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Resolver Ieee 2011 international conference on electric information and control engineering (iceice) wuhan, china (2011 04 15 2011 04 17) 2011 international conference on electric information and control engineering
Research on the Signal Process Circuit and Fault Diagnosis of Sine-cosine Resolver Qi-xun ZHOU Xi’an University of Science and Technology XUST Xi’an, China zhouqixun029@163.com Abstract—The sine-cosine resolver has reliable structure, good real-time performance and stable applicability As the angle sensor for rotary system, it has been widely used in accurate and reliable control field This paper analyses the working principle of sine-cosine resolver, and presents its mathematical model The high reliable sine signal generator for the sine-cosine resolver is designed, and the resolver-to-digital-convert circuit is also given This paper analyses a couple of typical fault of sine-cosine resolver, makes the simulation for the fault diagnosis used Mallat algorithm, and proposes the treatment processes The experiment results verified that the signal processing circuit in this paper has higher accuracy and reliability Keywords— sine-cosine resolver, sine signal generator, resolver-to digital converter, mallat arithmetic, fault diagnosis II ℷԭᓺᮟ䕀বय़఼Ꮉॳ⧚ ᮟ䕀বय़఼ᰃϔ⾡ᇚ䕀ᄤ䕀㾦বᤶ៤ϢПਜᶤϔߑ᭄ ݇㋏ⱘ⬉ֵোⱘܗӊDŽҢॳ⧚Ϟ䇈ˈᅗⳌᔧѢϔϾৃҹ䕀 ࡼⱘ⬉य़఼DŽҢ㒧ᵘϞ䇈ˈᅗⳌᔧѢϔϾᵕⳌ㒩㒓ᓣ ᓖℹ⬉ࡼᴎDŽᮟ䕀বय़఼ⱘᅮǃ䪕㢃⬅Ӭ䋼⸙䩶⠛催䬡 ড়䞥⠛៤DŽᅮǃ䕀ᄤ䪕㢃ῑ߿ߚݙ㺙᳝ϸϾ㒧ᵘᅠܼⳌ ৠ㗠ѦⳌൖⳈⱘ㒩㒘ˈ䕀ᄤ㒩㒘ৃ⬅⒥⦃⬉ࠋᓩߎDŽᣝ ݊䕧ߎ⬉य़Ϣ䕀ᄤ㾦П䯈ⱘߑ᭄݇㋏ˈজৃߚЎℷԭᓺᮟ 䕀বय़఼ǃ㒓ᗻᮟ䕀বय़఼↨՟ᓣᮟ䕀বय़఼ϝ⾡ [35] DŽℷԭᓺᮟ䕀বय़఼ⱘ㒧ᵘ⼎ᛣᎹॳ⧚ߚ߿བ ᠔⼎DŽ D1 I ᓩ㿔 催ᗻ㛑ᮟ䕀Ԏ᳡ࡼᴎᵘⱘ݇䬂ᡔᴃПϔѢབԩ ㊒⹂⌟䞣䕧ߎ䕈ⱘ㾦ᑺԡ㕂ˈᐌ⫼ⱘ⌟㾦ᑺӴᛳ఼᳝㒱 ᇍᓣܝᷙ㓪ⷕ఼ǃ䳡ᇨӴᛳ఼ᮟ䕀বय़఼DŽ㒱ᇍᓣܝᷙ 㓪ⷕ఼Ⳉᇚ䕀䕈㾦ᑺ䕀ᤶ៤᭄ᄫֵোˈᑨ⫼ㅔऩᮍ֓ˈ Ԛ⦃๗䗖ᑨᗻǃӋḐㄝ㋴㟈Փ䲒ҹᑓ⊯ᑨ⫼˗䳡ᇨӴ ᛳ఼㒧ᵘㅔऩˈԚ䲒ҹ䖒ࠄ催㊒ᑺ㾦ᑺ⌟䞣㽕∖㗠ফࠄ䰤 ࠊ˗ᮟ䕀বय़఼㒧ᵘৃ䴴ǃᅲᯊᗻདǃ⦃๗䗖ᑨᗻᔎㄝ Ӭ⚍㗠ᑓ⊯ᑨ⫼Ѣ催㊒ᑺԎ᳡㋏㒳Ё [1-2] DŽᮟ䕀বय़఼Ϣ Ԏ᳡ࡼᴎᵘৠ䕈ᅝ㺙ˈ݊Ꮉ⦃๗⬉⺕ాໄˈᑊϨֵ ো໘⧚⬉䏃䗮䖛䭓㒓Ϣ݊䖲ˈ䭓㒓Ӵ䕧ࡴњᬙ䱰থ⫳ ⱘৃ㛑ᗻDŽℸˈᓔሩ催ᗻ㛑ⱘֵো⬉䏃䆒䅵Ϣᬙ䱰䆞ᮁ ⷨおᇍѢᦤ催ᮟ䕀বय़఼⌟㾦㊒ᑺϢৃ䴴ᗻ᳝कߚ䞡㽕 ⱘᛣНDŽ ᴀ᭛䆺㒚ߚᵤᮟ䕀বय़఼Ꮉॳ⧚ⱘ⸔Ϟˈᇐ њℷԭᓺᮟ䕀বय़఼ⱘ䕧ܹ䕧ߎ݇㋏DŽЎᦤ催ֵো໘⧚⬉ 䏃ⱘ⦃๗䗖ᑨᗻˈ䆒䅵њᆑ⏽㣗ೈⱘℷᓺֵো▔ࢅ⬉䏃DŽ 䞛⫼催㊒ᑺϧ⫼䲚៤㾷ㅫ㢃⠛ᇍℷԭᓺᮟ䕀বय़఼䕧ߎⱘ ℷѸᢳ䞣ֵো䖯㸠㾷ㅫˈᕫࠄϢ㾦ᑺԡ㕂៤㒓ᗻ݇㋏ⱘ ᭄ᄫֵোDŽЎᦤ催ᮟ䕀বय़఼ঞ݊໘⧚⬉䏃ⱘৃ䴴ᗻϢع ᒋㅵ⧚㛑ˈ䞛⫼ᇣ⊶⧚䆎䖯㸠ᬙ䱰䆞ᮁDŽӓⳳϢ䆩偠䆕 ᯢ᠔䆒䅵ⱘℷԭᓺᮟ䕀বय़఼ֵো໘⧚⬉䏃Ϣᬙ䱰䆞ᮁᮍ ⊩ᦤ催њ⌟㾦㊒ᑺϢৃ䴴ᗻDŽ Supported by the Cultivation Fund of Xi'an University of Science & Technology No.200735˄㽓ᅝ⾥ᡔᄺ㚆䞥乍Ⳃ˅ˈSupported by the Specialized Research of Education Department of Shaanxi Province No.09JK586˄䰩㽓ⳕᬭ㚆ख़ϧ乍⾥ⷨ䅵ߦ乍Ⳃ˅ 978-1-4244-8039-5/11/$26.00 ©2011 IEEE • UD • UD D4 D3 D4 D2 Z4 Z1 Z1 D1 Z2 Φd D2 Z3 Z4 Z3 • U z12 • U z 34 D3 Z2 ˄a˅㒧ᵘ⼎ᛣ ˄b˅Ꮉॳ⧚ ᮟ䕀বय़఼ⱘ㒧ᵘ⼎ᛣᎹॳ⧚ D1D2 D3D4 ᰃᅮᄤ㒩㒘ˈD1ǃD3 ᰃ㒩㒘ⱘ佪ッˈ D2ǃD4 ᰃ㒩㒘ⱘッˈᅗӀⱘ᳝ᬜ᭄ࣱЎ NDDŽZ1Z2 Z3Z4 ᰃ䕀ᄤ㒩㒘ˈZ1ǃZ3 ᰃ㒩㒘ⱘ佪ッˈZ2ǃZ4 ᰃ㒩 㒘ⱘッˈᅗӀⱘ᳝ᬜ᭄ࣱЎ NZDŽᎹᯊˈᅮᄤ D1D2 • 㒩㒘ࡴϞᇣ乥⥛ϔᅮⱘѸ⌕⬉य़ U D ˈҹѻ⫳䳔㽕ⱘ Ꮉ⺕䗮ˈᬙ⿄Ўࢅ⺕㒩㒘DŽ䕀ᄤ㒩㒘⫼ᴹ䕧ߎ⬉य़ֵ োˈᬙ⿄䕧ߎ㒩㒘DŽ؛ᅮᅮᄤ D3D4ǃZ1Z2ǃZ3Z4 ᓔ 䏃ˈѸ⌕ࢅ⺕⬉⌕䗮䖛ࢅ⺕㒩㒘 D1D2 ᯊ᠔ᔶ៤ⱘࢅ⺕⺕ ࡼ Fb12 ᇚѻ⫳Ϣ D1D2 㒩㒘䕈㒓ᮍϔ㟈ⱘ㒉㛝ᤃ ⺕䗮 Φ d DŽབᵰᮟ䕀বय़఼ⱘ䕀ᄤ໘ѢЁ᠔⼎ⱘ Z1Z2 Ϣ D1D2 ϸ㒩㒘䕈㒓䞡ড়ⱘԡ㕂ᯊˈ㒉㛝ᤃ⺕䗮 Φ d ᇚܼ䚼 䗮䖛 Z1Z2 㒩㒘ˈѢᰃϢ᱂䗮ⱘ䴭ℶবय़఼ϔḋˈ Φ d ᇚ • C3 • D1D2 Z1Z2 㒩㒘Ёߚ߿ѻ⫳⬉ࡼ E D E z ˈ᳝݊ᬜؐ Ў ED = 4.44 fN D Φ dm ˄1˅ ® E = 4.44 fN Φ Z dm ¯ Z 300pF VEE -12V VEE 33kȍ 5% C4 300pF TL084CD 11 R8 Tektronix P G U1B R10 1.3kȍ 5% R12 TL084CD D2 1N4148 XSC1 T 12V VCC ⿄Ўᮟ䕀বय़఼ⱘব↨ˈབᵰᗑ⬹ࢅ⺕㒩㒘ⱘ⬉䰏ⓣ⬉ ᡫˈ᳝߭ U D = ED DŽZ1Z2 㒩㒘ϸッⱘ⬉य़ˈ⫼᳝ᬜؐ㸼⼎ VEE 33kȍ 5% VCC ˄2˅ -12V VEE R11 6.8kȍ 5% R9 1.3kȍ 5% 300pF U1A 1N4148 C5 11 R6 ᓣЁ Φ dm ᰃ㛝ᤃ⺕䗮 Φ d ⱘ ᳝ᬜؐˈ㗠 ED N D = =k EZ N Z D1 R7 VCC 6.8kȍ 5%12V VCC 33kȍ 5% ℷԭᓺᮟ䕀বय़఼▔ࢅ⬉䏃ॳ⧚ Ў U z12 = Ez ˈᬙ U z12 = kU D DŽ⬅Ѣ Φ d ⱘᮍϢ Z3Z4 㒩㒘 䕈㒓ൖⳈˈϡӮ䆹㒩㒘Ёѻ⫳ᛳᑨ⬉ࡼˈ㗠 Z3Z4 㒩㒘ϸッⱘ⬉य़ U z 34 = DŽᡞ ᠔⼎ⱘᅮǃ䕀ᄤⳌᇍԡ 㕂㾘ᅮЎᮟ䕀বय़఼ⱘ⇨⬉ޚ䳊ԡDŽ㗠ᡞ䕀ᄤ⾏أޚ ⬉⇨䳊ԡⱘ㾦ᑺ⿄Ў䕀ᄤ䕀㾦DŽᔧ䕀ᄤ䕀㾦ϡㄝѢ䳊ˈ՟ བҢ⇨⬉ޚ䳊ԡ乎ᯊ䩜ᮍأ䕀њ θ 㾦ᯊˈ㒉㛝ᤃ⺕ 䗮 Φ d 䗮䖛䕀ᄤϸ㒩㒘ⱘ⺕䗮ߚ߿Ў °Φ d 12 = Φ d cos θ ® D °¯Φ d 34 = Φ d cos(90 − θ ) = Φ d sin θ 㗠䕀ᄤ㒩㒘Ёѻ⫳ⱘᛳᑨ⬉ࡼߚ߿Ў Ez12 = Ez cos θ = kED cos θ ® ¯ Ez 34 = Ez sin θ = kED sin θ 䕧ߎ⬉य़߭Ў U z12 = kU D cos θ ® ¯U z 34 = kU D sin θ ˄3˅ ℷԭᓺᮟ䕀বय़఼▔ࢅֵো⊶ᔶ ˄4˅ ⬅ᇍᮟ䕀বय़఼Ꮉॳ⧚ⱘߚᵤৃⶹˈᔧᮟ䕀বय़఼ ▔⺕㒓䗮ܹ U ref = E sin 2π ft ⱘѸ⌕⬉य़ᯊˈ㑻㒓䕧 ˄5˅ ৃ㾕ˈা㽕ࢅ⺕⬉य़ U D ⱘᇣϡবˈ䕀ᄤ㒩㒘ⱘ䕧 ߎ⬉य़ህৃҹϢ䕀ᄤ䕀㾦ֱᣕⱘ⹂ޚℷǃԭᓺߑ᭄݇㋏DŽ III B ড作ֵো㾷ㅫ⬉䏃䆒䅵 ℷԭᓺᮟ䕀বय़఼ֵো໘⧚⬉䏃䆒䅵 A ▔ࢅֵোথ⫳⬉䏃䆒䅵 ᮟ䕀বय़఼▔ࢅֵো⬅ᬍ䖯ⱘ᭛⇣ḹ⬉䏃ѻ⫳ˈ ⾡ℷᓺ⊶থ⫳ᡔᴃЁˈ᭛⇣ḹᤃ㤵఼㹿䅸ЎᰃԢ乥ᑨ⫼ 乚ඳЁ᳔ㅔऩǃ㒣⌢ǃ៤❳ⱘϔ⾡DŽⳂࠡᇍ᭛⇣ḹℷᓺ⊶ থ⫳఼ⱘⷨお䲚ЁѢᠽሩ݊ᑨ⫼乥⥛ˈ䰡Ԣ᳝䰤Ⲟᏺ ᆑЬ⿃ⱘᕅડҹঞ䴲ᭈ᭄᭛⇣ḹᤃ㤵఼ㄝᮍ䴶ˈ㗠ᇍѢ ᇚ᭛⇣ḹℷᓺ⊶থ⫳఼ᑨ⫼ѢᎹ⦃๗ᙊࡷ催ৃ䴴㽕∖ ⱘ乚ඳⷨお䕗ᇥ [6-7] DŽᎹᅲ䏉Ёᐌ⫼ⱘ᭛⇣ḹ⬉䏃䖯㸠 催Ԣ⏽䆩偠ᯊˈ⏽ᑺ催Ѣ 75ćৢֵোᐙؐ䱣ⴔ⏽ᑺⱘछ 催䗤⏤ޣᇣˈ⏽ᑺ䖒ࠄ 90ćᎺেᯊℷᓺ⊶ᐙؐТ㹄 ࠄޣ0Vˈᴀ᭛䞛⫼ᬍ䖯ⱘ᭛⇣ḹℷᓺ⊶থ⫳఼Ўᮟ䕀 বय़఼▔ࢅֵোˈ䗮䖛䆩偠䆕ᯢ݊Ꮉ⏽ᑺ㣗ೈЎ-25ć ~+125ćˈᐙؐব࣪ᇣѢ 10%ˈ⬉䏃ॳ⧚བ ᠔⼎ˈ䞛 ⫼ঠ䖤ᬒᵘ៤ℷᓺ⊶ᤃ㤵⬉䏃ˈᑨ⫼ঠѠᵕㅵü⬉䰏㔥㒰 ࠊ⬉䏃ⱘ⦃䏃ⲞDŽᴀ⬉䏃䍋ᤃᯊ䯈ԢѢ 80msˈᤃ㤵 乥⥛ 15.5kHzˈዄዄؐЎ 5Vˈֵো⊶ᔶབ ᠔⼎DŽ ߎЎ˖ U sin = kE sin 2π ft sin ωt ® ¯U cos = kE sin 2π ft cos ωt ˄6˅ ᮟ䕀বय़఼䕧ߎⱘԡ㕂ֵো U sin U cos Ўᢳ䞣ˈᖙ乏䗮 䖛ᢳࠄ᭄ᄫⱘ㾷ㅫ⬉䏃ᠡ㛑Ϣ᭄ᄫԎ᳡ࠊ఼ষDŽ㕢 AD ݀ৌ⫳ѻⱘ AD2S80 ᰃҹ䡈ᐙᮍᓣᇍℷԭᓺᮟ䕀ব य़఼ֵো䖯㸠໘⧚ⱘϧ⫼㢃⠛ˈ䕀ᤶ㊒ᑺৃ䆒ᅮЎ 10ǃ 12ǃ14ǃ16 bit ⱘߚ䕼⥛ˈϡৠߚ䕼⥛ᇍᑨⱘ᳔䎳䏾䗳 ⥛ߚ߿Ў 62400ǃ15600ǃ3900ǃ975 r/minˈܕ䆌⫼᠋䗮 䖛ೈ఼ӊⱘϡৠ䖲䗝⫼ϡৠⱘߚ䕼⥛DŽAD2S80 Ϣ ೈ఼ӊⱘষ⬉䏃བ ᠔⼎ˈ▔ࢅֵোথ⫳⬉䏃ᦤկዄ ዄؐЎ 5Vǃ乥⥛Ў 15.5kHz ℷᓺֵোܹ REFERENCE I/P ᓩ㛮ˈᮟ䕀বय़఼ⱘℷ/ԭᓺড作ֵোߚ߿ܹ SINǃ SIN GOUND COSǃCOS GOUND ᓩ㛮ˈ䗮䖛᭄ᄫ䕀ᤶ 䕧ߎϢ⬉ᴎ䕀䕈㾦ԡ㕂៤㒓ᗻ݇㋏ⱘѠ䖯ࠊⷕⳈ䗕ܹԎ ᳡㋏㒳ⱘ᭄ᄫֵো໘⧚఼ЁDŽ Ёˈܗӊ R1ǃ R2ǃC1ǃC2 ᵘ៤催乥Ⓒ⊶఼˗R3ǃC3 ⹂ᅮޚ䕧ܹѸ ⌕㗺ড়খ᭄ˈ݊䗝পᑨ䆹ҹޚ乥⥛ fREF ϡѻ⫳ᯢᰒⳌ⿏ Ў˗߭ޚᬍব C4ǃC5ǃR5 ⱘؐৃҹᬍব䯁⦃ᏺᆑ˗ C6ǃR7 ᵘ៤Ⳍԡ㸹ٓ⬉䏃ˈ䗮ᐌ䗝 C6=470pFˈR7=68 ¡˗R8 R9 䇗㡖⿃ߚ఼䕧ܹッⱘ༅䇗⬉य़أ㕂⬉⌕[89] DŽ ⱘ䖤ㅫ䞣ˈᬙҙ䞛⫼Mallatㅫ⊩ⱘϔሖߚ㾷ֵোЎᬙ 䱰䆞ᮁⱘձDŽ REFERENCE OFFSET ADJUST I/P +12V R9 -12V C3 R2 R3 HF FILTER C2 C1 R4 R1 REF R1 ᣓ S1 Freq: 18kHz REF GROUND R3 䕀 S3 ব य़ S2 ེ S4 AC ERR DEM O/P I/P REFERENCE I/P SIN SIN GROUND DEM O/P RDC INT I/P COS GROUND C4 C5 BAND WIDTH SELECTION R5 INT O/P VELOCITY SIGNAL R6 TRICKING RATE SELECTION AD2S80A COS AGND TMS320F2812 A ▔ࢅֵোᬙ䱰䆞ᮁ R8 VCO I/P 12 DATA ITS R7 C6 ℷԭᓺড作ֵো㾷䇗⬉䏃 ᮟ䕀বय़఼ব↨ k = ˈ▔⺕⬉य़ዄዄؐЎ 5Vˈ▔⺕ 乥 ⥛ f = 15.5 kHz ˈ 䕀 ᄤ ᵕ ᇍ ᭄ p=1 ˈ ⬉ ᴎ 䕀 䗳 n = 120rpm ˈ ᮟ 䕀 ব य़ ఼ 㑻 㒓 䕧 ߎ ֵ ো 䗮 䖛 AD2S80 㾷ㅫⱘֵোབ ᠔⼎DŽ ˄a˅㑻㒓䕧ߎֵো ˄b˅AD2S80 㾷ㅫֵো ᮟ䕀বय़఼ড作ֵোϢ㾷ㅫֵো IV ˄1˅▔ࢅֵো⍜༅DŽབ᭛⇣ḹᤃ㤵఼ߎ⦄఼ܗӊᤳ ണㄝॳˈᇚᇐ㟈▔ࢅֵো⍜༅ⱘᬙ䱰ˈ䖭⾡ᬙ䱰㉏ൟ᳔ ЎᙊࡷˈᇚՓᮟ䕀বय़఼༅এ▔ࢅ⑤㗠᮴⊩Ꮉˈᮟ䕀Ԏ ᳡ᴎᵘԡ㕂ড作ಲ䏃ߛᮁDŽᬙ䱰ӓⳳঞ d1 ߚ㾷ֵোབ ᠔⼎ˈЁ s Ў⾏ᬷⱘ▔ࢅֵোˈd1 Ў Mallat ㅫ⊩ⱘ ϔሖߚ㾷ֵো˄ 6ü 10 ㉏ৠ˅ˈҢЁৃҹⳟߎˈ ▔ࢅֵো s ⍜༅ⱘᯊࠏˈd1 ߚ㾷ֵোߎ⦄䏇বDŽ ᮟ䕀বय़఼ᬙ䱰䆞ᮁ ᬙ䱰䆞ᮁ䖛ৃҹߚЎϝℹ偸˖ϔℹЎᬙ䱰ֵᙃ ⱘ㦋পˈѠℹЎᬙ䱰⡍ᕕⱘᦤপˈϝℹЎ⢊ᗕ䆚߿ 䆞ᮁˈᬙ䱰䆞ᮁѺৃ⧚㾷Ўֵো䆚߿ǃᦤপǃߚᵤϢ໘⧚ ⱘ䖛DŽӴ㒳ⱘֵোߚᵤᰃᓎゟ Fourier বᤶⱘ⸔Ϟ 䖯㸠ⱘϔ⾡ܼሔবᤶˈᇣ⊶ߚᵤᰃᑨ⫼᭄ᄺⱘ⸔Ϟথ ሩ䍋ᴹⱘϔ䮼ᮄ݈ᄺ⾥ˈ䖥कᑈᴹপᕫњ亲䗳ⱘথሩˈ ⬅Ѣᇣ⊶ߚᵤⱘĀ㞾䗖ᑨᗻ䋼āĀ᭄ᄺᰒᖂ䬰ᗻ䋼āˈ Փ݊㹿ᑓ⊯ᑨ⫼Ѣ⸔⾥ᄺǃᑨ⫼⾥ᄺᇸ݊ᰃֵᙃ⾥ᄺǃ ֵোߚᵤⱘᮍᮍ䴶䴶DŽ S MallatᦤߎⱘMallatㅫ⊩Ңֵোⱘߚ䕼⥛ぎ䯈ߚ 㾷ὖᗉߎথˈᇚֵোⱘߚ䕼⥛ߚᵤ䞛ḋ⥛Ⓒ⊶఼㒘 䖭ϸϾ乚ඳ㘨㋏䍋ᴹˈ߽⫼䞛ḋ⥛Ⓒ⊶఼㒘ⱘᮍ⊩ᅲ⦄ ֵোⱘᇣ⊶বᤶDŽ⫼Mallatㅫ⊩ᅲ⦄ϔ㓈⾏ᬷᇣ⊶বᤶ ⱘ䖛Ёˈ᠔䗝পⱘℷѸᇣ⊶ߑ᭄˄े↡ᇣ⊶˅ϡৠˈᇍ ᑨⱘሎᑺߑ᭄Ⓒ⊶఼㋏᭄гᰃϡৠⱘDŽℷᐌᎹᯊˈᮟ 䕀বय़఼ֵোЎ㾘߭ⱘℷᓺᑇ〇ֵোˈ▔ࢅֵো乥⥛䖒ࠄ 15.5kHzˈЎᦤ催㋏㒳ⱘᅲᯊડᑨ㛑ˈᑨሑ䞣ޣᇣCPU ▔ࢅ⍜༅ᬙ䱰ӓⳳঞֵোߚ㾷⊶ᔶ ˄2˅ᐙؐさবDŽᐙؐさবߎ⦄⬉䏃ফࠄᑆᡄㄝ ॳѻ⫳ˈབᵰাᰃऩᇣᐙؐさবˈϡᕅડ㋏㒳ℷᐌᎹ ˈԚབᵰߎ⦄਼ᳳᗻⱘᐙؐさবさবؐ䍙ߎᅝܼ䯔 ؐˈᇚᕅડ㋏㒳ℷᐌᎹᤳണ㋏㒳݊ᅗ⬉䏃DŽᬙ䱰ӓⳳ ঞ d1 ߚ㾷ֵোབ ᠔⼎ˈᅲᯊⲥ⌟ d1 ֵোⱘᵕؐᇣ Ϣߎ⦄乥⥛ˈ㋏㒳֓ৃᇍᐙؐさবߎড়⧚ⱘ߸ᮁDŽ ᐙؐさবᬙ䱰ӓⳳঞֵোߚ㾷⊶ᔶ ˄4˅乥⥛さবDŽ乥⥛さবᰃ਼ᳳֵোߎ⦄ᬙ䱰ⱘϔ ⾡ᐌ㾕ᔶᓣˈ Ў▔ࢅֵো乥⥛さবᬙ䱰ӓⳳঞߚ㾷ֵ ো⊶ᔶˈҢߚ㾷⊶ᔶЁᕜᆍᯧৃҹⳟߎ乥⥛さব⚍ d1 ߎ⦄䏇বDŽ 乥⥛さবᬙ䱰ӓⳳঞֵোߚ㾷⊶ᔶ ˄5˅ᓩܹాໄDŽЎ㡖ⳕぎ䯈ˈ▔ࢅֵো㒓ϔ㠀Ϣ ࡼᴎᵘࡳ⥛㒓㒥ᠢϔ䍋ˈЎޣᇣࡳ⥛ֵোᇍᇣֵোⱘ ᑆᡄˈϔ㠀䛑خሖሣ㬑DŽԚབᵰᎹ䖛Ёሣ㬑ߎ⦄ 㾺ϡ㡃݊ᅗ⦄䈵㗠ՓᑆᡄֵোІܹ▔ࢅֵোЁˈᇚᕅ ડ㾦ᑺԡ㕂ⱘ㾷ㅫ㊒ᑺ⫮㟇ᕫϡࠄℷ⹂ⱘ㾷ㅫ㒧ᵰDŽ Ў▔ࢅֵোІܹ催ᮃⱑాໄⱘᬙ䱰ӓⳳঞߚ㾷ֵো⊶ᔶˈ ҢЁৃҹⳟߎߎ⦄ాໄৢˈd1 ᇚߎ⦄ᯢᰒব࣪DŽ ᓩܹాໄᬙ䱰ӓⳳঞֵোߚ㾷⊶ᔶ B VI ড作ֵোᬙ䱰䆞ᮁ ⬅ ৃⶹᮟ䕀বय़఼Ѡ㒓䕧ߎֵোࣙᣀϢ▔ࢅ ֵোৠ乥ⱘ䕑⊶ֵোҹঞϢ㾦ᑺԡ㕂Ⳍ݇ⱘࣙ㒰ֵোDŽ㗠 Ԏ᳡ࡼ఼䖭㉏㋏㒳Ё䕀䕈䕀䗳乥㐕ব࣪ˈԚ⬅Ѣ݊ᛃ ᗻⱘᄬˈ䕀䗳ϡৃ㛑さবˈℸˈᇍ▔ࢅֵো䖯㸠ᅲ ᯊⲥ⌟ৢˈ䕧ߎֵোা䳔ⲥ⌟ࣙ㒰ֵোⱘさবҹঞᓩܹా ໄϸ⾡ᬙ䱰ᔶᓣDŽབ 10 ᠔⼎ˈЁ s Ўᮟ䕀বय़఼䕧 ߎⱘℷᓺֵোˈ ໘থ⫳ֵো⍜༅ᬙ䱰ˈ ໘ᓩܹ催 ᮃⱑాໄˈ䗮䖛ߚ㾷ৢⱘ d1 ֵোৃ⹂ޚẔ⌟ߎ䖭ϸ⾡㉏ ൟⱘᬙ䱰DŽԭᓺֵোⱘᬙ䱰ߚᵤϢℸ㉏ৠˈϡݡ䌬䗄DŽ ᮟ䕀বय़఼ҹ㗤⊍∵ǃᆑ⏽㣗ೈǃᡫߏކᤃࡼǃᡫ 䕤ᇘㄝӬ䍞ᗻ㛑㗠ᑓ⊯ᑨ⫼Ѣᶨᗻࠊ䗴㋏㒳ǃᴎ఼Ҏǃࡲ ݀㞾ࡼ࣪ǃ᭄ᴎᑞ㟾ぎ㟾ㄝ乚ඳDŽԚᮟ䕀বय़఼ⱘ 䕧ߎᰃϸ䏃ℷѸⱘᢳ䞣ˈ䳔໘⧚៤Ⳍᑨⱘ᭄ᄫֵোᠡ㛑 Ϣ DSP ㄝ᭄ᄫԎ᳡ࠊ఼㘨ˈ໘⧚⬉䏃䕗ЎᴖˈЎᦤ 催ᮟ䕀বय़఼Ꮉⱘৃ䴴ᗻˈᴀ᭛ߚᵤ݊Ꮉॳ⧚ⱘ ⸔Ϟˈ䆒䅵њ▔ࢅথ⫳⬉䏃Ϣ㾷ㅫ⬉䏃ˈ䩜ᇍᮟ䕀বय़఼ ᆍᯧথ⫳ⱘ⾡ൟᬙ䱰ˈ䞛⫼ Mallat ㅫ⊩䖯㸠њᬙ䱰䆞 ᮁDŽЎᮟ䕀বय़఼ᑨ⫼Ѣ㟾ぎ㟾ǃݯᎹㄝ催ৃ䴴ᗻ㽕∖ ⱘ乚ඳᦤկњᮄⱘᗱ䏃DŽ 10 ᮟ䕀বय़఼䕧ߎֵোᬙ䱰ӓⳳঞֵোߚ㾷⊶ᔶ V ᬙ䱰䆞ᮁ DSP Ёⱘᅲ⦄ ᇚ▔ࢅֵো䗕᭄ܹᄫֵো໘⧚఼ⱘ⠛ݙ$'䕀ᤶ఼Ёˈ $'䕀ᤶ఼ⱘ䞛ḋ䕀ᤶ乥⥛Ў N+]ˈे▔ࢅֵোϔϾ਼ ᳳ䞛ḋ䕀ᤶϾ⚍DŽ↣䕀ᤶߎϔϾ▔ࢅֵোⱘ⾏ᬷؐৢ ᄬܹ),)2BUHIˈ),)2BUHIЁѢϾ䕀ᤶ᭄ᯊ䇗⫼ϔ ሎᑺ0DOODWㅫ⊩ˈᕫࠄԢ乥ߚ䞣DaD 催乥ߚ䞣GaG ˈ ✊ৢ䖯㸠ҹϟ䖤ㅫ˖ ˄˅ 䆒ᅮ催乥ߚ䞣䯔ؐЎ'ˈᇚ催乥ߚ䞣GaG ߚ߿Ѣ 䯔ؐ'↨䕗ˈᔧѢ'ᯊˈ䍙䯔ؐᷛᖫ'Iࡴ˗ ˄˅ 䆒ᅮԢ乥ߚ䞣ᵕؐ䮼䰤Ў$BPLQǃ$BPD[ˈ∖পԢ 乥ߚ䞣DaD㒱ᇍؐⱘ᳔ؐˈབᵰ᳔ؐ䍙ߎ䮼 䰤ˈ0Iࡴ˗ ˄˅ Ẕ⌟Ԣ乥ߚ䞣DaDⱘ䖛䳊⚍᭄ˈ䆄Ў=I˗ ˄˅ 䆒ᅮԢ乥ߚ䞣ব࣪ᵕؐ䮼䰤ЎƸ$ˈ∖পԢ乥ߚ䞣 DaDⳌ䚏ܗ㋴П䯈ⱘᏂؐᑊপ㒱ᇍؐˈབᵰѢ Ƹ$ˈ߭ᇚᅮԢ乥ߚ䞣ব࣪ᷛᖫƸIࡴDŽ ᬙ䱰߸ᮁձབ㸼᠔⼎ˈḍℸ㸼ৃ㊒⹂ᅮԡ▔ࢅ ֵোᬙ䱰㉏ൟҹঞথ⫳ᬙ䱰ⱘᯊ䯈ˈᅲ⦄▔ࢅֵোⱘᬙ䱰 䆞ᮁDŽ 㸼▔ࢅֵোᬙ䱰߸ᮁձ㸼 ձ ㉏ൟ 'I ᮴ᬙ䱰 ▔ࢅ⍜༅ !'I! ᐙؐさব !'I! ᐙؐ⏤ব 乥⥛さব !'I! 乥⥛⏤ব ᓩܹాໄ ! ⊼˖ 㸼⼎ϡЎ߸ᮁձDŽ 0I =I ƸI ! ! ! ᘏ㒧 㟈䇶 㗙ℸᛳ䇶㽓ᅝ⾥ᡔᄺ㚆䞥ྨਬӮᦤկⱘ乍 Ⳃ䌘䞥ᬃᣕDŽ REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] Bunte Andreas, Beineke Stephan High-Performance Speed Measurement by Suppression of Systematic Resolver and Encoder Errors[J] IEEE Trans.actions on Industrial Electronics, 2004, 51(1): 4953 Benammar Mohieddine, Ben-Brahim Lazhar, Alhamadi Mohd A A Novel Resolver-to-360° Linearized Converter[J] IEEE Sensors Journal, 2004, 4(1): 96-101 M.Nirei, Y.yananoto, K.kitazawa et al Angular error analysis of an 8XVR resolver with an eccentric rotor[J] Journal of Magnetism and Magnetic Materials, 2002, 24(2-5): 1202-1205 Nowlin N, McEndree S, Butcher D A radiation-hardened high-precision 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