manufacture The complete experimental setup is shown in Fig A.1 The manufacturer website for the prototype linear PMSM is: https://www.dunkermotoren.com A.2 Description of 3-Phase Voltage Source Inverter The 3-phase 2-level voltage source inverter used for the prototype linear PMSM is manufactured by Semikron The model no “SKS 35F B6U+E1C1F+B6C1 21 V12” The manufacturer website is: https://www.semikron.com A.3 Description of Voltage Sensing Board The schematic diagram for the voltage sensing board is provided in Fig A.2 A.4 Description of Current Sensing Board The schematic diagram for the current sensing board is provided in Fig A.3 © Springer Nature Switzerland AG 2020 M A M Cheema and J E Fletcher, Advanced Direct Thrust Force Control of Linear Permanent Magnet Synchronous Motor, Power Systems, https://doi.org/10.1007/978-3-030-40325-6 215 216 Appendix A: Description of the Experimental Setup Braking Resistor Load LPMSM Prototype LPMSM Interface /Measurement Board DS1104 Controller Board 3-Phase Inverter Fig A.1 Experimental setup A.5 Description of dSPACE© DS 1104 R&D Controller Board In this research, DS 1104 controller board is used for the implementation of the control algorithms, processing of the feedback signals from current, voltage and speed sensors and generation of PWM signals for the voltage source inverter The DS1104 controller board is specifically designed for development of high speed multilevel digital controllers and real-time simulations in various fields It is a complete realtime control system based on a 603 Power PC floating point processor of 250 MHz For advance I/O purposes, the board includes a slave DSP subsystem which performs digital input and output along with generation of PWM signals The heart of this subsystem is a TMS320F240 digital signal processor from Texas Instruments The controller board can be directly programmed using MATLAB/SIMULINK or C program An overview of the features provided by the DS1104 board and technical specifications of the board are given in the The architectural overview of the DS 1104 board is provided in Fig A.4 The technical specifications of the controller board are provided in Table A.1 -15 2 +15 -15 -15 R7 100R 5K6 R8 R9 5K6 R1 5K6 R2 5K6 P3 20K C4 10nF U1B LF347 330pF LF347 C3 R12 22K 10 10nF C2 U1C 330pF P1 20K C1 R3 22K -15 U1A LF347 LF347 U1D +15 13 12 11 JUMPER J2 -15 +15 R6 10K J1 JUMPER R11 10K P4 2K R10 10K -15V M +15V VT1 +15 - + LV25P C14 10uF C13 10uF +15 R5 10K C15 10uF P2 2K 14 D3 1N4148 R13 10K D2 9.1VZ A4 Date: File: +15 R16 10K +5 V VW +15 10-Feb-2004 C:\My Documents\appendix\3chvt.DDB Number Sheet of Drawn By: CN1 DB9 C D KVB Revision R0 P5 10K R14 10K A 0-CROSS -V VW B CH VOLTAGE SENSOR R15 10K U4 LM311 Size Title C5 47pF D1 9.1VZ R4 1K Fig A.2 Schematic circuit diagram of voltage sensing board CN3 CON2 CN4 CON2 +5 A 47K 25W +V -V +5V +15V 0V -15V CN2 CON4 B C D Appendix A: Description of the Experimental Setup 217 -15 U1B LF347 10nF +15 10K R17 IW CN2 DB9 11 A4 Date: File: 11-Feb-2004 C:\My Documents\appendix\3chct.DDB Number Sheet of Drawn By: KVB R0 Revision 3CH CURRENT SENSOR BOARD R21 100K CN1 DB15 Title 1N4148 D5 10 11 12 13 14 15 CN3 CURRENT LIMIT SIGNAL Size C6 27pF I W(CL) D2 9.1VZ D1 9.1VZ D4 -15 LF347 U1A R4 1K 10K R15 C5 27pF -15 LF34 7 R20 4K7 0-CROSS-V VW C2 U2B LF347 I V (FAULT) +5 V VW Fig A.3 Schematic circuit diagram of current sensing board R1 5K6 R2 5K6 10K R13 10K R12 U2 A D3 R19 10K 27pF C7 I U (FAULT) R18 10K LM311 +15 U6 0-CROSS-V UV A CT3 +15 330pF 14 +15 -15 R23 10K R16 10K P13 10K R22 10K V UV IW C1 13 12 U1D LF347 11 P3 50K U1C LF347 10nF C4 -15 R3 22K 10 330pF C3 R14 10K +15 R6 10K R7 5K6 R8 5K6 R9 22K P1 20K C22 10uF GND 2K J1 C21 10uF C20 10uF 1N4148 P4 JUMPER J2 +15 JUMPER -15 +5 B R5 10K R11 10K 2K P2 R10 10K 3 V DC +15 -15 +15 -15V 0V +15V CN4 CON4 C D +5V A B C D 218 Appendix A: Description of the Experimental Setup 1N4148 Appendix A: Description of the Experimental Setup 219 Fig A.4 Architectural overview of DS 1104 controller board Table A.1 Technical specifications of the DS1104 controller board Manufacturer dSPACE GmbH Technologiepark 25, 33100 Paderborn, Germany Processor • MPC 8240 with PPC630e core and on chip peripherals • 64-bit floating point processor • 250 MHz CPU Memory • Global memory: 32 MB SDRAM • flash memory: MB ADC • multiplexed channels 16 bit resolution, às conversion time A/D channels, 12 bit resolution and 800 ns conversion time Incremental encoder interface • • • • • • channels Single ended TTL or differential RS422 input fold subdivision Max 1.65 MHz 24-bit loadable position counter Rest on index Slave DSP • • • • Texas instruments TMS320F240 DSP 20 MHz clock frequency 1X3-phase PWM output 4X1 phase PWM output Appendix B Derivation of Expressions for B.1 Derivation of Expression for Voltages The values of i α , i β , dλα dt and dλβ dt d FT dt d FT dt and dλs dt in Terms of Inverter can be achieved from (2.94) to (2.97) as: dλα = vα − Rs i α dt (B.1) dλβ = vβ − Rs i β dt (B.2) iα = λα − λ pm,α Ls (B.3) iβ = λβ − λ pm,β Ls (B.4) By substituting (B.1) to (B.4) in (2.109) yields: 3π di β di α d FT = k F P (vα − Rs i α )i β + λα − vβ − Rs i β i α − λβ dt 2τ dt dt (B.5) Equation (B.5) simplifies to: 3π di β di α d FT = k F P vα i β − vβ i sα + λα − λβ dt 2τ dt dt (B.6) di Now the values of didtα and dtβ can be achieved by differentiation of (B.3) and di (B.4) respectively Substituting these values of didtα and dtβ into (B.6): © Springer Nature Switzerland AG 2020 M A M Cheema and J E Fletcher, Advanced Direct Thrust Force Control of Linear Permanent Magnet Synchronous Motor, Power Systems, https://doi.org/10.1007/978-3-030-40325-6 221 222 Appendix B: Derivation of Expressions for 3π d FT λα = k F P vα i β − vβ i α + dt 2τ Ls The value of dλr α dt dλ pm,β dλβ − dt dt − λβ Ls d FT dt and dλs dt dλ pm,α dλα − dt dt (B.7) can be obtained by differentiating (2.98) as: d λ f cos θr dλ pm,α dθr = = −λ f sin θr dt dt dt (B.8) From (2.99), it is clear that λ f sin θr = λ pm,β , therefore (B.8) becomes: dλ pm,α = −λ pm,β ωr dt Similarly, the values of dλrβ dt can be achieved by differentiating (2.98) as: dλ pm,β = λ pm,α ωr dt Substituting of values of (B.7): (B.9) dλ pm,α dt and dλ pm,β dt (B.10) from (B.9) and (B.10) respectively, into 3π d FT λα = k F P vα i β − vβ i α + vβ − Rs i β − λ pm,α ωr dt 2τ Ls − λβ vα − Rs i α + λ pm,β ωr Ls (B.11) Substituting the values of i α and i β from (B.3) and (B.4) in the first two terms of (B.11) within the brackets results in: λβ − λ pm,β λα − λ pm,α 3π d FT − vβ = k F P vα dt 2τ Ls Ls λα λβ + vβ − Rs i β − λ pm,α ωr − vα − Rs i α + λ pm,β ωr Ls Ls (B.12) Simplifying (B.13) by re-arranging terms: π kF P d FT = (vα λβ − vα λ pm,β − vβ λα + vβ λ pm,α + λα vβ − λα Rs i β dt τ Ls (B.13) −λα λ pm,α ωr − λβ vsα + λβ Rs i α − λβ λ pm,β ωr Equation (B.13) can be re-arranged to cancel the similar terms with opposite signs as: Appendix B: Derivation of Expressions for d FT dt and dλs dt 223 (B.14) The zero terms in (B.14) can be omitted to achieve the following expression for as: d FT dt d FT π kF P = −Rs λα i β − λβ i α − vα λ pm,β + vβ λ pm,α dt τ Ls −ωr λα λ pm,α + λβ λ pm,β (B.15) In (B.15), λα λ pm,α +λβ λ pm,α represents the scalar product of the stator flux space − → − → vector λs and the rotor flux space vector λ f in αβ-reference frame It is clear form − → − → Fig 2.8 that the angle between λs and λ f is δ therefore: − →− → λsα λr α + λsβ λβα = λs λr = λs λ f cos δ (B.16) From (B.15) into (B.16): π kF P d FT = −Rs λα i β − λβ i α − vα λ pm,β + vβ λ pm,α − ωr λs λ f cos δ dt τ Ls (B.17) Equation (B.17) is simplified by re-arranging the terms: ⎛ ⎞ ⎟ Rs ⎜ π d FT =− ⎜ k F P λα i β − λβ i α ⎟ ⎠ dt Ls ⎝ τ FT π kF P −vα λ pm,β + vβ λ pm,α − ωr λs λ f cos δ + τ Ls (B.18) From (1.62), it is clear that in (B.18), 23 πτ P λα i β − λβ i α represent the thrust force FT , therefore (B.18) can be written as: d FT Rs π kF P = − FT + −vα λ pm,β + vβ λ pm,α − ωr λs λ f cos δ dt Ls τ Ls (B.19) Since, FT on right hand side of (B.19) is the initial operating thrust force at the current instant of time; therefore replacing FT by F0 results in: 224 Appendix B: Derivation of Expressions for d FT dt Rs d FT π kF P = − F0 + −vα λ pm,β + vβ λ pm,α − ωr λs λ f cos δ dt Ls τ Ls and dλs dt (B.20) Substituting the value of ωr from (2.44) into (B.20): d FT π kF P π Rs −vα λ pm,β + vβ λ pm,α − P λs λ f vm cos δ = − F0 + dt Ls τ Ls τ (B.21) The effect of the various voltage vectors applied by the voltage source inverter on the thrust force of the surface-mount linear PMSM can be evaluated by using (B.21) Equation (B.21) can be solved using the prototype linear PMSM parameters in Table 1.1 for various voltage vectors to compute the rate of change of thrust force B.2 Derivation of Expression for Voltages dλs dt in Terms of Inverter In order to formulate the effect of the inverter voltage vectors on the rate of change of stator flux, first the magnitude of the stator flux space vector is expressed in terms of αβ-components by using (2.132) as: λs = λ2α + λ2β (B.22) Taking the time derivative of (B.22): dλs = dt λ2α + λ2β λα dλα dλβ + λβ dt dt Substituting (2.94) to (2.97) in (B.23), the following expression for given as: Rs Rs dλs = − λs + vα λα + vβ λβ λ f cos δ + dt Ls Ls λs (B.23) dλs dt can be (B.24) The rate of change in the stator flux magnitude is computed from (B.24) using the parameters of the prototype linear PMSM ... http://www.springer.com/series/4622 Muhammad Ali Masood Cheema John Edward Fletcher • Advanced Direct Thrust Force Control of Linear Permanent Magnet Synchronous Motor 123 Muhammad Ali Masood Cheema Research... Canada John Edward Fletcher The University of New South Wales Sydney, NSW, Australia ISSN 161 2-1 287 ISSN 186 0-4 676 (electronic) Power Systems ISBN 97 8-3 -0 3 0-4 032 4-9 ISBN 97 8-3 -0 3 0-4 032 5-6 (eBook)... inductance and short pole-pitch © Springer Nature Switzerland AG 2020 M A M Cheema and J E Fletcher, Advanced Direct Thrust Force Control of Linear Permanent Magnet Synchronous Motor, Power Systems,