A New Approach to Parameter Tuning of Controllers by Using One-Shot Experimental Data-A Proposal of Fictitious Reference Iterative Tuning

Abstract

In this paper, we propose one of the powerful iterative tuning methods for the parameters of the controller of a closed loop system. The method we provide here requires only one-shot experiment and then an iterative non-linear optimization for obtaining the optimum parameters of the controller can be performed off-line by using the fictitious reference signal computed by the first experimental data (from this reason, we refer to our method as "fictitious reference iterative tuning" , which is abbreviated to "FRIT"). The main concept and the algorithm of FRIT are provided as our main results of this paper. Moreover, we give a control experiment of the cart-system in order to show the validity of FRIT. 1. ‚Í ‚ ¶ ‚ß ‚É PID• § OEä Ší([8]‚È ‚Ç)‚É 'ã •\ ‚³ ‚ê ‚é '² •®‰Â "\ ‚ȃpƒ‰ ƒ••[ ƒ^([6]‚È ‚Ç)‚ð ‚à‚• § OEä Ší ‚ðŽÀ '• ‚µ‚½•Âƒ‹ •[ ƒvOEn ‚ae‚è"¾‚ç ‚ê ‚½ƒf•[ ƒ^‚©‚ç,•] ‰¿ ŠÖ •"(‚½ ‚AE ‚¦ ‚Î-Ú •W 'l ‚AE ‰ž "š ‚AE ‚Ì OEë •· "ñ•ae˜a ‚È‚Ç)‚ª •Å•¬‚É‚È‚é ‚ae‚¤‚É• §OEä Ší ‚Ì ƒpƒ‰ ƒ••[ ƒ^‚ð'€ ŽŸ •X•V‚µ•Å"K‚ȃpƒ‰ ƒ• •[ ƒ^‚AE ‚È‚é ‚ae‚¤‚É ƒ`ƒ… •[ ƒj ƒ"ƒO ‚· ‚éŽè-@ ‚AE ‚µ‚ÄIterative Feedback Tuning (ˆÈ•~IFT‚AE-ª ‚· ‚é)‚ª 'ñˆÄ‚³ ‚ê ‚Ä‚¢‚é([21‚È ‚Ç).‚± ‚ê ‚Í,ƒv ƒ‰ ƒ"ƒg‚Ì •" Ž® ƒ‚ƒfƒ‹‚ª •s-¾‚AE ‚¢ ‚¤•ó ‹µ‚Ì ‚à ‚AE ‚Å OEo OE± ‚â Š¨‚É‚àŠ¨‚É‚à ‚AE ‚Â-ƒpƒ‰ ƒ••[ ƒ^‚ð-p ‚¢ ‚½• §OEä OEn ‚ª •\ •¬ ‚³ ‚ê,‚· ‚łɉ^-p ‚³ ‚ê ‚Ä‚¢‚é •ê • ‡ ‚É‚¨‚¢‚Ä‚É‚¨‚¢‚Ä,‚» ‚Ì ŽÀ OE± ƒf•[ ƒ^‚©‚ç•Å"K‚È• §OEä Šíƒpƒ‰ ƒ••[ ƒ^‚ðƒ`ƒ^‚ðƒ`ƒ… •[ ƒj ƒ"ƒO‚µ‚Ä‚¢ ‚-‚AE ‚¢ ‚¤"ñ•í ‚É-L-p ‚ÈŽè-@ ‚Å‚ ‚é.ŽÀ •Û‚Ì OE» •ê ‚È‚Ç‚É‚¨‚¯‚È‚Ç‚É‚¨‚¯ ‚é ƒvƒ•ƒZƒX • §OEä '• 'u ‚â,ƒ• ƒJƒj ƒJƒ‹OEn ‚ð' †•S ‚AE‚µ‚½FA ‹@Ší‚Ì • §OEä '• 'u ‚È‚Ç‚Å‚Í,‰^-p •ã '² •®‰Â "\ ‚ȃpƒ‰ ƒ••[ ƒ^ ‚ð ‚à‚• §OEä Ší ‚ðŽae‚è•t ‚¯ ‚ç‚ê ‚Ä‚¢ ‚é•ê • ‡‚ª '½‚¢ ‚±‚AE ‚ð•l ‚¦ ‚é ‚AE,IFT‚ª ‹-Í‚ÈŽè-@ ‚AE ‚È‚é•ê-Ê‚Í '½‚¢‚Å‚ ‚ë ‚¤. ŽÀ •Û‚ÉŽQ •l • ¶OE£[4]‚â[5]‚Å ‚Í ŽÀ ƒV ƒX ƒeƒ€‚É'Î ‚· ‚é"K-p-á ‚ª •ñ•• ‚³ ‚ê,-Ç•D‚È•¬‰Ê ‚ª "¾‚ç‚ê ‚Ä‚¢ ‚é.‚½ ‚¾‚µ.‚± ‚ê ‚ç‚ÌIFT‚É ‚ae‚é ƒ`ƒ… •[ ƒj ƒ"ƒO ‚Í ƒKƒE ƒX•E ƒj ƒ… •[ ƒgƒ"-@ ‚È ‚Ç‚Ì "ñ•üOE`üOE`•Å"K‰» OEv ŽZ(‚½ ‚AE ‚¦ ‚Î ŽQ •l • ¶OE£[10]‚È‚Ç)‚É Šî‚«,‚» ‚Ì •Û‚É•K-v ‚É‚È‚éOEù "z ‚âHessian‚È ‚Ç‚ª • §OEä Ší ‚Ì ƒpƒ‰ ƒ••[ ƒ^‚ɈË' ¶ ‚µ‚½•Âƒ‹ •[ ƒvOEn ‚©‚ç"¾‚ç‚ê ‚éŽÀ OE± ƒf•[ ƒ^‚É‚ae‚èŽae "¾‚· ‚é•K-v ‚ª ‚ ‚é.‚µ ‚½‚ª ‚Á‚Ä,‚± ‚ê ‚Ü ‚Å'ñˆÄ‚³ ‚ê ‚Ä‚¢ ‚éŽè-@,‚¨‚ae‚Ñ‚¨‚ae‚Ñ•ñ•• ‚³ ‚ê ‚Ä‚¢‚é "K-p-á ‚É ‚¨‚¢‚Ä‚Í‚¨‚¢‚Ä‚Í •Å"K‚È• §OEä Ší ‚Ì ƒpƒ‰ ƒ••[ ƒ^‚ð"¾‚é ‚½‚ß ‚É'½•" ‰ñ ‚É‚í ‚½‚éOEJ •Ô‚µŽÀ OE± ‚ð•K-v ‚AE ‚· ‚é.‚± ‚ê ‚Í ŽÀ •Û‚Ì OE» •ê ‚É ‚¨‚¯‚¨‚¯ ‚é ƒV ƒXƒeƒ€‰^-p •ã ‚Ì ŠÏ "_‚©‚ç•l ‚¦ ‚é ‚AE,OEo"ï ‚â ŽžŠÔ ‚ª ‚©‚©‚è,ŽÀ-p •ã ‚Ì 'å ‚«‚È•á •Ç‚É‚È‚é.-{˜_ • ¶ ‚Å‚Í,‚» ‚Ì ‚ae‚¤‚È-â'è ‚ð•Ž•ž ‚· ‚é ‚½‚ß ‚̈ê‚Ìˆê ‚Â ‚Ì Žè-@‚AE ‚µ‚Ä,Unfalsified Control[7]‚É ‚¨‚¯‚¨‚¯ ‚é • §OEä Ší 'I 'è ‚Ì •Û‚ÉOE» ‚ê ‚é‹[iŽ-ŽQ •AE•M • †(Fictitious Reference Signal)‚ð-p ‚¢‚é ‚± ‚AE ‚É‚ae‚è,ˆê ‰ñ ‚Ì •Âƒ‹•[ ƒvOEn ‚Ì • §OEä ŽÀ OE± ‚Å"¾‚ç‚ê ‚½ŽÀ OE± ƒf •[ ƒ^‚ð ‚à ‚AE ‚É• §OEä Ší ‚Ì ƒpƒ‰ ƒ••[ ƒ^ ƒ` ƒ… •[ ƒj ƒ"ƒO ‚ðƒI ƒt ƒ‰ ƒCƒ"•ˆ-• ‚ÅŽÀ •s ‚· ‚é ‚± ‚AE ‚Å,•Å "K ‚ȃpƒ‰ ƒ••[ ƒ^‚ð"¾‚é ‚½‚ß‚Ì 'S ‚-•V ‚µ‚¢Žè-@ ‚ðFictitious Reference Iterative Tuning(ˆÈ •~FRIT‚AE-ª ‚· ‚é)‚AE ‚µ‚Ä'ñ ˆÄ‚· ‚é.ˆê ‰ñ ‚Ì ŽÀ OE± ‚³ ‚¦ ŽÀ •s ‚Å‚«‚ê ‚Î •Å"K‚ȃp ƒ‰ ƒ• •[ ƒ^‚ð‹• ‚ß ‚é ‚± ‚AE ‚ª ‚Å‚«‚é,‚AE ‚¢ ‚¤-{˜_ • ¶ ‚Ì Žè-@ (FRIT)‚Í,Žž ŠÔ ‚â "ï-p ‚Ȃǂ̘J‚Ȃǂ̘J-Í •í OE¸‚Ì-§ •ê ‚©‚ç•l ‚¦ ‚é ‚AE OE» •ê ‚Ì ŽÀ ƒvƒ•ƒZƒX ‚Å‚Ì '² •®‚É‚¨‚¯®‚É‚¨‚¯ ‚é-L-Í ‚ÈŽè-@ ‚Å‚ ‚é ‚AE ‚¢‚¦ ‚é ‚¾‚ë ‚¤. ‚Ü‚½,-{ ˜_ • ¶ ‚Ì •Ê ‚Ì '¤-Ê‚AE‚µ‚Ä,-{ OE¤‹ † ‚Ì •¬‰Ê ‚Í 'O •q ‚Ì ‚AE ‚¨‚è‚ÉSafonov‚炨‚è‚ÉSafonov‚ç ‚É‚ae‚è'ñ ˆÄ‚³ ‚ê ‚½Unfalsified * OE´•OE´•eŽó•t2004"N4OEŽ13"ú •õ 'å •ã 'å Šw Šî'b •HŠw •" Faculty of Engineering Science , Osaka University; 1-3 Machikaneyamacho, Toy-onaka city, Osaka 560-8531, JAPAN