[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-121792-en":3,"doc-seo-121792-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},121792,16904993612988,"Olivia Brown","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",6,"Technology","Machine learning-based model predictive control with Koopman linearization","Piezoelectric actuators (PEA)-based systems operating at high speed and precision require accurate real-time trajectory tracking. Model-based control can achieve the needed accuracy, while Long Short-Term Memory (LSTM) networks can capture the nonlinear dynamics of nanopositioning systems. The thesis proposes combining an inversion LSTM model with a Koopman linearization approach and implementing model predictive control for precision tracking in PEA systems. It further addresses limitations caused by LSTM accuracy being guaranteed only within training frequency/amplitude ranges and by PEA dynamics changing with conditions such as temperature and humidity, which affects nonlinearity compensation.","Machine learning-based model predictive control with koopman linearization  \nby  \nBharat Charuku  \nA thesis submitted to the graduate faculty in partial fulfillment of the requirements for the degree of  \nMASTER OF SCIENCE  \nMajor: Mechanical Engineering  \nProgram of Study Committee:  \nJuan Ren, Major Professor  \nBeiwen Li  \nHantang Qin  \nThe student author, whose presentation of the scholarship herein was approved by the program of study committee, is solely responsible for the content of this thesis. The Graduate College will ensure this thesis is globally accessible and will not permit alterations after a degree is conferred.  \nIowa State University  \nAmes, Iowa  \n2022  \nCopyright © Bharat Charuku, 2022. All rights reserved.  \nii  \nDEDICATION  \nThis thesis is dedicated to my mother Archana and father Praveen for their love, endless support and encouragement without which this beautiful experience would not be possible.  \niii  \nTABLE OF CONTENTS  \nPage  \nLIST OF FIGURES ....................................................................................................................... iv  \nLIST OF TABLES ...........................................................................................................................v  \n[NOMENCLATURE ...................................................................................................................... vi](NOMENCLATURE ...................................................................................................................... vi)  \n[ACKNOWLEDGMENTS ............................................................................................................ vii](ACKNOWLEDGMENTS ............................................................................................................ vii)  \n[ABSTRACT................................................................................................................................. viii](ABSTRACT................................................................................................................................. viii)  \n[CHAPTER 1](CHAPTER 1) . INTRODUCTION ...................................................................................................1  \nCHAPTER 2. LITERATURE REVIEW .........................................................................................2  \nCHAPTER 3. METHOD ...............................................................................................................11  \nCHAPTER 4. RESULTS AND DISCUSSION.............................................................................24  \nCHAPTER 5. CONCLUSION AND FUTURE WORK ...............................................................30  \nREFERENCES ..............................................................................................................................32  \nAPPENDIX MATLAB CODES…………………………………………………………………39  \niv  \nLIST OF FIGURES  \nPage  \nFigure 1. Nonlinear behavior exhibited by PEAs 3  \nFigure 2. Creep behavior exhibited by PEAs 4  \nFigure 3. Structure of LSTM 14  \nFigure 4. Individual LSTM cell structure 15  \nFigure 5. MPC control framework 18  \nFigure 6: Koopman based MPC control framework 23  \nFigure 7. Input Signal U 25  \nFigure 8a. Nonlinear behavior of PEA at 10kHz 26  \nFigure 8b. Reduced nonlinearities of the PEA using the designed controller at 10kHz 26  \nFigure 9. Tracking Performance and its corresponding RMS error at 10, 50 and 120Hz sinusoidal signals 27  \nFigure 10. Tracking Performance and its corresponding RMS error for complex signal 28  \nv  \nLIST OF TABLES  \nPage  \nTable 1. Comparison of the Koopman based model predictive control with existing  \naugmented predictive control and PID controller ................. 29  \nvi  \nNOMENCLATURE  \nPEA Piezoelectric Actuator  \nMPC Model Predictive Control  \nLSTM Long Short-Term Memory  \nNN Neural Network  \nFB Feedback  \nFF Feed Forward  \nAPC Augmented Predictive Control  \nvii  \nACKNOWLEDGMENTS  \nI would like to thank my committee chair, Dr","cbCaiuEoyOcJHBt0","https://ap.wps.com/l/cbCaiuEoyOcJHBt0","pdf",3737510,1,51,"English","en",105,"# Introduction\n# Literature Review\n# Method\n# Results and Discussion\n# Conclusion and Future Work\n# References\n# Appendix: MATLAB Codes","[{\"question\":\"What problem does the thesis address for piezoelectric actuator systems?\",\"answer\":\"It targets accurate real-time trajectory tracking at high speed and high precision, where nonlinear dynamics make control challenging.\"},{\"question\":\"How does the thesis use machine learning in the control design?\",\"answer\":\"It uses an inversion LSTM model to capture nonlinear dynamics of nanopositioning/PEA systems, enabling a learning-based modeling component for control.\"},{\"question\":\"Why is the proposed approach sensitive to operating conditions?\",\"answer\":\"The LSTM model’s accuracy is guaranteed only within its training frequency and amplitude ranges, and PEA dynamics vary with environment (e.g., temperature and humidity), which can reduce effectiveness when conditions change.\"}]","Machine learning-based model predictive control with Koopman linearization | PDF",1785806884,129,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-based-model-predictive-control-with-koopman-linearization","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/technology/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-based-model-predictive-control-with-koopman-linearization/121792/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the thesis address for piezoelectric actuator systems?","Question",{"text":75,"@type":76},"It targets accurate real-time trajectory tracking at high speed and high precision, where nonlinear dynamics make control challenging.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the thesis use machine learning in the control design?",{"text":80,"@type":76},"It uses an inversion LSTM model to capture nonlinear dynamics of nanopositioning/PEA systems, enabling a learning-based modeling component for control.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is the proposed approach sensitive to operating conditions?",{"text":84,"@type":76},"The LSTM model’s accuracy is guaranteed only within its training frequency and amplitude ranges, and PEA dynamics vary with environment (e.g., temperature and humidity), which can reduce effectiveness when conditions change.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,113,118,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":111,"slug":112},50,"technology",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},8,"Research & Report",30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]