• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance?

    2017-05-09 11:46:24DaWeiDing丁大為FangFangLiu劉芳芳HuiChen陳輝NianWang王年andDongLiang梁棟
    Communications in Theoretical Physics 2017年12期
    關(guān)鍵詞:陳輝

    Da-Wei Ding(丁大為)Fang-Fang Liu(劉芳芳)Hui Chen(陳輝)Nian Wang(王年)? and Dong Liang(梁棟)

    1Key Laboratory of Intelligent Computing and Signal Processing,Ministry of Education,Anhui University,Hefei 230601,China

    2School of Electronics and Information Engineering,Anhui University,Hefei 230601,China

    1 Introduction

    Leon Chua predicted that there should be a fourth type of electronic components,the memristor,based on the physics symmetry.[1]The memristor was not developed or researched within circuit theory until 2008,when HP’s Stan Williamset al.created a solid-state implementation of the memristor.[2]Many studies on the memristor for application development have been published now,such as the memristor-based circuits[3?4]and memristor oscillators.[5?6]

    In recent years,more and more scholars are interested in the fractional-order system.In Ref.[7],for the purpose of investigating the nonlinear dynamics of the system,a fractional-order Chua’s circuit based on the memristor,which derives from the integer-order counterparts was provided.The fractional-order system is widely applied in many aspects,such as the oscillator theory,[8]the control field,[9?11]and the energy field.[12]Some of the classic systems have been extended to their fractionalorder counterparts,for example,the Liu system,[13?14]the Chen system,[15]the Duffing system,[16]and the viscoelastic system.[17]

    Time delay exists in many engineering systems,causing system instability and bad performance.And it is unavoidable in many dynamical systems,such as biological systems,[18]neural networks,[19]system control,[20]and so on.Therefore,it is signi ficant to investigate the timedelayed effect on dynamical behaviors of complex systems theoretically and practically.

    Furthermore,the fractional-order delayed system involves non-integer order derivatives as well as time delay.These have been proved useful in financial system,[21]signal processing,[22]biology,[23]and so on.Many researchers have studied the fractional-order delayed system.[24?29]In Ref.[28],the bifurcation in Duffing-van der Pol oscillators with time delay was analyzed.In Ref.[29],the bifurcation and stability in three neurons fractional-order neural network were investigated by applying the sum of time delay as the bifurcation parameter.Additionally,chaos behaviors in the fractional-order delayed system have become the key focus.[30?31]In Ref.[30],the chaos in a delayed Bloch model was discussed and found that time delay can affect the system stability in this system.In Ref.[31],the discrete chaotic dynamics in fractional delayed logistic maps was studied,and the discrete chaotic attractor was discovered.In Ref.[32],we have analyzed the stability and Hopf bifurcation of fractional-order delayed memristor-based chaotic system by choosing the time delay and fractional-order as the bifurcation parameter.

    Chaotic control is to make the trajectories of initial chaotic system approach a steady state.Many control schemes for fractional-order chaotic systems have been proposed,including active control,[33]impulsive control,[34]adaptive control,[35]passive control[36]and generalized projective control.[37]Sliding mode control has received much attention due to its major advantages such as robustness against parameter variations,guaranteed stability,simplicity in implementation and fast dynamic response.Therefore,in recent years,sliding mode control has been investigated for linear and nonlinear systems.[38?41]Many vital results have been reported for the synchronization and control of fractional-order chaotic systems by using the sliding mode control strategy.In Ref.[42],to realize complete synchronization of a class of three-dimensional fractional-order chaotic systems,the author modi fied sliding mode control scheme,and designed a single-state sliding mode controller.In Ref.[43],Tanmoy Dasguptaet al.proposed a novel fractional-order sliding mode controller for synchronization of fractional order chaotic systems,and achieved its application in secure communication.The scholars studied the adaptive sliding mode synchronization control for a class of fractional-order chaotic systems with unknown bounded disturbances in Ref.[44].In order to achieve finite time convergence of the system states,a terminal sliding mode control method was firstly proposed by Zak in Ref.[45].In Ref.[46],the terminal sliding mode control technique that offers some superior properties such as fast response and finite time convergence was proposed,which is particularly suitable for high-precision control as it speeds up the rate of convergence near the origin.In Ref.[47],they investigated the chaotic control of a class of fractional-order chaotic systems via sliding mode control.In Ref.[48],the authors derived new results based on the sliding mode control for the anti-synchronization of four-wing chaotic systems.

    Motivated by aforementioned analysis,the main purpose of this paper is to design a fractional-order sliding mode controller,which is the combination of fractional calculus theory and the sliding mode control technique in order to control the fractional-order delayed memristive chaotic system.For this purpose,sliding mode control scheme is utilized along with Lyapunov stability theory to design the suitable control structure.Recall that slide mode controllers,which applied to the fractionalorder chaotic system may be numerous,while applied to fractional-order delayed memristor system are few.The proposed controller makes the system states asymptotically stable and robust against the system’s uncertainty in the presence of an external disturbance.Simulation results illustrate that the proposed method can eliminate chaos and stabilize the system in a finite time.

    The rest of this paper is organized as follows.In Sec.2,we discuss a fractional-order delayed memristive chaotic system.According to the sliding mode control theory,a controller is proposed to control the commensurate and non-commensurate fractional-order delayed chaotic system in Sec.3,the design procedure of fractional-order sliding mode approach is described in this section.Numerical simulations results are shown in Sec.4.Finally,some conclusions are drawn in Sec.5.

    2 System Description

    A memristor is a passive two-terminal circuital element,and it is described by a nonlinear characteristic:iM=W(φ)vM,vM=M(z)iM,whereiM,vM,φ,andzare the current,the voltage,the flux,and the charge in memristor.W(φ)=dz(φ)/dφandM(z)=dφ(z)/dzexpress as inductance and memristance respectively.

    Furthermore,the relationship ofφ(z)andz(φ)can be de fined with the charge-controlled memristor and fluxcontrolled memristor.We choose the flux-controlled memristive system:

    whereiMandvMdescribe the current and the voltage through the memristor,andf(t,x,vM)is the internal state function.

    De finition 1(Ref.[49]):In this paper,a continuous functionf:R+→Rrepresents the Caputo fractional derivative,which has a fractional-orderq:

    where Γ(q)is the gamma function,m?1<q≤m,m∈N.

    The simplest delayed memristive chaotic system includes a resistorR,a voltage followerU2,a capacitorC,a flux-controlled memristorM,a time delay unit,and an integratorU1(Fig.1 in Ref.[50]).The following equations describe the delayed memristive chaotic system in Fig.1.

    whereτis the time delay,yis the state variable of the memristor,andA,B,a,bandlare the constants.

    From the integer-order system,we derive the equations of the fractional-order memristive system,and it can be calculated as:

    whereq1andq2are the fractional-order of the capacitorCand memristorM.

    Fig.1 Model of the delayed memristive chaotic system.

    Then,we get the following equations:

    3 Designing the Sliding Mode Control

    We add the control inputu(t)to the state equations in system(6)to control the chaos behavior:

    where,f(x,y)=nxy,g(x,y)=ax+lxyis assumed.

    Our aim is to design a fractional-order sliding mode controller.The first step is constructing a fractional-order sliding surface that represents a desired system dynamics.Then,a switching control law should be developed,and any states outside the surface are driven to reach the surface in a finite time.[51]Therefore,we choose a sliding surface:

    According to the sliding mode method,the sliding surface and its derivative must satisfy the following conditions:

    The equivalent control law is calculated as:

    The switching control can keep the system within the sliding manifold.To satisfy the sliding condition,the discontinuous reaching law is chosen as follows:

    Therefore,the total control law can be de fined as:

    Theorem 1Considering the fractional-order delayed memristive chaotic system(8),and the control law(16),if the controller gainKr<0,the system is asymptotically stable.

    ProofThe Lyapunov candidate is selected as:

    WhenKr<0,˙V<0 fors(t)/=0.In other words,the controlled system satis fies the reaching condition.Therefore,a Lyapunov function has been found that it satis fies the conditions of the Lyapunov stability theorem(V>0,˙V<0).Thus,the closed-loop system in the presence of the controller(16)is globally asymptotically stable.

    Theorem 2Considering the system(8)being perturbed by uncertainties and an external disturbance,it can be modeled as follows:

    where Δg(x,y)andd(t)are assumed to be bounded,i.e.|Δg(x,y)|≤e1and|d(t)|≤e2.The closed-loop system with the sliding mode control(16)is globally asymptotically stable whenKr<?(e1+e2).

    ProofSelecting the Lyapunov candidate(17),we have

    Therefore,in view of the uncertainty and external disturbance,when the controller gainKr<?(e1+e2),the controller(16)can make the system states asymptotically stable in limited time.

    Thus,the theorem is proofed completely.

    4 Numerical Simulation

    The chaotic states and dynamical behaviors of the uncontrolled system(6)have been discussed in Ref.[50].This section of the paper presents four illustrative examples to verify and demonstrate the effectiveness of the proposed control scheme.In this paper,the modi fied Adams–Bashforth–Moulton predictor-corrector algorithm[52]is used to solve the numerical simulations in the fractionalorder differential equations with time delay.It should be noticed that the controller is applied att=15 s.Here,some parameters are given to calculate in the system:a=2.5b=?0.5,l=?5,c=1.5,m=?2,andn=?2.

    Case 1Non-commensurate order

    When assuming the different orders of derivatives in state equations(6),i.e.q1/=q2,we get a general noncommensurate order system.The fractional-order delayed memristive chaotic system is chaotic whenq1=0.88 andq2=0.98,which are shown in Fig.2.

    Fig.2 Time-domain diagram and phase diagram of the fractional-order system(6)when q1=0.88,q2=0.98,τ=1.5 without controller.

    Fig.3 Time response of controlled non-commensurate fractional-order system states(The control u(t)is activated at t=15 s).

    In order to satisfy the condition in Theorem 1,we select the gain of the controllerKr=?1 in system(8).To stabilize this system,the control law(16)is applied and the simulation results are depicted in Fig.3.It shows the obtained theoretic results are feasible and efficient for the controlling fractional-order delayed memristive system.

    Case 2Non-commensurate order with uncertainty and an external disturbance

    In this case,the fractional-order delayed memristive chaotic system is perturbed by an uncertainty term Δg(x,y)=0.45sin(πx)cos(πy)and an external disturbanced(t)=0.5sin(πt),where|Δg(x,y)|≤e1=0.45 and|d(t)|≤e2=0.5.The system state responses of the closed-loop system in the presence of the control law(16)are shown in Fig.4 when the gain of the controllerKr=?1,which conforms to the condition of Theorem 2.

    Fig.4 Time response of controlled non-commensurate fractional-order system states in the presence of uncertainty and an external disturbance(The control u(t)is activated at t=15 s).

    Case 3Commensurate order

    When assuming the same orders of derivatives in the state equations(6),i.e.,q1=q2=q,we get a commensurate order system.The system(6)without the controller exhibits a chaotic behavior as shown in Fig.5 with the commensurate orderq=0.99 of the derivatives.

    Fig.5 Time-domain diagram and phase diagram of the fractional-order system(6)when q1=q2=0.99,τ=1.5 without controller.

    To demonstrate the chaotic behaviors,the Largest Lyapunov Exponent(LLE)should be considered.In this paper,the Wolf algorithm is chosen to calculate LLE in this fractional-order delayed memristive chaotic system.It is known that the Max Lyapunov Exponent(MLE)increases from the negative number to zero when periodic cycles appear,and the chaotic dynamics occurs when MLE is positive.By fixing the parameter of the fractional-order(q=0.9)and varying the parameter of the time delay(τ∈[0.4,1.6]),the transitions from one cycle to two cycles,two cycles to four cycles,and four cycles to chaos are observed atτ=1.18,τ=1.27,andτ=1.28.In the interval 0.54<τ<1.18,one cycle is observed.Chaos is observed in the intervalτ>1.28.The bifurcation diagram and the MLE are shown in Fig.6.

    The states of the system(6)under the designed controller(16)are illustrated in Fig.7 whenKr=?1,which shows that the sliding control law guarantees the states reaching the sliding surface and finally stabilization.

    Fig.6 Bifurcation diagram and Max Lyapunov Exponent with q=0.9.

    Fig.7 Time response of controlled commensurate fractional-order system states(The control u(t)is activated at t=15 s).

    Case 4Commensurate order with uncertainty and an external disturbance

    Fig.8 Time response of controlled commensurate fractional-order system states in the presence of uncertainty and an external disturbance(The control u(t)is activated at t=15 s).

    In this case,the fractional-order delayed commensurate system(q=0.99)is perturbed by an uncertainty term Δg(x,y)=0.45sin(πx)cos(πy)and an external disturbanced(t)=0.5sin(πt),where|Δg(x,y)|≤e1=0.45 and|d(t)|≤e2=0.5.The system state responses of the closed-loop system in the presence of the control law(16)are illustrated in Fig.8 whenKr=?1,which satis fies Theorem 2.

    5 Conclusions

    In this paper,a fractional-order delayed memristive chaotic system has been introduced and a fractional-order sliding mode controller is proposed in order to control the chaotic behavior in the system. According to the Lyapunov stability theorem,the control law can asymptotically stabilize the fractional-order delayed memristive chaotic system.The proposed control method is simple,robust and theoretically rigorous,and its performance is satisfactory in the presence of uncertainty and an external disturbance within non-commensurate order system and commensurate order system.It indicates that the sliding mode control has the anti-jamming capability.Finally,numerical simulations present the effectiveness of the control scheme.

    Considering that the current system research is not perfect,these studies tend to be more numerical simulation of the system,and did not develop to realize the hardware circuits.In the future,we should focus on how to construct chaotic hardware circuits with associated delay factors.

    [1]Leon O.Chua,IEEE Trans.Circuit Theory 18(1971)507.

    [2]D.B.Strukov,G.S.Snider,D.R.Stewart,and R.S.Williams,Nature(London)453(2008)80.

    [3]B.Muthuswamy and P.P.Kokate,IETE Tech.Rev.26(2009)417.

    [4]I.Vourkas and G.C.Sirakoulis,IEEE Trans.Nanotechnol.11(2012)1151.

    [5]Makoto Itoh and Leon O.Chua,Inter.J.Bifurcat.Chaos 18(2008)3183.

    [6]Corinto,Fernando,A.Ascoli,and M.Gilli,IEEE Trans.Circuits Syst.I,Reg.Papers 58(2011)1323.

    [7]D.W.Ding,S.J.Li,and N.Wang,Dynamic Analysis of Fractional-Order Memristive Chaotic System,J.Harbin Inst.Tech.(2017);doi:10.11916/j.issn.1005-9113.16136.

    [8]Abbas,Syed,V.S.Erturk,and S.Momani,Signal Process.102(2014)171.

    [9]A.K.Golmankhaneh,R.Are fi,and D.Baleanu,J.Vib.Control.21(2002)85.

    [10]Girejko,Ewa,and E.Pawluszewicz,J.Dynam.Control Syst.(2016)1.

    [11]Kamaljeet and D.Bahuguna,J.Dyn.Control Syst.22(2015)1.

    [12]Xu Beibei,et al.,Nonlinear Dynam.81(2005)19.

    [13]J.G.Lu,Phys.Lett.A 354(2006)301.

    [14]A.K.Golmankhaneh,R.Are fi,and D.Baleanu,Adv.Math.Phys.2013(2013)84.

    [15]C.Li and G.Chen,Chaos,Solitons and Fractals 22(2004)549.

    [16]J.Cao,C.Ma,H.Xie,and Z.Jiang,J.Computat.Nonlinear Dynam.(2010);doi:10.1115/1.4002092.

    [17]Xu,Yong,Y.Li,and D.Liu,J.Comput.Nonlinear Dynam.9(2014)031015.

    [18]Gui-Quan Sun,et al.,Sci.Rep.5(2015)11246.

    [19]Chang-Jin Xu,Pei-Luan Li,and Yi-Cheng Pang,Commun.Theor.Phys.67(2017)137.

    [20]L.Liu,F.Pan,and D.Xue,Opt.Inter.J.Light Electron Opt.125(2014)7020.

    [21]J.Cao,C.Ma,H.Xie,and Z.Jiang,J.Comput.Nonlinear Dynam.4(2010)1003.

    [22]R.Li,Opt.Int.J.Light Electron Opt.127(2016)6695.

    [23]Z.Wang,X.Huang,and G.Shi,Comput.Math.Appl.62(2011)1531.

    [24]Liping Chen,et al.,J.Comput.Nonlinear Dynam.10(2015).

    [25]G.Velmurugan and R.Rakkiyappan,Nonlinear Dynam.11(2015)1.

    [26]A.Babakhani,D.Baleanu,and R.Khanbabaie,Nonlinear Dynam.69(2012)721.

    [27]M.Xiao,W.X.Zheng,and J.Cao,IEEE Trans.Neur.Net.Lear.Syst.24(2012)118.

    [28]A.Y.T.Leung,H.X.Yang,and P.Zhu,Commun.Nonlinear Sci.19(2014)1142.

    [29]Chengdai Huang,J.Cao,and Z.Ma,Inter.J.Syst.Sci.47(2015)1.

    [30]Baleanu,Dumitru,et al.,Commun.Nonlinear Sci.25(2015)41.

    [31]G.C.Wu and D.Baleanu,Nonlinear Dynam.80(2015)1697.

    [32]W.Hu,D.Ding,Y.Zhang,N.Wang,and D.Liang,Optik 130(2017)189.

    [33]S.K.Agrawal,M.Srivastava,and S.Das,Chaos,Solitons&Fractals 45(2012)628.

    [34]H.Xi,S.Yu,R.Zhang,et al.,Opt.Inter.J.Light Electron Opt.125(2014)2036.

    [35]S.Kuntanapreeda,Nonlinear Dynam.84(2016)2505.

    [36]Kocamaz,Ugur Erkin,Y.Uyaroglu,and S.Vaidyanathan,Advances and Applications in Chaotic Systems,Springer International Publishing,Berlin(2016).

    [37]A.Boulkroune,A.Bouzeriba,and T.Bouden,Neurocomputing 173(2016)606.

    [38]Jun-Jun Liu,Xin Chen,and Jun-Min Wang,J.Dynam.Control Syst.22(2016)117.

    [39]Bao-Zhu Guo,Hua-Cheng Zhou,et al.,J.Dynam.Control Syst.20(2014)539.

    [40]B.Jiang,P.Shi,and Z.Mao,Circ.Syst.Signal Process.30(2011)1.

    [41]Z.Gao,B.Jiang,P.Shi,et al.,J.Franklin Inst.349(2012)1543.

    [42]L.Gao,Z.Wang,K.Zhou,et al.,Neurocomputing 166(2015)53.

    [43]Dasgupta Tanmoy,P.Paral,and S.Bhattacharya,Int.Conference Comput.Commun.Inform.IEEE(2015)pp.1-6.

    [44]S.Shao,M.Chen,and X.Yan,Nonlinear Dynam.83(2016)1855.

    [45]M.Zak,Phys.Lett.A 133(1988)18.

    [46]S.Mobayen,Nonlinear Dynam.82(2015)599.

    [47]Di-Yi Chen,Yu-Xiao Liu,and Xiao-Yi Ma,Nonlinear Dynam.67(2011)893.

    [48]Sundarapandian Vaidyanathan and Sivaperumal Sampath,Inter.J.Automat.Comput.9(2012)274.

    [49]I.Podlubny,Math.Sci.Eng.(1999).

    [50]W.Hu,D.Ding,and N.Wang,J.Comput.Nonlinear Dynam.12(2017)0410031.

    [51]Dadras Sara and H.R.Momeni,Phys.A Stat.Mech.Appl.389(2010)2434.

    [52]S.Bhalekar and V.Daftardar-Gejji,Fract.Calc.Appl.Anal.1(2011)1.

    猜你喜歡
    陳輝
    革命烈士和詩人陳輝
    Superconductivity and unconventional density waves in vanadium-based kagome materials AV3Sb5
    “購物式”相親不可取
    Kinetic theory of Jeans’gravitational instability in millicharged dark matter system
    Robustness of the unidirectional stripe order in the kagome superconductor CsV3Sb5
    要想腸胃功能好 按摩中脘不可少
    保健與生活(2022年8期)2022-04-08 21:48:33
    Edge-and strain-induced band bending in bilayer-monolayer Pb2Se3 heterostructures*
    Second-order interference of two independent photons with different spectra?
    真誠的道歉
    民間文學(2019年12期)2019-05-26 14:12:45
    見者發(fā)財
    一本—道久久a久久精品蜜桃钙片| 精品一区二区三区av网在线观看 | 两人在一起打扑克的视频| 男男h啪啪无遮挡| 国产一级毛片在线| 国产99久久九九免费精品| 婷婷色av中文字幕| 欧美成狂野欧美在线观看| 国产精品1区2区在线观看. | 日韩欧美免费精品| 亚洲成人手机| 国产成人精品在线电影| 久久人人爽av亚洲精品天堂| a级片在线免费高清观看视频| 午夜激情久久久久久久| 啦啦啦免费观看视频1| 自拍欧美九色日韩亚洲蝌蚪91| av线在线观看网站| 欧美日韩一级在线毛片| 老汉色∧v一级毛片| 亚洲激情五月婷婷啪啪| 一级黄色大片毛片| 又大又爽又粗| 久久人人爽人人片av| 汤姆久久久久久久影院中文字幕| 精品福利观看| 久久天躁狠狠躁夜夜2o2o| 久久人人爽人人片av| 亚洲熟女精品中文字幕| 飞空精品影院首页| 大香蕉久久成人网| 性色av一级| 女警被强在线播放| 久久久国产欧美日韩av| 婷婷丁香在线五月| 久热这里只有精品99| 正在播放国产对白刺激| 欧美黑人欧美精品刺激| 啦啦啦在线免费观看视频4| 19禁男女啪啪无遮挡网站| 一区二区三区乱码不卡18| 一个人免费看片子| 日韩中文字幕视频在线看片| 欧美97在线视频| 男女国产视频网站| 亚洲国产精品999| 国精品久久久久久国模美| 亚洲精品国产精品久久久不卡| 在线观看免费高清a一片| 天堂中文最新版在线下载| 97人妻天天添夜夜摸| 国产精品偷伦视频观看了| 老司机靠b影院| 日本撒尿小便嘘嘘汇集6| 国产xxxxx性猛交| 黑人猛操日本美女一级片| 午夜福利,免费看| 99国产精品99久久久久| 黄频高清免费视频| 亚洲欧美激情在线| 视频区图区小说| 一个人免费看片子| 国产人伦9x9x在线观看| 日韩,欧美,国产一区二区三区| av国产精品久久久久影院| 肉色欧美久久久久久久蜜桃| 色老头精品视频在线观看| tocl精华| 久久国产精品男人的天堂亚洲| 久久久精品94久久精品| 久久精品成人免费网站| 亚洲九九香蕉| 国产精品久久久人人做人人爽| 老熟女久久久| 亚洲专区国产一区二区| 999久久久精品免费观看国产| 国产成人欧美| 黄色a级毛片大全视频| 又大又爽又粗| 男人添女人高潮全过程视频| 亚洲精品久久午夜乱码| 狠狠狠狠99中文字幕| 国产高清视频在线播放一区 | 久热爱精品视频在线9| 亚洲伊人久久精品综合| 久久天堂一区二区三区四区| 亚洲av片天天在线观看| tocl精华| av又黄又爽大尺度在线免费看| 后天国语完整版免费观看| 天堂中文最新版在线下载| 国产三级黄色录像| 一区福利在线观看| 精品亚洲乱码少妇综合久久| 久久精品国产a三级三级三级| 成人影院久久| 成人免费观看视频高清| 久久人人爽人人片av| 国产男人的电影天堂91| 一二三四社区在线视频社区8| 欧美精品啪啪一区二区三区 | 欧美黄色淫秽网站| 国产三级黄色录像| 麻豆乱淫一区二区| 亚洲国产欧美在线一区| 一二三四社区在线视频社区8| 国产精品久久久久久精品电影小说| 一区在线观看完整版| 男女无遮挡免费网站观看| av国产精品久久久久影院| 视频在线观看一区二区三区| 国产在线一区二区三区精| 国产日韩一区二区三区精品不卡| 成人亚洲精品一区在线观看| 另类精品久久| 久久久久国产精品人妻一区二区| 欧美日韩成人在线一区二区| 亚洲国产看品久久| 日韩免费高清中文字幕av| 最黄视频免费看| 国产欧美日韩一区二区三 | 97人妻天天添夜夜摸| 一本—道久久a久久精品蜜桃钙片| 亚洲精品美女久久av网站| 99热全是精品| 成人三级做爰电影| 久久精品人人爽人人爽视色| 丰满饥渴人妻一区二区三| 人妻久久中文字幕网| 老司机影院毛片| 亚洲精品在线美女| 午夜久久久在线观看| 天堂中文最新版在线下载| 99久久人妻综合| 啦啦啦视频在线资源免费观看| 国产黄色免费在线视频| 一个人免费看片子| 黑人操中国人逼视频| 久久久国产一区二区| 美女扒开内裤让男人捅视频| 99精国产麻豆久久婷婷| 亚洲 国产 在线| 啦啦啦视频在线资源免费观看| 两性夫妻黄色片| 亚洲第一青青草原| 亚洲专区国产一区二区| 亚洲欧洲日产国产| 国产免费福利视频在线观看| 一个人免费看片子| 一本久久精品| 女人精品久久久久毛片| 最近中文字幕2019免费版| 天天躁夜夜躁狠狠躁躁| 日日摸夜夜添夜夜添小说| 后天国语完整版免费观看| 日本精品一区二区三区蜜桃| 国产亚洲一区二区精品| 伦理电影免费视频| 色精品久久人妻99蜜桃| 精品一品国产午夜福利视频| av不卡在线播放| 18禁裸乳无遮挡动漫免费视频| 成人亚洲精品一区在线观看| 黑人巨大精品欧美一区二区蜜桃| 一级毛片精品| 免费在线观看黄色视频的| 中文字幕人妻丝袜一区二区| 亚洲熟女毛片儿| 国产日韩一区二区三区精品不卡| 18在线观看网站| 人人妻人人爽人人添夜夜欢视频| 性色av一级| 脱女人内裤的视频| 黄色片一级片一级黄色片| 国产一区二区激情短视频 | 中文字幕人妻丝袜制服| 99久久人妻综合| 国产在视频线精品| 久久人人爽人人片av| 国产一级毛片在线| 999久久久国产精品视频| 飞空精品影院首页| 久久久久久久国产电影| 亚洲伊人色综图| 在线十欧美十亚洲十日本专区| 欧美国产精品一级二级三级| 亚洲美女黄色视频免费看| 午夜福利免费观看在线| 乱人伦中国视频| 老司机影院成人| 国产精品一区二区在线不卡| 亚洲五月婷婷丁香| 老汉色av国产亚洲站长工具| 不卡av一区二区三区| 亚洲av男天堂| 中文字幕最新亚洲高清| 国产99久久九九免费精品| 欧美日韩国产mv在线观看视频| av电影中文网址| 亚洲一区中文字幕在线| a级毛片黄视频| 日韩 亚洲 欧美在线| 涩涩av久久男人的天堂| 亚洲精品成人av观看孕妇| xxxhd国产人妻xxx| 18禁裸乳无遮挡动漫免费视频| 中亚洲国语对白在线视频| 国产在线免费精品| 巨乳人妻的诱惑在线观看| 又紧又爽又黄一区二区| 久久综合国产亚洲精品| 久久精品久久久久久噜噜老黄| 国内毛片毛片毛片毛片毛片| 欧美午夜高清在线| 久久久久久人人人人人| 午夜福利影视在线免费观看| 久久久精品94久久精品| 国产欧美日韩综合在线一区二区| 国产有黄有色有爽视频| 国产不卡av网站在线观看| 久久人人97超碰香蕉20202| 色老头精品视频在线观看| 黄色a级毛片大全视频| e午夜精品久久久久久久| 久久精品成人免费网站| 黄色视频不卡| 亚洲精品一卡2卡三卡4卡5卡 | 国产精品偷伦视频观看了| 91成年电影在线观看| 久热这里只有精品99| 久久人人97超碰香蕉20202| 亚洲国产精品成人久久小说| 看免费av毛片| 97精品久久久久久久久久精品| 在线av久久热| 亚洲激情五月婷婷啪啪| 91成年电影在线观看| 少妇被粗大的猛进出69影院| 18禁观看日本| 曰老女人黄片| 99国产精品99久久久久| 夫妻午夜视频| 老司机午夜十八禁免费视频| 母亲3免费完整高清在线观看| 五月开心婷婷网| 青春草视频在线免费观看| 中文字幕制服av| 国产精品一区二区精品视频观看| 脱女人内裤的视频| 亚洲欧洲日产国产| 日本vs欧美在线观看视频| 中亚洲国语对白在线视频| 日韩视频一区二区在线观看| 欧美激情 高清一区二区三区| 老熟女久久久| 亚洲精品在线美女| 色老头精品视频在线观看| 啦啦啦视频在线资源免费观看| 亚洲欧洲日产国产| 桃花免费在线播放| 一区在线观看完整版| 老鸭窝网址在线观看| 俄罗斯特黄特色一大片| 在线精品无人区一区二区三| 男女无遮挡免费网站观看| av线在线观看网站| 亚洲精品中文字幕在线视频| 午夜激情av网站| 亚洲欧美清纯卡通| 色视频在线一区二区三区| 成人三级做爰电影| 亚洲伊人久久精品综合| 国产欧美日韩一区二区精品| cao死你这个sao货| www.av在线官网国产| av视频免费观看在线观看| 国产精品影院久久| 一级黄色大片毛片| 久久久久网色| 一区二区三区乱码不卡18| 丁香六月欧美| 国产老妇伦熟女老妇高清| 久久99热这里只频精品6学生| 欧美日韩亚洲国产一区二区在线观看 | 精品国产一区二区三区四区第35| 欧美 日韩 精品 国产| 欧美成人午夜精品| 九色亚洲精品在线播放| 我要看黄色一级片免费的| 日日摸夜夜添夜夜添小说| 人人妻人人添人人爽欧美一区卜| 欧美另类亚洲清纯唯美| av片东京热男人的天堂| 69精品国产乱码久久久| 最新的欧美精品一区二区| 欧美久久黑人一区二区| 国产精品久久久久久精品电影小说| 久久久久久久大尺度免费视频| 美女中出高潮动态图| 19禁男女啪啪无遮挡网站| 久久免费观看电影| 婷婷丁香在线五月| 一级片'在线观看视频| 可以免费在线观看a视频的电影网站| 99久久精品国产亚洲精品| 操出白浆在线播放| 精品熟女少妇八av免费久了| 别揉我奶头~嗯~啊~动态视频 | 国产成人a∨麻豆精品| 国产99久久九九免费精品| 黄色怎么调成土黄色| 久久国产精品人妻蜜桃| 国产日韩一区二区三区精品不卡| 久久久精品94久久精品| 亚洲国产精品成人久久小说| 久久av网站| 久久天躁狠狠躁夜夜2o2o| 亚洲第一欧美日韩一区二区三区 | 日本a在线网址| 男女下面插进去视频免费观看| 黄色视频,在线免费观看| 国产有黄有色有爽视频| 天堂中文最新版在线下载| 亚洲国产精品一区二区三区在线| 精品免费久久久久久久清纯 | 成人三级做爰电影| 亚洲avbb在线观看| 男女国产视频网站| 青春草亚洲视频在线观看| 亚洲情色 制服丝袜| 黄片播放在线免费| 黄色a级毛片大全视频| av在线播放精品| 精品少妇内射三级| 大片免费播放器 马上看| 天天躁日日躁夜夜躁夜夜| 国产成+人综合+亚洲专区| 亚洲va日本ⅴa欧美va伊人久久 | 热re99久久精品国产66热6| 999精品在线视频| 国产一级毛片在线| 久久久久久久国产电影| 十八禁高潮呻吟视频| tube8黄色片| 国产xxxxx性猛交| 国产精品国产av在线观看| 日本精品一区二区三区蜜桃| 大香蕉久久网| 欧美日韩亚洲综合一区二区三区_| 欧美日韩亚洲综合一区二区三区_| 日本a在线网址| 母亲3免费完整高清在线观看| 最新的欧美精品一区二区| 亚洲天堂av无毛| 国产成人一区二区三区免费视频网站| 99久久国产精品久久久| 性少妇av在线| 日本猛色少妇xxxxx猛交久久| av一本久久久久| av在线播放精品| 一本久久精品| 九色亚洲精品在线播放| 999久久久精品免费观看国产| 天天躁夜夜躁狠狠躁躁| 国产精品久久久av美女十八| 日韩欧美一区二区三区在线观看 | 宅男免费午夜| 女人久久www免费人成看片| 国产伦人伦偷精品视频| 亚洲av国产av综合av卡| 欧美日韩福利视频一区二区| 国产精品亚洲av一区麻豆| 多毛熟女@视频| 免费在线观看日本一区| 午夜激情久久久久久久| 欧美另类一区| 国产成人免费无遮挡视频| 午夜福利影视在线免费观看| 久久国产精品影院| 亚洲全国av大片| 精品视频人人做人人爽| 日本黄色日本黄色录像| 男女之事视频高清在线观看| 中亚洲国语对白在线视频| 99热国产这里只有精品6| 色综合欧美亚洲国产小说| 91老司机精品| 99国产精品一区二区三区| 精品少妇一区二区三区视频日本电影| 美女视频免费永久观看网站| 精品人妻1区二区| 久久精品aⅴ一区二区三区四区| 蜜桃在线观看..| 国产精品自产拍在线观看55亚洲 | 777米奇影视久久| 高清在线国产一区| 欧美日韩国产mv在线观看视频| 狂野欧美激情性bbbbbb| 三上悠亚av全集在线观看| 日韩 欧美 亚洲 中文字幕| 精品人妻熟女毛片av久久网站| 国产亚洲精品久久久久5区| 青草久久国产| 成人国语在线视频| 亚洲av电影在线观看一区二区三区| 黑人操中国人逼视频| 亚洲成人免费电影在线观看| 久久久国产欧美日韩av| 亚洲精品美女久久久久99蜜臀| 国产伦人伦偷精品视频| 麻豆国产av国片精品| 2018国产大陆天天弄谢| 在线观看免费高清a一片| 一级黄色大片毛片| 日本91视频免费播放| 精品乱码久久久久久99久播| 欧美xxⅹ黑人| bbb黄色大片| 成人18禁高潮啪啪吃奶动态图| 天天躁日日躁夜夜躁夜夜| 老汉色∧v一级毛片| 精品人妻在线不人妻| 午夜福利免费观看在线| 国产精品偷伦视频观看了| 亚洲综合色网址| 色播在线永久视频| 欧美亚洲日本最大视频资源| 日韩欧美一区视频在线观看| 日本av免费视频播放| 欧美国产精品va在线观看不卡| 91精品三级在线观看| 一级毛片电影观看| 日韩免费高清中文字幕av| 久久久久久人人人人人| 亚洲九九香蕉| av国产精品久久久久影院| av在线app专区| 丝袜美腿诱惑在线| 中文精品一卡2卡3卡4更新| 黄色视频在线播放观看不卡| 亚洲成人国产一区在线观看| 后天国语完整版免费观看| 欧美性长视频在线观看| 久久久国产欧美日韩av| 人人妻人人澡人人爽人人夜夜| 大香蕉久久成人网| 正在播放国产对白刺激| 欧美日韩精品网址| 青春草视频在线免费观看| 狠狠婷婷综合久久久久久88av| 热99re8久久精品国产| 一级毛片精品| 午夜视频精品福利| 亚洲精品美女久久久久99蜜臀| 在线十欧美十亚洲十日本专区| 蜜桃在线观看..| 日韩有码中文字幕| 午夜精品国产一区二区电影| 后天国语完整版免费观看| 欧美日韩黄片免| 最新的欧美精品一区二区| 欧美日韩精品网址| 精品福利永久在线观看| 精品卡一卡二卡四卡免费| 亚洲国产日韩一区二区| 91老司机精品| 国产伦理片在线播放av一区| 黄片大片在线免费观看| 男女下面插进去视频免费观看| 国产激情久久老熟女| 啦啦啦免费观看视频1| 亚洲成国产人片在线观看| 无限看片的www在线观看| 涩涩av久久男人的天堂| 大陆偷拍与自拍| 国产成人啪精品午夜网站| 欧美av亚洲av综合av国产av| 嫁个100分男人电影在线观看| 一本大道久久a久久精品| 在线永久观看黄色视频| 亚洲天堂av无毛| 成年人午夜在线观看视频| 国产伦理片在线播放av一区| 99久久精品国产亚洲精品| 侵犯人妻中文字幕一二三四区| 精品人妻熟女毛片av久久网站| 久久久久国产一级毛片高清牌| 999精品在线视频| 美女脱内裤让男人舔精品视频| 香蕉国产在线看| 男女无遮挡免费网站观看| 人成视频在线观看免费观看| 99香蕉大伊视频| 高潮久久久久久久久久久不卡| 飞空精品影院首页| 91成年电影在线观看| 18禁裸乳无遮挡动漫免费视频| 欧美精品啪啪一区二区三区 | 国产精品影院久久| 日韩欧美免费精品| 国产男女内射视频| 午夜两性在线视频| 成年人免费黄色播放视频| 精品国产乱码久久久久久小说| 国产免费视频播放在线视频| 欧美日韩亚洲高清精品| videosex国产| 国产成人av教育| 免费一级毛片在线播放高清视频 | 岛国毛片在线播放| e午夜精品久久久久久久| 男人爽女人下面视频在线观看| 国产主播在线观看一区二区| 在线观看免费日韩欧美大片| 亚洲欧美日韩高清在线视频 | av不卡在线播放| 午夜福利一区二区在线看| 亚洲人成电影观看| 国产成人免费无遮挡视频| 丝袜喷水一区| av网站免费在线观看视频| 久久热在线av| 好男人电影高清在线观看| 天堂中文最新版在线下载| 正在播放国产对白刺激| 女人被躁到高潮嗷嗷叫费观| 91av网站免费观看| www.精华液| 不卡一级毛片| 精品国产一区二区三区久久久樱花| 色综合欧美亚洲国产小说| 日韩中文字幕欧美一区二区| 视频区欧美日本亚洲| 高清av免费在线| 蜜桃国产av成人99| 久久人妻福利社区极品人妻图片| 免费av中文字幕在线| 国产高清视频在线播放一区 | 欧美大码av| 久久久久久人人人人人| 亚洲精品中文字幕一二三四区 | 69精品国产乱码久久久| 高清欧美精品videossex| 黄片小视频在线播放| 三级毛片av免费| 亚洲欧美精品综合一区二区三区| 欧美黑人欧美精品刺激| 极品人妻少妇av视频| 久热爱精品视频在线9| 午夜福利免费观看在线| 午夜成年电影在线免费观看| 亚洲全国av大片| 久久免费观看电影| 男男h啪啪无遮挡| 在线永久观看黄色视频| 菩萨蛮人人尽说江南好唐韦庄| 精品福利观看| 久久女婷五月综合色啪小说| 高清在线国产一区| av在线app专区| 国产色视频综合| 五月天丁香电影| 女人久久www免费人成看片| www.精华液| 午夜免费成人在线视频| 国产精品偷伦视频观看了| 亚洲自偷自拍图片 自拍| 国产欧美日韩精品亚洲av| 人妻久久中文字幕网| 亚洲 国产 在线| 欧美日韩成人在线一区二区| 又黄又粗又硬又大视频| 啦啦啦 在线观看视频| 久久久精品94久久精品| 涩涩av久久男人的天堂| 后天国语完整版免费观看| 曰老女人黄片| 亚洲性夜色夜夜综合| 国产成人av激情在线播放| 男人添女人高潮全过程视频| bbb黄色大片| 热re99久久精品国产66热6| 69av精品久久久久久 | 精品久久蜜臀av无| 好男人电影高清在线观看| 亚洲精品久久久久久婷婷小说| 国产成+人综合+亚洲专区| 国产三级黄色录像| 丰满迷人的少妇在线观看| 亚洲国产看品久久| 亚洲av男天堂| 国产欧美日韩一区二区三区在线| 亚洲一区二区三区欧美精品| 欧美 亚洲 国产 日韩一| videosex国产| 脱女人内裤的视频| 国产91精品成人一区二区三区 | 久久免费观看电影| 在线十欧美十亚洲十日本专区| 视频区欧美日本亚洲| 看免费av毛片| 免费在线观看完整版高清| 国产亚洲午夜精品一区二区久久| 老熟女久久久| 欧美日韩福利视频一区二区| 国产精品一二三区在线看| av超薄肉色丝袜交足视频| 色婷婷久久久亚洲欧美| 亚洲九九香蕉| 99久久99久久久精品蜜桃| 亚洲中文av在线| 日日夜夜操网爽| www.999成人在线观看| 久久国产精品人妻蜜桃| 热99久久久久精品小说推荐|