7沼津工業高等専門学校研究報告
第 55 号，2021 年 1 月

㸱㍈ࢫࢸ࣮ࢪࢆ⏝࠸ࡓ㠀᥋ゐᦙ㏦࡟࠾ࡅࡿᆶ┤᪉ྥࡢືస࡟ᑐࡍࡿไᚚᡭἲࡢ᳨ウ୕㇂♸୍ᮁ 
Investigation of the Magnetic Levitation Control Method to the Vertical Direction ofthe Non-contact Conveyance System Using Three-axis Stage
MITANI Yuuichiroh*1
Abstract: The vertical movement of the non-contact conveyance system can be controlled byadding another signal to the magnetic levitation control input signal. The goal of the non-contact
conveyance system is to convey an assembly part or an industrial product in a three-dimensional
space without grasping of the object by a chuck or a robot hand. The control of the horizontal
movement was achieved successfully with a combination of the PID and robust controller
designed by the FNFR (Finite Number Frequency Response) modeling method. In this study,
three kinds of design methods are investigated to control the vertical movement of the threeaxis stage to move the levitation object upward without destabilization of the levitation system.
The first design method is MPC (Model Predictive Control) which is increasingly applied toindustrial manufacturing systems because of the usability. MPC can be designed withconstrained conditions explicitly. Moreover, the way to stabilize the magnetic levitation unstablesystem is interesting. The second design method also applies MPC to the stabilized system by
the PID controller as a comparison of the first design method. The third method is thecancellation of the vertical motion using an adaptive inverse controller. The effectiveness of all
three methods is shown through the simulation results.
Key Words:

Magnetic levitation, Non-contact conveyance, PID control, Model predictive control, Filtered-HLMSalgorithm䠍䠊⥴ゝᵓ⠏ࡢࡓࡵࡢᢏ⾡⪅ᩍ⫱ࡀ㸪࣒࢜ࣟࣥ♫ෆ࡛άⓎ࡟⾜ࢃࢀ࡚࠾ࡾ㸪ࡑࡢࡓࡵࡢ᪂ࡋ࠸ไᚚ⿦⨨࡜ࡋ࡚〇సࢆ౫㢗ࡉࢀࡓ㸬ᕤᴗ⏺࡟࠾ࡅࡿேᡭ୙㊊ࡣ῝้࡛࠶ࡾ㸪௒ᚋࡲࡍࡲࡍ⏕⏘ࡑࢀࡲ࡛࡟ࡶ࣒࢜ࣟࣥ♫ෆ࡛ 3 ㍈ࢫࢸ࣮ࢪࢆ฼⏝ࡋࡓᩍ⫱ࡣᕤ⛬ࡢ⮬ື໬ࡀ㐍ࡴ࡜ᛮࢃࢀࡿ㸬ࡑࢀ࡟௜㝶ࡍࡿࡼ࠺࡟㸪⏕࡞ࡉࢀ࡚࠸ࡓࡀ㸪ࡑࡢ㝿࡟⏝࠸ࡽࢀ࡚࠸ࡓᶵᮦࡣ㸪኱ேࡀ஧⏘タഛ࡜ࡋ࡚ᚲ㡲ࡢ PLC (Programmable Logic Controller)ேࡀ࠿ࡾ࡛ࡸࡗ࡜㐠࡭ࡿ኱ࡀ࠿ࡾ࡞ࡶࡢ࡛࠶ࡾ㸪ࢥࣥࣃࢡࢺ

ࡣ㧗㏿㸪㧗ᶵ⬟໬ࡋ࡚࠾ࡾ㸪ᚑ᮶ࡢ PLC ࡛ࡣᑐฎ࡛ࡁ࡞࠿ࡗ໬ࡀᙉࡃᮃࡲࢀ࡚࠸ࡓ㸬࠸ࡃࡘ࠿ࡢタィ௙ᵝࡀᥦ♧ࡉࢀ㸪〇ࡓ」㞧࡞ไᚚ⣔ࢆ㧗㏿࡟ฎ⌮࡛ࡁࡿࡼ࠺࡟࡞ࡗࡓ㸬౛࠼ࡤ㸪

సࡋࡓ 3 ㍈ࢫࢸ࣮ࢪࡣ㸪ືసࡢ⢭ᗘࢆྥୖࡉࡏࡘࡘ㸪୍ே࡛⏕⏘ࣛ࢖ࣥ࡟࠾ࡅࡿ࢔ࣛ࢖࣓ࣥࢺ➼࡟฼⏝ࡉࢀࡿ㸪┤஺ 3 ㍈㐠ᦙྍ⬟࡞ࢥࣥࣃࢡࢺ࡞ࡶࡢ࡜࡞ࡗࡓ㸬ࢫࢸ࣮ࢪ࡟࠾࠸࡚㸪࣒࢜ࣟࣥᰴᘧ఍♫㸦௨ୗ㸪࣒࢜ࣟࣥ࡜⛠〇సᙜึࡣ㸪ᆶ┤㥑ື㍈㸦Z ㍈㸧࡟ࢳࣕࢵࢡࢆྲྀࡾ௜ࡅ㸪ࡍ㸧ࡢ᪂ᆺ PLC ࡛࠶ࡿ Sysmac NJ ࡜ AC ࢧ࣮࣮࣎ࣔࢱ 1S

ᚑ᮶ࡢ࢔ࣛ࢖࣓ࣥࢺࢆ᝿ᐃࡋࡓ⿦⨨࡜ࡋࡓ㸬2017 ᖺᗘ㸪ࡑࢀࢩ࣮ࣜࢬࢆ⤌ࡳྜࢃࡏࢀࡤ㸪࠾ࡼࡑ 10nm ࡢ⢭ᗘ࡛఩⨨ỴࡵࢆᨵⰋࡋ㸪Z ㍈࡟ኚ఩ࢭࣥࢧෆໟᆺ㟁☢▼ࢆྲྀࡾ௜ࡅࡿࡇ࡜

ࡀྍ⬟࡛࠶ࡿ㸬ᮏ◊✲࡛ࡣ㸪ࡑࢀࡽࡢไᚚᶵჾࢆ⏝࠸㸪㟁☢

࡛㸪㠀᥋ゐᦙ㏦⿦⨨࡟ᣑᙇࡋࡓ[1]㸬ࡑࡋ࡚ 2019 ᖺᗘ㸪PID ไ▼࡟ࡼࡿ㠀᥋ゐᦙ㏦࡟࠾ࡅࡿ㸪ᆶ┤᪉ྥࡢᏳᐃ㥑ືࡢࡓࡵࡢᚚ࡟ࡼࡾᏳᐃ໬ࡋࡓᾋୖ⣔࡟ᑐࡋ㸪FNFR (Finite Numberไᚚ⣔タィ᪉ἲ࡟ࡘ࠸᳨࡚ウࡍࡿ㸬Frequency Response) ࣔࢹࣝࢆ฼⏝ࡋࡓࣟࣂࢫࢺไᚚ⣔ࢆᮏ◊✲࡛⏝࠸ࡿ 3 ㍈ࢫࢸ࣮ࢪࡣ㸪2016 ᖺᗘ࡟࣒࢜ࣟࣥ♫ᵓ⠏ࡍࡿࡇ࡜࡛㸪▷᫬㛫࡛ᾋୖ≀యࡢᦂࢀࢆᢚ࠼ࡓỈᖹ᪉ྥဨࡼࡾ〇స౫㢗ࡉࢀ㸪἟ὠ㧗ᑓ࡟࡚タィ㸪〇సࡋࡓࡶࡢ࡛࠶

ࡢᦙ㏦ไᚚࢆ☜❧ࡋࡓ[2]㸬ᮏ◊✲࡛ࡣ㸪ᆶ┤᪉ྥࡢᦙ㏦ࢆᏳࡿ㸬⏬ീฎ⌮ࢆక࠺ 3 ㍈ࢫࢸ࣮ࢪ࡟ࡼࡿ࢔ࣛ࢖࣓ࣥࢺไᚚ⣔ᐃ࡟ไᚚࡍࡿࡓࡵ࡟㸪2 ✀㢮ࡢไᚚჾࢆ⏝࠸ࡿࡇ࡜ࢆ᳨ウࡍ*1 ᶵᲔᕤᏛ⛉ Department of 0HFKDQLFDO(QJLQHHULQJࡿ㸬୍ࡘ┠࡜ࡋ࡚㸪MPC (Model Predictive Control) ࢆ฼⏝8

沼津工業高等専門学校研究報告

ࡍࡿ㸬MPC ࡣ㸪PID ไᚚ࡜ྠ➼ࡢタィࡢᐜ᫆ࡉࢆᣢࡕ࡞ࡀࡽ㸪ࣁ࣮ࢻ࢙࢘࢔࡟࠾ࡅࡿไ⣙᮲௳ࢆ㝧࡟⪃៖ࡋ࡚タィ࡛ࡁ㸪㏆ᖺᕤᴗ⏺࡟࡚ᛂ⏝౛ࡀᗈࡲࡾࡘࡘ࠶ࡿ㸬஧ࡘ┠࡜ࡋ࡚㸪እ஘ࡢ࢟ࣕࣥࢭ࣮ࣞࢩࣙࣥࡀྍ⬟࡞㐺ᛂ㏫ไᚚ (AdaptiveInverse Control) ࢆ⏝࠸ࡿ㸬3 ㍈ࢫࢸ࣮ࢪࡢ Z ㍈ࡢືసࢆ㸪ᾋୖ⣔࡟࠾ࡅࡿእ஘࡜ぢ࡞ࡋ㸪㏫ࣔࢹࣝ࡟ࡼࡿ࢟ࣕࣥࢭ࣮ࣞ
ࢩࣙࣥࢆ⾜࠺㸬MATLAB® / Simulink®ࢆ⏝࠸࡚タィࡋ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡾࡑࢀࡒࢀࡢไᚚ⣔ࡢ᭷ຠᛶࢆ☜ㄆࡍࡿ㸬第 55 号㘒ㄗ࡟࡚ồࡵࡓ㸬௨ୗ࡟㸪ࡑࢀࡒࢀࡢヲ⣽࡟ࡘ࠸࡚㏙࡭ࡿ㸬㸱㸬㸯 MPC ࡟ࡼࡿไᚚ⣔୙Ᏻᐃ⣔࡟ᑐࡍࡿ MPC ࡢタィ౛࡜ࡋ࡚㸪MathWorks ࡢ࣮࣒࣮࣍࣌ࢪ࡟࠶ࡿಽ❧᣺Ꮚ࡟࠾ࡅࡿไᚚ⣔タィ౛㸦Controlof an Inverted Pendulum on a Cart㸧ࢆཧ↷ࡋࡓ[3]㸬ไᚚᑐ㇟ࢆ P㸪ࢥࣥࢺ࣮ࣟࣛࢆ MPC ࡜ࡋ࡚㸪ᅗ 2 ࡟ࣈࣟࢵࢡ⥺ᅗࢆ♧ࡍ㸬ไᚚᑐ㇟࡟ࡣ㸪┠ᶆ఩⨨࡛ࡢᾋୖ࡟ᚲせ࡞ࣂ࢖࢔ࢫ㟁ὶࢆຍ࠼ࡿ㸬ࡲࡓ㸪ࢫࢸ࣮ࢪࡢ Z ㍈ࡢືసࢆእ஘࡜ぢ࡞ࡍ㸬䠎䠊☢Ẽᾋୖ⣔䛾䝰䝕䝹ᅗ㸯࡟㸪☢Ẽᾋୖ⣔ࡢࣔࢹࣝᅗࢆ♧ࡍ㸬࠶ࡿ఩⨨ࢆᾋୖ≀యࡢኚ఩‫ ݔ‬ൌ Ͳ࡜ࡋ㸪ࡑࡢ఩⨨࠿ࡽୖ᪉ྥࢆṇ࡟ྲྀࡿ㸬৯ఏகংॖ॔५ਗ਼૴

03&ਗ਼჌લ

ਗೊ

3೟঱ਜ਼઼

ᅗ 2 MPC ࣈࣟࢵࢡ⥺ᅗࡲࡎ㸪ᘧ(1)㸪(2)࡛⾲ࡉࢀࡿ୙Ᏻᐃ࡞ᾋୖ⣔࡟ᑐࡋ࡚㸪Simulink Control Design™ ࡢ ࢥ ࣐ ࣥ ࢻ linio ࠾ ࡼ ࡧ
linearize ࢆ⏝࠸࡚⥺ᙧ໬ࡋࡓ⣔ࢆసᡂࡋࡓ㸬MPC ࢆタィࡍࡿ㝿࡟㸪᭱ࡶ㔜せ࡜࡞ࡿࣃ࣓࣮ࣛࢱ㸪ண ࣍ࣛ࢖ࢬࣥ࠾ࡼࡧไᚚ࣍ࣛ࢖ࢬࣥࡣࡑࢀࡒࢀ㸪200㸪5 ࡜୚࠼ࡓ㸬ᩥ⊩[3]࡟⩦೟঱੟৬࠸㸪⾲ 1 ࡟♧ࡍタィࣃ࣓࣮ࣛࢱࢆ⏝࠸ࡓ㸬࡞࠾㸪ྛࣃ࣓࣮ࣛࢱࡢෑ㢌࡟グ㍕ࡋࡓ mpcobj ࡣ㸪ࢥ࣐ࣥࢻ mpc ࡼࡾ⏕ᡂࡉࢀ
ࡿ MPC ࢜ࣈࢪ࢙ࢡࢺ࡛࠶ࡿ㸬ᅗ 1 ☢Ẽᾋୖ⣔ࡢࣔࢹࣝ⾲㸯 MPC タィࣃ࣓࣮ࣛࢱ

㟁☢▼࡟ධຊ㟁ᅽܸ௜ ࢆ༳ຍࡋࡓ᫬࡟ὶࢀࡿ㟁ὶࢆ݅㸪ᾋୖ≀యࡀ㟁☢▼࠿ࡽཷࡅࡿຊࢆ‫ܨ‬㸪ᾋୖ≀య࡟స⏝ࡍࡿ㔜ຊࢆ݉݃࡜ࡍࡿ࡜㸪㐠ື᪉⛬ᘧࡣ௨ୗࡢࡼ࠺࡟᭩ࡅࡿ㸬݉‫ݔ‬ሷ ൌ ‫ ܨ‬െ ݉݃ଶ݅‫ ܨ‬ൌ݇൬
൰ܺെ‫ݔ‬ሺͳሻሺʹሻࡇࡇ࡛㸪݇࠾ࡼࡧܺࡣ㸪㟁☢▼࠾ࡼࡧᾋୖ≀య࡟ࡼࡾỴࡲࡿᐃᩘ࡛࠶ࡾ㸪‫ࢆ݅࡜ܨ‬ᐇ ࡍࡿࡇ࡜࡟ࡼࡗ࡚ᚓࡽࢀࡿ㸬ᮏሗ࡛ࡣ㐺ᙜ࡞್ࢆᐃࡵ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡿไᚚᛶ⬟ࡢ᳨

mpcobj.MV.Min

᧯స㔞ࡢ᭱ᑠ್

mpcobj.MV.Max᧯స㔞ࡢ᭱኱್

mpcobj.MV.ScaleFactor᧯స㔞࡟ᑐࡍࡿ㔜ࡳ᧯స㔞ࡢኚ໬⋡࡟ᑐࡍࡿ㔜ࡳไᚚ㔞࡟ᑐࡍࡿ㔜ࡳ

mpcobj.Weights.MVRatempcobj.Weights.OV

タィࣃ࣓࣮ࣛࢱࡣ㸪ヨ⾜㘒ㄗ࡟ࡼࡾ௨ୗࡢࡼ࠺࡟Ỵᐃࡋࡓ㸬࡞࠾ࡇࡇ࡛ࡣ㸪᧯స㔞ࡢ᭱኱࠾ࡼࡧ᭱ᑠ್ࡣไ㝈ࡏࡎ㸪Inf㸦↓㝈኱㸧࡜ࡋࡓ㸬ドࡢࡳ⾜࠺࡜ࡍࡿ㸬

mpcobj.MV.Min = -Inf, mpcobj.MV.Max = Inf䠏䠊ไᚚჾ䛾タィ

mpcobj.MV.ScaleFactor = 1500

3 ㍈┤⾜ࢫࢸ࣮ࢪࡢ Z ㍈ࢆ㸪2.5 ⛊࠿ࡅ࡚ 100mm ୖ᪉ྥ

mpcobj.Weights.MVRate = 100
mpcobj.Weights.OV = 100࡬ືసࡉࡏࡿࡇ࡜ࢆ᝿ᐃࡋ㸪ไᚚჾࡢタィࢆ⾜ࡗࡓ㸬タィ᪉ἲࡣ㸪௨ୗࡢ 3 ㏻ࡾ࡜ࡋࡓ㸬ձ

MPC ࡢࡳ⏝࠸࡚Ᏻᐃ໬ࡍࡿ㸬ղ

PID ไᚚ࡟࡚Ᏻᐃ໬ࡋࡓ⣔࡟ᑐࡋ࡚㸪MPC ࢆ⏝࠸ࡿ㸬ճ

PID ไᚚ࡟࡚Ᏻᐃ໬ࡋࡓ⣔࡟ᑐࡋ࡚㸪㐺ᛂ㏫ไᚚࢆ⏝࠸ࡿ㸬ࢧࣥࣉࣜࣥࢢࢱ࢖࣒ࢆྵࡵ㸪ไᚚࣃ࣓࣮ࣛࢱࡢከࡃࡣ㸪ヨ⾜ࡲࡓ㸪እ஘ࣔࢹࣝࢆᵓ⠏ࡋ㸪ࡑࡢ㝿ࡢタᐃࣃ࣓࣮ࣛࢱࡣ㸪௨ୗࡢࡼ࠺࡟ᩥ⊩[3]࡜ྠ୍್࡜ࡋࡓ㸬
disturbance_model = getindist( mpcobj )setindist( mpcobj, 'model', disturbance_model*10 )disturbance_model = getoutdist( mpcobj )9３軸ステージを用いた非接触搬送における垂直方向の動作に対する制御手法の検討

setoutdist( mpcobj0, 'model', disturbance_model*10 )Model Predictive Control Toolbox™ ࡢࢥ࣐ࣥࢻ MPC ࢆ⏝࠸ࡓタィᚋࡢ㸪review ࢥ࣐ࣥࢻ࡟ࡼࡿࣞࣅ࣮ࣗ⤖ᯝࢆᅗ 3࡟♧ࡍ㸬OP Hessian Matrix Validity ࡢ㆙࿌ࡣ㸪タィࣃ࣓࣮ࣛࢱࡢㄪᩚ࡛ゎᾘ࡛ࡁࡿࡼ࠺ࡔࡀ㸪⌧᫬Ⅼ࡛ゎỴ࡛ࡁ࡚࠸࡞࠸㸬ᅗ 4 ࡟㸪タィࡋࡓࢥࣥࢺ࣮ࣟࣛࢆ⏝࠸ࡓ㸪㛢࣮ࣝࣉ⣔ࡢࢫࢸࢵࣉᛂ⟅ࢆ♧ࡍ㸬ࢧࣥࣉࣜࣥࢢࢱ࢖࣒ࡣ 0.01[sec]࡛࠶ࡿ㸬Ᏻᐃ໬ࡍࡿࡇ࡜ࡣ࡛ࡁࡓࡶࡢࡢ㸪⌧≧࡛ࡣ㸪MPC ࡢࢧࣥࣉࣜࣥࢢࢱ࢖࣒ࢆ௚ࡢไᚚᡭἲࡼࡾ㛗ࡃྲྀࡽ࡞ࡅࢀࡤ㸪ᾋୖ࡟⮳ࡽ࡞࠸㸬ࡲࡓ㸪┠ᶆ఩⨨࡟ᾋୖࡉࡏࡿࡓࡵ࡟ᚲせ࡞ࣂ࢖࢔ࢫ㟁ὶࢆຍ࠼࡚࠸ࡿ㛵ಀ࡛㸪ไᚚධຊࡣࢮࣟ࡟཰᮰ࡋ࡚࠸ࡿ㸬
MPC ࡟ࡼࡿಽ❧ไᚚࢆཧ⪃࡜ࡋࡓ⤖ᯝ࡛࠶ࡿࡀ㸪ᮏ᮶ MPC
ࡣ㸪ࡇࡢሙྜ࡟ࡣ୙せ࡞ᐃᖖ೫ᕪࢆᇙࡵࡿࡓࡵࡢ✚ศ≉ᛶࢆᣢࡗ࡚࠾ࡾ㸪タィ⤖ᯝࡢᏳᐃవ⿱ࡢ☜ㄆࡀᚲせ࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬㸱㸬㸰 Ᏻᐃ໬ࡋࡓ⣔࡟ᑐࡍࡿ MPC ࡟ࡼࡿไᚚ⣔ḟ࡟㸪PID ไᚚ࡟ࡼࡾᏳᐃ໬ࡋࡓᾋୖ⣔࡟ᑐࡋ࡚ MPC ࢆタィࡋࡓ㸬ไᚚࣈࣟࢵࢡ⥺ᅗࢆᅗ 5 ࡟♧ࡍ㸬グྕࡢព࿡ࡣᅗ
2 ࡜ྠᵝ࡛࠶ࡾ㸪PID ࡣ㸪ᾋୖ⣔ࢆᏳᐃ໬ࡍࡿࡓࡵࡢ PID ไᚚჾࢆ⾲ࡍ㸬ংॖ॔५ਗ਼૴
৯ఏக03&ਗೊ

3,'3೟঱ਜ਼઼ᅗ 5 PID࣭MPC ࣈࣟࢵࢡ⥺ᅗࡇࡢሙྜࡶ㸱㸬㸯࡜ྠᵝࡢᡭἲࢆ⏝࠸࡚㸪ࡲࡎࡣ⣔ࢆ⥺ᙧ໬ࡋ㸪ண ࣍ࣛ࢖ࢬࣥ㸪ไᚚ࣍ࣛ࢖ࢬࣥࢆࡑࢀࡒࢀ㸪50㸪5 ࡜

ᅗ 3 MPC タィࣞࣅ࣮ࣗ⤖ᯝタᐃࡋࡓ㸬ࡲࡓ㸪እ஘ࣔࢹࣝࡶᵓ⠏ࡋࡓࡀ㸪ࡇࡇ࡛ࡣእ஘ࡢ

250ᙳ㡪ࢆ㸱㸬㸯ࡢሙྜࡢ 5 ಸ࡟タᐃࡋࡓ㸬௨ୗ࡟㸪ヨ⾜㘒ㄗ࡟200ไᚚධຊ >$@150ࡼࡾỴᐃࡋࡓタィࣃ࣓࣮ࣛࢱࢆ♧ࡍ㸬

100
50

mpcobj.MV.Min = -Inf㸪mpcobj0.MV.Max = Inf

0-50

mpcobj.MV.ScaleFactor = 1-100-150

mpcobj.Weights.MVRate = 10-200

-250

00.03

0.06

0.09

᫬㛫 >VHF@

disturbance_model = getindist( mpcobj )setindist( mpcobj, 'model', disturbance_model*50 )(a) ไᚚධຊ

disturbance_model = getoutdist( mpcobj )setoutdist( mpcobj, 'model', disturbance_model*50 )1.21

఩⨨ >P@

mpcobj.Weights.OV = 10.8

௨ୖࡢタᐃ್ࢆ⏝࠸࡚ MPC ࢆタィࡋࡓ㝿ࡢ㸪ࣞࣅ࣮ࣗ⤖ᯝ

0.6

ࢆᅗ 6 ࡟♧ࡍ㸬ࡇࡇ࡛ࡣ㸪ࡍ࡭࡚ࠕࣃࢫࠖ࡜࡞ࡾ㸪タィୖࡢ

0.4

㆙࿌ࡣ࡞࠿ࡗࡓ㸬0.2

ᅗ 7 ࡟㸪タィࡋࡓࢥࣥࢺ࣮ࣟࣛࢆ⏝࠸ࡓ㸪㛢࣮ࣝࣉ⣔ࡢࢫ0-0.2

ࢸࢵࣉᛂ⟅ࢆ♧ࡍ㸬ࢧࣥࣉࣜࣥࢢࢱ࢖࣒ࡣ 1[msec]࡛࠶ࡿ㸬
00.03

0.06

᫬㛫 >VHF@(b) ఩⨨
ᅗ 4 MPC タィ⤖ᯝ0.09ᾋୖ఩⨨ࡣ㸪
࠾ࡼࡑ0.1⛊࡛1࡟཰᮰ࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬ࡲࡓ㸪ࡇࡢ᫬ࡢไᚚධຊ್ࡣ㸪ෆഃࡢ PID ࣮ࣝࣉࡢ┠ᶆ್࡛࠶ࡿࡀ㸪bias ࡟ྵࡲࢀࡿࢃࡎ࠿࡞ㄗᕪࡀ㸪ไᚚධຊࡢ㸪㸯࠿ࡽࡢࡎࢀ࡟࡞ࡗ࡚⾲ࢀࡓ࡜ᛮࢃࢀࡿ㸬

10

沼津工業高等専門学校研究報告

第 55 号

ࢹࣝ࡟ᑐࡋ࡚㸪LMS (Least Mean Squares) ࢔ࣝࢦࣜࢬ࣒࡟
ࡼࡾ㏲ḟⓗ࡟ࣔࢹࣜࣥࢢࢆ⾜࠺ᡭἲ࡛࠶ࡿ[4]㸬ࡇࡇ࡛ࡣ㸪ከධຊከฟຊ⣔࡟ࡶᣑᙇ࡛ࡁࡿ㸪Filtered-HLMS ࢔ࣝࢦࣜࢬ࣒ࢆ⏝࠸ࡓ㸬ᅗ 8 ࡟㸪ไᚚࣈࣟࢵࢡ⥺ᅗࢆ♧ࡍ㸬PID ไᚚ࡟ࡼࡾ㸪┠ᶆ఩⨨࡟ᾋୖࡍࡿ⣔࡟ᑐࡋ࡚㸪Z ㍈࡟ࡼࡿᆶ┤᪉ྥࡢືస࡟ࡼࡾ㟁☢▼ࡀ⛣ືࡍࡿ㝿㸪ࡑࡢ㐠ືࡣ Z ㍈ࡢࢧ࣮࣎ࢻ
ࣛ࢖ࣂࡼࡾྲྀᚓ࡛ࡁࡿ㸬ࡋࡓࡀࡗ࡚㸪㐺ᛂ㏫ไᚚࢆᛂ⏝ࡍࢀࡤ㸪እ஘ࡢᙳ㡪ࢆࣇ࢕࣮ࢻࣇ࢛࣮࣡ࢻ㸦FF㸧ไᚚჾ࡟࡚࢟ࣕࣥࢭࣝࡍࡿࡇ࡜ࡀྍ⬟࡛࠶ࡿ㸬࡞࠾㸪ไᚚ࡟࠾ࡅࡿࢧࣥࣉࣜ
ࣥࢢࢱ࢖࣒ࡣ 1[msec]࡜ࡋࡓ㸬ਗೊংॖ॔५ਗ਼૴৯ఏக3,'))

3

೟঱ਜ਼઼

ᅗ 8 Filtered-Hࣈࣟࢵࢡ⥺ᅗ
ࡇࡇ࡛㸪PID ࡟ࡼࡿᏳᐃ໬ࡋࡓ⣔ࢆ FF ไᚚ࡟࠾ࡅࡿไᚚᑐ㇟࡜ࡍࡿ࡜ࡁ㸪ไᚚᑐ㇟㸪ࡑࡢ㏫ࢩࢫࢸ࣒㸪FF ไᚚჾࡢࡑ

ᅗ 6 MPC タィࣞࣅ࣮ࣗ⤖ᯝࢀࡒࢀࢆ LMS ࢔ࣝࢦࣜࢬ࣒࡟࡚㏲ḟⓗ࡟ᑟฟࡍࡿ㝿ࡢ㸪ㅖタᐃ್ࢆ⾲ 2 ࡟♧ࡍ㸬1.2

⾲ 2 LMS ࢔ࣝࢦࣜࢬ࣒࡟࠾ࡅࡿㅖタᐃ್ไᚚධຊ >P@1
0.80.6

⧞㏉ࡋᅇᩘ
᥎ᐃࣃ࣓ࣛ
࣮ࢱᩘ
᥎ᐃ㔜ࡳ

0.4
0.20







㏫ࢩࢫࢸ࣒

FF ไᚚჾ

600,000

10,000,000

3,000,000

300

50250

300.030.000001

᫬㛫 >VHF@

㸱㸬㸱㸬㸯 ไᚚᑐ㇟ࣔࢹࣝࡢ᥎ᐃ
ࡲࡎ㸪PID ไᚚ࡟ࡼࡾᏳᐃ໬ࡋࡓ⣔࡟ᑐࡋ࡚㸪LMS ࢔ࣝ(a) ไᚚධຊ఩⨨ >P@ไᚚᑐᑐ㇟ࢦࣜࢬ࣒ࢆ⏝࠸㸪FIR ࣔࢹࣝࢆ㏲ḟⓗ࡟ᑟฟࡍࡿ㸬 ᅗ 9 ࡟㸪

1.2FF ไᚚ࡟࠾ࡅࡿไᚚᑐ㇟ࢆ᥎ᐃࡍࡿࡓࡵࡢࣈࣟࢵࢡ⥺ᅗࢆ

1♧ࡍ㸬᥎ᐃࣔࢹࣝ M ࡢฟຊ࡜㸪P ࡢฟຊಙྕ࡜ࡢㄗᕪࡀ᭱ᑠ

0.8

࡟࡞ࡿࡼ࠺࡟ M ࡢ FIR ࣔࢹࣝࢆ㏲ḟⓗ࡟᥎ᐃࡍࡿ㸬᥎ᐃ⤖0.6

ᯝࢆᅗ 10 ࡟♧ࡍ㸬(a)ࡀ᥎ᐃㄗᕪࡢ᥎⛣㸪(b)ࡀ P ࡢฟຊ್࡜

0.4

M ࠿ࡽࡢ᥎ᐃ್ࡢ཰᮰್࡜ࡢẚ㍑㸪(c)ࡀ᥎ᐃࡉࢀࡓ FIR ࣔ0.2

ࢹ࡛ࣝ࠶ࡿ㸬Ⰻዲ࡟᥎ᐃࡉࢀ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬

0







᫬㛫 >VHF@(b) ఩⨨ংॖ॔५ਗ਼૴

৯ఏகছথॲ঒ਦಀ

3,'3

ᅗ 7 MPC タィ⤖ᯝ㸱㸬㸱 㐺ᛂ㏫ไᚚ࡟ࡼࡿไᚚ⣔0ࡇࡇ࡛⏝࠸ࡓ㐺ᛂ࢔ࣝࢦࣜࢬ࣒ࡣ㸪࢘࢕ࢼ࣮ࣇ࢕ࣝࢱ࡜࿧
ࡤࢀࡿ㸪Z ኚ᥮ࢆ⏝࠸ࡓ FIR (Finite Impulse Response) ࣔᅗ 9 FF ไᚚ࡟࠾ࡅࡿไᚚᑐ㇟ࡢ᥎ᐃ

11

３軸ステージを用いた非接触搬送における垂直方向の動作に対する制御手法の検討

0.001ছথॲ঒ਦಀ
ㄗᕪ >P@0 ̆

00.0005

0-0.0005-0.001

̆0100

200

300

400500600

ᅗ 11 ไᚚᑐ㇟ࡢ㏫ࣔࢹࣝࡢ᥎ᐃ

᫬㛫 >VHF@(a) ไᚚᑐ㇟ࡢ᥎ᐃㄗᕪࡢ᥎⛣0.8
0.60.0015

ฟຊ >P@

ฟຊ >P@

0.4

ड़ྙ஍

0.001

ਬఈ஍

0.000500-0.2-0.4-0.0005-0.6-0.001-0.0015

0.2-0.8





02000

4000

6000

8000

10000

᫬㛫 >VHF@᫬㛫 >VHF@(a) ㏫ࣔࢹࣝࡢ᥎ᐃㄗᕪࡢ᥎⛣(b) ฟຊಙྕࡢẚ㍑

0.6

ฟຊ >P@

ኚ఩ >PP@

0.04
0.020ਬఈ஍

0.2
0-0.2-0.4-0.02-0.04

ड़ྙ஍

0.4

0.06

-0.6




00.01

0.02

0.03

0.04

0.05

0.040.05

᫬㛫 >VHF@᫬㛫 >VHF@(b) ฟຊಙྕࡢẚ㍑(c) ᥎ᐃࡉࢀࡓ FIR ࣔࢹࣝ80ᅗ 10 ไᚚᑐ㇟ࡢ᥎ᐃ⤖ᯝ60ḟ࡟㸪ồࡵࡓไᚚᑐ㇟ࡢ㏫ࣔࢹࣝࢆ㸪㏲ḟⓗ࡟ᑟฟࡍࡿ㸬㞳ᩓ໬ࡋࡓࣔࢹࣝࡣ୍⯡࡟㠀᭱ᑠ఩┦⣔࡛࠶ࡾ㸪ࡋࡓࡀࡗ࡚

ฟຊ >P@

40

㸱㸬㸱㸬㸰 ไᚚᑐ㇟ࡢ㏫ࣔࢹࣝࡢ᥎ᐃ

200-20-40㏫ࣔࢹࣝࡣ୙Ᏻᐃ࡜࡞ࡿࡢ࡛㸪㏲ḟⓗ࡟ᑟฟ࡛ࡁ࡞࠸㸬ࡑࡇ

-60

࡛ᅗ 11 ࡟♧ࡍࡼ࠺࡟㸪㐜ࢀせ⣲Ǽࢆ⏝ពࡋ㸪㐜ࢀࢫࢸࢵࣉᩘ

-80ࢆ㸪ồࡵࡿࣃ࣓࣮ࣛࢱᩘࡢ༙ᩘ࡜ࡍࡿࡇ࡜࡛㸪᭱㐺࡞㏫ࣔࢹ
ࣝࢆᑟฟࡍࡿࡇ࡜ࡀྍ⬟࡜࡞ࡿ[4]㸬ᅗ 12 ࡟㸪ồࡵࡓ㏫ࣔࢹࣝࢆ♧ࡍ㸬(a)ࡣ㸪㐜ࢀせ⣲࠿ࡽࡢฟຊ࡜㸪ᑟฟࡍࡿ㏫ࣔࢹࣝࡢ
ฟຊ࡜ࡢㄗᕪࡢ᫬㛫᥎⛣㸪(b)ࡣ㸪㐜ࢀせ⣲࠿ࡽࡢฟຊ࡜㸪཰
᮰ᚋࡢ㏫ࣔࢹࣝࡢฟຊಙྕ࡜ࡢẚ㍑㸪(c)ࡣ㸪ồࡵࡓ FIR ࣔࢹ࡛ࣝ࠶ࡿ㸬(b)࡟ⱝᖸࡢㄗᕪࡀࡳࡽࢀࡿࡀ㸪࠾࠾ࡴࡡⰋዲ࡟ᑟฟࡉࢀ࡚࠸ࡿ࡜࠸࠼ࡿ㸬

00.01

0.020.03

᫬㛫 >VHF@(c) ᥎ᐃࡉࢀࡓ FIR ࣔࢹࣝᅗ 12 ㏫ࣔࢹࣝࡢ᥎ᐃ⤖ᯝ㸱㸬㸱㸬㸱 FF ไᚚჾࡢᑟฟ
᭱ᚋ࡟㸪㏫ࣔࢹࣝࢆ⏝࠸࡚ FF ไᚚჾࢆ㏲ḟⓗ࡟ᑟฟࡍࡿ㸬ࣈࣟࢵࢡ⥺ᅗࢆᅗ 13 ࡟♧ࡍ㸬Z ㍈ࢆࣛࣥࢲ࣒࡟㥑ືࡍࡿ࡜ྠ᫬࡟㸪ࡑࡢࣛࣥࢲ࣒ಙྕࢆ㐜ࢀせ⣲Ǽ࡟㏻㐣ࡉࡏ㸪ᵓ⠏ࡍ

12

沼津工業高等専門学校研究報告ࡿ FF ไᚚჾࡢධຊ࡜ࡍࡿ㸬FF ไᚚჾࡢ㏲ḟⓗ࡞ㄪᩚࡣ㸪ᾋ

0.0001FF ไᚚჾ࡟ࢥࣆ࣮ࡋ࡚⏝࠸ࡿ㸬ࡇࡢࡼ࠺࡞ไᚚ⣔ࢆᵓ⠏ࡍࡿࡇ࡜࡟ࡼࡾ㸪እ஘࡜ࡋ࡚ຍ࠼ࡓࣛࣥࢲ࣒ಙྕࡢᙳ㡪ࢆ㸪఩⨨ಙྕ࠿ࡽ࢟ࣕࣥࢭࣝࡍࡿࡼ࠺࡞ไᚚධຊࡀ FF ࡼࡾ⏕ᡂࡉ࢟ࣕࣥࢭࣝṧᕪ >P@ୖ఩⨨ಙྕࢆ㏫ࣔࢹࣝ࡟㏻㐣ࡉࡏࡓಙྕࢆ⏝࠸ࡿ㸬㏲ḟⓗ࡟ồࡵࡽࢀࡿ FF ไᚚჾࡣ㸪ࡑࡢ㒔ᗘไᚚᑐ㇟ࡢ๓࡟㓄⨨ࡋࡓ

第 55 号

ࢀࡿ㸬

0.00005

0-0.00005-0.0001

ছথॲ঒ਦಀ3,'))

3









(a) ࢥࣥࢺ࣮ࣟࣛࡢ᥎ᐃㄗᕪࡢ᥎⛣೟঱ਜ਼઼))0 ̆

ฟຊ >P@

FRS\̆᫬㛫 >VHF@

ংॖ॔५ਗ਼૴৯ఏக



0.0003֐ཛྷͶଲͤΖड़ྙ

0.0002੏‫ޜ‬೘ྙͶଲͤΖड़ྙ

0.00010-0.0001-0.0002

ᅗ 13 FF ไᚚჾࡢᑟฟ-0.0003

ᅗ 14 ࡟㸪FF ไᚚჾࡢᑟฟ⤖ᯝࢆ♧ࡍ㸬(a)ࡣ㸪᥎ᐃㄗᕪࡢ



0.00002ࡿ㸬࡞࠾㸪ࣛࣥࢲ࣒ಙྕࡢ࿘ᮇࡣ 0.1 ⛊࡜ࡋࡓ㸬(a)ࡼࡾ㸪᏶0.00001

䠐䠊ไᚚ䝅䝭䝳䝺䞊䝅䝵䞁⤖ᯝ
๓㏙ࡋࡓ㸱✀㢮ࡢไᚚ⣔ࢆタィࡋ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ⾜ࡗࡓ㸬┤஺ 3 ㍈ࢫࢸ࣮ࢪࡢᆶ┤㍈࡛࠶ࡿ Z ㍈ࢆ㸪ୖ᪉ྥ࡬
0.1m ື࠿ࡍࡇ࡜ࢆ᝿ᐃࡋ࡚࠸ࡿ㸬Z ㍈࡟ࡣ㸪ኚ఩ࢭࣥࢧࢆෆໟࡍࡿ㟁☢▼ࡀᅛᐃࡉࢀ࡚࠾ࡾ㸪Z ㍈࡜㟁☢▼ࡣ㸪᏶඲࡟ྠࡌືࡁࢆࡍࡿ࡜௬ᐃࡍࡿ㸬ࡘࡲࡾ㸪ᅛᐃ㒊ࡢᙎᛶኚᙧࡣ⪃៖ࡋ࡞࠸㸬᝿ᐃࡍࡿ Z ㍈ࡢືసࡣ㸪0.5 ⛊㛫 0.1m/s2 ࡛ຍ㏿ࡋ㸪1.5 ⛊㛫➼㏿㐠ືࡋࡓᚋ㸪෌ࡧ 0.5 ⛊㛫 0.1m/s2 ࡛ῶ㏿ࡋ࡚೵Ṇࡍࡿ㸬ࡇࡢᵝᏊࢆࢢࣛࣇ࡟ࡋࡓࡶࡢࢆᅗ 15 ࡢ(a)㸪(b)࡟♧ࡍ㸬(a)ࡀ
Z ㍈ࡢୖ᪉ྥࡢືస㸦఩⨨㸧㸪(b)ࡀ Z ㍈ࡢຍ㏿ᗘ࡛࠶ࡿ㸬ࡇࡢືసࡀ㸪ᾋୖ⣔࡟࠾࠸࡚ࡣእ஘࡜ࡋ࡚స⏝ࡋ㸪ᾋୖ≀యࡢᾋୖ఩⨨ࢆኚ໬ࡉࡏࡿ㸬๓㏙ࡋࡓ 3 ࡘࡢไᚚ⣔ࢆ⏝࠸ࡓ㝿ࡢ㸪ᾋୖ≀యࡢ఩⨨ࢆ㸪ᅗ 15 ࡢ(c)࡟♧ࡍ㸬┠ᶆᾋୖ఩⨨ࡣ 5[mm]࡜ࡋ㸪㟁☢▼࡟ᑐࡍࡿᾋୖ≀యࡢ┦ᑐ఩⨨ࢆࢢࣛࣇ໬ࡋࡓ㸬㟷Ⰽࡢ◚⥺ࡀ㸪MPC ࢆ⏝࠸࡚ᾋୖ⣔ࢆᏳᐃ໬ࡋࡓሙྜࡢ㸪ᾋୖ఩⨨ࡢኚ໬࡛࠶ࡿ㸬㸱㸬㸯࡛♧ࡋࡓ࡜࠾ࡾ㸪㠀ᖖ࡟ಇᩄ࡟እ஘࡟ᑐࡋ࡚ᛂ⟅ࡋ࡚࠸ࡿࡀ㸪೫ᕪࢆᇙࡵࡿࡇ࡜ࡀ࡛ࡁ࡚

ไᚚධຊ >P@Ἴᙧࡢẚ㍑㸪(c)ࡣ㸪ᑟฟࡉࢀࡓ FF ไᚚჾࡢ FIR ࣔࢹ࡛ࣝ࠶ࡓ㸬(b) ฟຊಙྕࡢẚ㍑

஘㸧࡟ᑐࡍࡿฟຊ㸦ᾋୖ఩⨨㸧࡜㸪ไᚚධຊ࡟ᑐࡍࡿฟຊࡢ

ᙧࡢẚ㍑ࡼࡾ㸪FF ไᚚჾࡢᑟฟ᫬㛫ࡣ඘ศ࡛࠶ࡿ࡜ุ᩿ࡋ

᫬㛫 >VHF@᫬㛫ⓗ᥎⛣㸪(b)ࡣ㸪FF ไᚚჾࡀ཰᮰ᚋࡢ㸪ࣛࣥࢲ࣒ಙྕ㸦እ඲࡟ FF ไᚚჾࡀ཰᮰ࡋ࡚࠸࡞࠸ࡼ࠺࡟ࡶࡳ࠼ࡿࡀ㸪(b)ࡢἼ



0-0.00001-0.00002-0.00003-0.00004-0.00005







᫬㛫 >VHF@(c) ᑟฟࡉࢀࡓ FIR ࣔࢹࣝᅗ 14 ไᚚჾࡢᑟฟ⤖ᯝ࠸࡞࠸㸬㛢࣮ࣝࣉࡢ࿘Ἴᩘᛂ⟅ࢆồࡵ㸪పᇦ࡟࠾ࡅࡿ✚ศ≉ᛶࡸ㸪Ᏻᐃవ⿱ࢆㄪᰝࡍࡿᚲせࡀ࠶ࡿ࡜ᛮࢃࢀࡿ㸬㉥ࡢ◚⥺ࡀ㸪PID ไᚚ࡟ࡼࡾᏳᐃ໬ࡋࡓ⣔࡟ᑐࡋ࡚㸪MPC ࢆ⏝࠸ࡓไᚚ⣔ࡢᛂ⟅࡛࠶ࡿ㸬ࡇࡕࡽࡶ㸱㸬㸰࡛♧ࡋࡓ࡜࠾ࡾ㸪ẚ㍑ⓗ⦆ࡸ࠿࡞ᛂ⟅࡜࡞ࡗ࡚࠸ࡿ㸬0.1[mm]⛬ᗘࡢᾋୖ≀యࡢ᣺ࢀࡀ
ࡳࡽࢀࡿࡀ㸪⣙ 0.5 ⛊࡛┠ᶆ఩⨨࡟཰᮰ࡉࡏࡿࡇ࡜ࡀ࡛ࡁ࡚࠸ࡿ㸬㯮⥺ࡣ㸪PID ไᚚ࡟ࡼࡾᏳᐃ໬ࡋࡓ⣔࡟ᑐࡋ࡚㸪FF ไᚚჾࢆ⏝࠸࡚እ஘ࢆ࢟ࣕࣥࢭ࣮ࣞࢩࣙࣥࡋࡓ⤖ᯝ࡛࠶ࡿ㸬ࢢࣛࣇ࠿ࡽࡣㄞࡳྲྀࢀ࡞࠸ࡀ㸪⣙ 0.002[mm]⛬ᗘࡢᦂࢀࡀṧࡗ࡚࠸ࡿࡢࡳ࡛㸪࡯ࡰ᏶඲࡟࢟ࣕࣥࢭ࣮ࣞࢩࣙࣥ࡟ᡂຌࡋ࡚࠸ࡿ㸬࡞࠾㸪ᅗ 15 ࡢ(d)࡟ࡣ㸪3 ࡘࡢไᚚ᪉ἲࢆ⏝࠸ࡓ㝿ࡢ㸪㟁☢▼࡟ὶࢀࡿไᚚධຊ㟁ὶ್ࢆ♧ࡋࡓ㸬㠀ᖖ࡟⯆࿡῝࠸ࡢࡣ㸪እ஘ࡢຍ㏿ᗘࡀ୙㐃⥆࡟ኚ໬ࡋࡓ▐㛫࡟㸪Ἴᙧ࡟ⱝᖸࡢᕪ␗

13

３軸ステージを用いた非接触搬送における垂直方向の動作に対する制御手法の検討୙㐃⥆࡟ኚ໬ࡋࡓ▐㛫ࡢไᚚධຊ್ࡀ㸪ᾋୖ≀యࡢእ஘࡟ᑐ
0.12ࡍࡿືసࢆᨭ㓄ࡋ࡚࠸ࡿ࡜࠸࠼ࡿ㸬఩⨨ >P@

0.10.08

ᅗ 16 ࡟㸪ᅗ 15(d) ࡟࠾ࡅࡿ㸪እ஘ࡢຍ㏿ᗘࡀ୙㐃⥆࡟ኚ໬0.06

ࡍࡿ 1 ⛊௜㏆ࡢἼᙧࢆᣑ኱ࡋࡓࡶࡢࢆ♧ࡍ㸬ࡇࡇ࡛ࡉࡽ࡟⯆0.04

࿡῝࠸ࡢࡣ㸪FF ไᚚჾ࡛࠶ࡿ Filtered-Hࡢࡳࡀ㸪᭱ึ࡟㏫᪉

0.02ྥ࡬ࡢධຊࢆ⏕ᡂࡋ࡚࠸ࡿⅬ࡛࠶ࡿ㸬ࡇࢀࡣ㸪㠀᭱ᑠ఩┦⣔0-0.02࡟࠾ࡅࡿࢫࢸࢵࣉᛂ⟅࡟ぢࡽࢀࡿ⌧㇟࡛࠶ࡾ㸪ࡍ࡞ࢃࡕ㸪࢟
01

2

345

᫬㛫 >VHF@ࣕࣥࢭ࣮ࣞࢩࣙࣥࢆᐇ⌧ࡍࡿࡓࡵࡢ FF ไᚚჾࡣ㸪୙Ᏻᐃ㞽Ⅼࢆᣢࡗ࡚࠸ࡿ࡜࠸࠼ࡿ㸬(a) Z ㍈ࡢ఩⨨

0.313

0.15

㟁ὶ >$@

ຍ㏿ᗘ >PV@

0.05
00.3110.310.309

-0.05

0.308

-0.1-0.1503&3,'03&)LOWHUHGH

0.312

0.1

012

34

0.95

1

1.05

1.1

1.15

1.2

᫬㛫 >VHF@

5᫬㛫 >VHF@ᅗ 16 ไᚚධຊ㟁ὶ㸦ᣑ኱ᅗ㸧(b) Z ㍈ࡢຍ㏿ᗘ䠑䠊⤖ゝ
3 ㍈ࢫࢸ࣮ࢪࡢᆶ┤㥑ື㍈࡛࠶ࡿ Z ㍈࡟㸪ኚ఩ࢭࣥࢧࢆෆໟࡋࡓ㟁☢▼ࢆタ⨨ࡋ㸪ᾋୖ≀యࢆୖ᪉ྥ࡬ᦙ㏦ࡍࡿ㝿ࡢ㸪
Ᏻᐃ࡟ᦙ㏦ࡍࡿࡓࡵࡢไᚚ⣔ࡢᵓ⠏࠾ࡼࡧ㸪ࡑࡢᛶ⬟ホ౯ࡢࡓࡵࡢࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ⾜ࡗࡓ㸬MPC ࡢࡳࢆ⏝࠸ࡓሙྜ㸪
PID ไᚚ࡟ࡼࡾᏳᐃ໬ࡋࡓ⣔࡟ᑐࡋ࡚ MPC ࢆ⏝࠸ࡓሙྜ㸪
Filtered-Hࢆ⏝࠸ࡓ FF ไᚚࢆ⏝࠸ࡓሙྜࡢ㸪3 ✀㢮ࡢไᚚ⣔ࢆᵓ⠏ࡋ㸪Z ㍈ࡢືస࡟ᑐࡍࡿᾋୖ≀యࡢኚ఩ࢆィ⟬ࡋࡓ㸬FFไᚚჾࢆ⏝࠸ࡓሙྜࡀ㸪᭱ࡶⰋዲ࡟ᦙ㏦࡛ࡁࡿࡇ࡜ࡀศ࠿ࡗ(c) ᾋୖ≀యࡢ఩⨨ࡓ㸬ࡓࡔࡋ㸪ไᚚჾࡢᑟฟ࡟㛗᫬㛫࠿࠿ࡿ࡜࠸࠺ၥ㢟ࡀ࠶ࡾ㸪
MPC ࡜ FF ไᚚ࡜ࡢే⏝ࡀ⌧ᐇⓗࡔ࡜⪃࠼࡚࠸ࡿ㸬ᐇᶵࢆ⏝0.315

࠸ࡓᐇ㦂࡟ࡼࡾ᳨ドࡍࡿணᐃ࡛࠶ࡿ㸬0.314

㟁ὶ >$@

0.313ཧ⪃ᩥ⊩㻌

0.312

[1]

0.311

0.310.308

Control System with Self-identification Function of the03&3,'03&)LOWHUHGH0.309

012

34

Y. Mitani, R. Tanaka, et al., Non-contact Conveyance
Levitation Object -Investigation of Stability of theConveyance Control System-, MoViC2018, (2018)5᫬㛫 >VHF@(d) ไᚚධຊ㟁ὶᅗ 15 ᆶ┤ᦙ㏦ࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝ

[2]

1RSS 
[3]࡟ࡣࡑࢀࡀዲࡲࡋࡃ࡞࠸᣺ືࢆᘬࡁ㉳ࡇࡍ㸬እ஘ࡢຍ㏿ᗘࡀ

Mathworks, Control of an Inverted Pendulum on a Cart,
https://jp.mathworks.com/help/mpc/ug/control-of-aninverted-pendulum-on-a-cart.html㸦2020.7.29 ཧ↷㸧ࡀㄆࡵࡽࢀࡿࡀ㸪ࡑࢀ௨እࡣ࡯ࡰྠᙧ࡛࠶ࡿⅬ࡛࠶ࡿ㸬ຍ㏿ᗘࡀ୙㐃⥆࡟ኚ໬ࡍࢀࡤ㸪ᑐ㇟≀࡟ࡣ⾪ᧁຊࡀຍࢃࡾ㸪୍⯡ୖ㸪⏣୰㸪୕㇂㸪ᘏᒣ㸪㟁ẼᏛ఍ㄽᩥㄅ C㸪9RO

[4]

R. Widrow, E.Walach, Adaptive Inverse Control,
Prentice Hall, (1996)