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Trong bài báo này, điều khiển kiểu trượt cho những công trình xây dựng sử dụng bộ giảm xóc MR (Magnetorheological) được đề xuất cho việc giảm rung của tòa nhàkhi có động. Đầu tiên, hệ thống điều khiển kiểu trượt gián tiếp cho những cấu trúc xây dựng được thiết kế. Tuy nhiên, để giải quyết vấn đề phi tuyến được tạo ra bởi điều khiển gián tiếp, một luật thích nghi cho điều khiển kiểu trượt được áp dụng để tính toán sự bền vững của bộ điều khiển này. Tiếp theo, bộ điều khiển kiểu trượt thích nghi được tính toán cho sự ổn định của hệ thống dựa vào lý thuyết Lyapunov. Cuối cùng, những kết quả mô phỏng cho thấy sự hiệu quả của bộ điều kiển kiến nghị.
Science & Technology Development, Vol 14, No.K4- 2011 ADAPTIVE SLIDING MODE CONTROL FOR BUILDING STRUCTURES USING MAGNETORHEOLOGICAL DAMPERS Nguyen Thanh Hai(1), Duong Hoai Nghia(2), Lam Quang Chuyen(3) (1) International University, VNU-HCM (2) University of Technology, VNU-HCM (3) Ho Chi Minh Industries and Trade College (Manuscript Received on December 14th 2010, Manuscript Revised August 17th 2011) ABSTRACT: The adaptive sliding mode control for civil structures using Magnetorheological (MR) dampers is proposed for reducing the vibration of the building in this paper Firstly, the indirect sliding mode control of the structures using these MR dampers is designed Therefore, in order to solve the nonlinear problem generated by the indirect control, an adaptive law for sliding mode control (SMC) is applied to take into account the controller robustness Secondly, the adaptive SMC is calculated for the stability of the system based on the Lyapunov theory Finally, simulation results are shown to demonstrate the effectiveness of the proposed controller Keywords: MR damper; structural control; SMC; adaptive SMC INTRODUCTION Bingham visco-plastic model [9, 10], the BoucWen model [11], the modified Bouc-Wen Earthquake is one of the several disasters which can occur anywhere in the world There are a lot of damages to, such as, infrastructures and buildings This problem has attracted many engineers and researchers to investigate and develop effective approaches to eliminate the losses [1, 2, 3] One of the approaches to reduce structural responses against earthquake is to use a MR damper as a semi-active device in building control [4-5] The MR damper is made up of tiny magnetizable particles which are immersed in a carrier fluid and the application of a magnetic field aligns the particles in chain-like structures [6, 7] The modelling of the MR damper was introduced in [8], and there are many types of MR damper models such as the Trang 92 model [12] and many others In addition, a MR damper model based on an algebraic expression for the damper characteristics is used in the system to reduce the controller complexity [13] Variable structure system or SMC theory is properly introduced for the structural certainties, such as, seismic-excitation linear structures, non-linear plants or hysteresis [14, 15, 16] A dynamic output feedback control approach using SMC theory and either the method of LQR or pole assignment control for the building structure was used [17, 18] Application of SMC theory for the building structures was also found [19] According to characteristics of MR dampers, SMC are applied for the building structure [20] TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 14, SOÁ K4 - 2011 For the control effectiveness of the model, and modified Bouc-Wen model systems, it is tackled in this work by means of However, the MR damper model proposed here an adaptive control motivated by the work in has the simple mathematic equations for adaptive control or adaptive SMC [21, 22, 23, application in structural control as shown in 24] In this paper, an adaptive law is chosen to Fig 1, [9] The equations of the MR damper apply to SMC such that the nonlinear system is [13] are presented as follows: robust and stable on the sliding surface In addition, the stability of the system is proven based on the Lyapunov function The paper is organized as follows In section 2, the MR damper is described In section 3, the indirect control of a building structure model is presented with the equation f = cx& + kx + αz + f , (1a) z = (βx& + δsign(x)), (1b) c = c1i + c0 = 3.32i + 0.78, (1c) k = k1i + k0 = −i + 3.97 , (1d) α = α2i + α1i + α0 = −264i + 939.73i + 45.86 , (1e) of motion consisting of nonlinear inputs and disturbances A SMC algorithm is applied to δ = δ1i + δ0 = 0.44i + 0.48, design the control forces in Section An f = h1i + h0 = −18.21i − 256.50, (1g) adaptive SMC is proposed in the system in where i is the input current to the MR Section In section 6, results of numerical simulation for the system with MR dampers are (1f) damper, f is the output force, z is the f is the damper force illustrated Finally, section concludes the hysteresis function, paper offset, β = 0.09 is a constant against the MAGNETORHEOLOGICAL DAMPER supplied current values, α is the scaling parameter and There are many kinds of MR damper c, k are the viscous and stiffness coefficients models such as Bingham model, Bouc-Wen hysteresis spring k0 damping force dashpot c0 displacement Fig Schematic of the MR damper Trang 93 Science & Technology Development, Vol 14, No.K4- 2011 CONTROL OF earthquake && xg (t ) , the responses to be regulated BUILDING STRUCTURE are the displacements, velocities, and accelerations ( x, x& , &x& ) of the structure, where Consider the civil structure with n-storey x is the displacement of the floors The subjected to earthquake excitation && xg (t ) as controller with the current driver will excite the shown in Fig Assume that a control system MR dampers and the forces f will be generated installed at the structure consists of MR to eliminate the vibration of the structure The dampers, controller and current driver When the structure is influenced by output y is an r-dimensional vector the Disturbanc x, x& MR i + f − Current − y Buildin u + Controll Fig The sliding mode control The vector equation of motion [2] is matrix denoting the location of r controllers presented by and Λ ∈ R n is a vector denoting the influence &&(t ) + Cx& (t ) + Kx(t ) = Γf (t ) + MΛ&& Mx xg (t ), (2) of the earthquake excitation in Equation (2) can be rewritten in the state- which x(t ) = [ x1 x2 , , xn ]T , x(t ) ∈ R n is space form as follows: an n z& (t ) = Az (t ) + B 0f (t ) + E0 (t ) , vector of the displacement, f (t ) ∈ R is a vector r where consisting of the control forces, && xg (t ) is an vector, A ∈ R nx n is earthquake excitation acceleration, parameters M∈R nxn , C∈ R nxn , K∈R nxn z (t ) ∈ R n is E0 (t ) ∈ R n damping and stiffness matrices Γ ∈ R nxr is a is a a gain I 0 , B = −1 , E0 (t ) = && xg (t ) −1 −M C M Γ Λ (4) From Eq (1), we can rewrite the equation of the MR damper as follows: f = ( c x& + k x + h ) i + ( c = B i + D , Trang 94 x& + k x + h ) + α z (5) state system matrix disturbance respectively, given by x z (t ) = , A = −1 x& −M K a a matrix, B ∈ R nxr is are the mass, (3) and vector, TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 14, SOÁ K4 - 2011 B = (c1 x& + k1 x + h1 ) and where D = (c0 x& + k0 x + h0 ) + α z are non-linear Assume that each MR damper can be installed at each floor of the structure, we can rewrite functions Assume that the MR dampers are installed (6) f = B* ( x ) i + D0 , (10) ˆ is definite and invertible and is matrix Β (7) defined as where f = [ f1 , f , , f r ]T is a force vector, a current 0 Bˆ = ˆ Brr vector, D0 = [ D1 ( x), D2 ( x), , Dr ( x)]T can be known as a disturbance vector and B ( x) ∈ R * rxr is an gain nonlinear function (11) SLIDING MODE CONTROL The main advantage of the SMC is known to be robust against variations in system Substitution of Eq (7) into Eq (3) leads to parameters or external disturbance The selection of the control gain ηa is related to the the following Az = B [B* ( x)i + D0 ( x)] + E0 (8) magnitude of uncertainty to keep the trajectory where x and t has been dropped for clarity The state equation can be rewritten as on the sliding surface In the design of the sliding surface, the external disturbance are neglected, however it follows z& = Az + Bi + E, where diagonal B are all known as Bˆ jj , j = 1, 2, , r The The force equation can be rewritten as is with Assumption: the bounds of the elements of f j = B j ( x)i j + D j ( x), j = 1, 2, , r i = [i1 , i2 , , ir ] B 0 B= b rr vibration, the equations of the MR dampers can T matrix elements B jj , j = 1, 2, , r as at floors of the structure to eliminate its be rewritten as follows the is taken into account in the design of (9) B = B0B , * B ( x) ∈ R * controllers For simplicity, let σ = be an r nxr is an dimensional sliding surface consisting of a unknown gain matrix and E = B D0 + E0 is linear combination of state variables, the p =ρ, defined as not exactly known, but estimated as E the vector norm E p is p E p p = ∑ ei , p = 1, 2, i surface [14] is expressed as σ = Sz, (12a) taking derivative of the function σ , we obtain as σ& = Sz& , (12b) Trang 95 Science & Technology Development, Vol 14, No.K4- 2011 in which σ ∈ R r is a vector consisting of r V = σ , (16a) sliding variables, σ ,σ , , σ r and S ∈ R rx2n is taking derivative of the Lyapunov function, a matrix to be determined such that the motion we obtain on the sliding surface is stable V& = σ T σ& (16b) In the case of a full state feedback, either the method of LQR or pole assignment will be used to design the controllers The design of Substitution of Eqs (9) and (12b) into Eq (16b) leads to the following the sliding surface is obtained by minimizing V& = σ T σ& = σ T S( Az + Bi + E), (17) the integral of the quadratic function of the in which E can be neglected in designing state vector The SMC output i consists of two the equivalent controller For V& = σ T σ& = , we can rewrite Eq (17) as components as i = i e + i s , (13) σ T S( Az + Bi e ) = 0, (18) where i e , i s are the equivalent control according to the above Assumption, the output and the switching control output, ˆ can be matrix B is unknown, its estimation B respectively used to construct the equivalent controller ˆi e , A cost function [17, 18] is defined as the controller output is presented as follows T J = ∫ z Qzdt , ˆi = −(SB ˆ )−1 SAz e (14) To after determining the cost matrix Q and the LQR gain F in [14, 16], the equivalent the switching controller, according to the Lyapunov condition, the system is stable on the sliding surface if and controller i e will be found as follows i e = −Fz design (19) only if (15) V& < Substitution of Eqs (9), (12b) and (13) into To obtain the design of the controllers, a Eq (16b) leads to the following Lyapunov function is considered V&a = σ T S( Az + Bˆ i + E) = σ T S( Az + Bˆ ˆi e ) + σ T S(Bˆ ˆi s + E) , where ˆˆ ) = σ T S( Az + Bi e equivalent controller The equation is rewritten as Trang 96 is the (20) ˆ ˆ + E) = σ T S(Bi ˆ ˆ + ρ ) (21) V&a = σ T S(Bi s s For V&a < , we can choose the equation as TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 14, SỐ K4 - 2011 ˆ ˆ + ρ ) = −η sign(σ ) , S(Bi s a component i e guarantees the states on the (22a) sliding surface and the nonlinear switched then, the possible switching controller is feedback control component i s is used to depicted by compensate the disturbance The magnitude of ˆi = −(SBˆ ) −1 (η sign(σ ) + Sρ ) (22b) s a The SMC output components i e and i s used involves to ηa > depends on the expected uncertainty in two drive the external excitation or parameter variation the so that the system is stable on the sliding trajectories of the controlled system on the sliding surface The equivalent surface control Disturbance x, x& − + MR damper f Building y Adaptive law i Current driver − + u SMC Fig 3: The adaptive sliding mode control ADAPTIVE SLIDING MODE CONTROL values, as provided by a parameter estimator Thus, a self-tuning controller is a controller, which performs simultaneous identification of As shown in Fig 1, this control system proposed with a parameter estimator is the adaptive controller, which is based on the control parameters There is a mechanism for the unknown plant We now show how to derive an adaptive law to adjust the controller parameters such adjusting these parameters on-line based on that the estimated equivalent control ˆi e can signals in the system In the building structure, optimally approximate the equivalent control of the so-called self-tuning adaptive control the SMC, given the unknown function B We method is proposed as in Fig According to construct the switching control to guarantee the the figure, the sliding mode control is used to system’s stability by the Lyapunov theory so constrain trajectories on the sliding surface so that the that the system is robust and stable onto that accomplished surface With the adaptive SMC, if the plant parameters are not known, it is intuitively ultimately bounded tracking is We choose the control law as follows: i = ˆi e + ˆi s , (23) reasonable to replace them by their estimated Trang 97 Science & Technology Development, Vol 14, No.K4- 2011 We will further determine the adaptive law where i is the SMC output and we use an estimation law to generate the estimated parameter for adjusting those parameters Bˆ as assumed Consider the equation of motion as follows: z& = Az + Bi + E = Az + B(ˆi e + ˆi s ) + E + Bˆ ˆie − Bˆ ˆi e , (24) substitution of Eq (19) into Eq (24) leads to as z& = (B − Bˆ )ˆi e + Biˆs + E (25) % ˆ + Biˆ + E) + (B% γ )T (B&% γ ) V&b = σ T S(Bi e s % ˆ + (B% γ )T (B%& γ ) + σ T S(Biˆ + E) = σ T SBi e s (30) Assume that we have an estimated error The tracking error allows us to choose the function as follows: B% = B − Bˆ (26) adaptive law for the parameter Bˆ as Substituting Eq (26) into Eq (25), we can rewrite the equation of motion as follows: % ˆ + Biˆ + E (27) z& = Bi e s Now, consider the Lyapunov function candidate (31a) From Eq (26), the following relation is used Vb = [σ T σ + (B% γ )T (B% γ )] where & % ˆ γ T (γγ T ) −1 Bˆ = [(B% γ )(B% γ )T ]−1 (B% γ )σ T BSi e γ (28) & B&% = −Bˆ for B& = , we obtain as & % ˆ γ T (γγ T ) −1 B% = −[(B% γ )(B% γ )T ]−1 (B% γ )σ T BSi e is a positive constant gain of the adaptive algorithm Taking the derivative of the Lyapunov function in [17], we can obtain as & V&b = [σ T σ& + (B% γ )T (B% γ )] (29) Substitution of Eqs (12b) and (27) into Eq (29) leads to as follows: (31b) then, the Lyapunov equation is written as follows: V&b = σ T S(Biˆs + E) , according estimation E to p the above ˆ , the = ρ and Assumption B equation can be rewritten as follows: ˆ ˆ + ρ) V&b = σ T S(Bi sb Trang 98 (32a) (32b) TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 14, SỐ K4 - 2011 With the adaptive law in Eq (31), the Consider the structure of a five-storey asymptotic stability of the adaptive sliding building model which has two MR dampers mode control system can be guaranteed installed at the first floor and the second floor Such that V&b < , we can write as follows: ˆ ˆ + ρ ) = −η sign(σ ) , (33a) S(Bi sb b the switching controller can be expressed as follows: as shown in Fig 4, x = [ x1 , x2 , x3 , x4 , x5 ]T is the displacement vector, f1 and f are forces of these damper and parameters mi , ki , ci (i = 1,2, ,5) are mass, damping and stiffness coefficients, respectively ˆi = −(SBˆ ) −1[η sign(σ ) + Sρ ] sb b (33b) The corresponding matrices M , C and K are as follows: The magnitude of ηb > depends on the expected uncertainty in the external disturbance or parameter variation so that the system is stable on the sliding surface Combine Eq (22b) and Eq (33b), we should take η = max{ηa ,ηb } , MR (34) such that the system globally satisfies to be 0 337 330 0 M= 0 330 0 kg , 0 330 0 0 337 −7 225 −157 26 −157 300 −126 25 − Ns C = 26 −126 299 −156 16 , m − 25 − 156 279 − 125 −4 16 −125 125 (35) (36) −234 27 3766 −2869 467 −2869 5149 −2959 446 − 70 kN K = 467 −2959 5233 −2836 280 m − 234 446 − 2836 4763 − 2277 27 280 −2277 2052 −70 stable on the sliding surface SIMULATION RESULTS (37) mi , ci , ki x2 , x&2 , && x2 MR damper f2 x1 , x&1 , && x1 f1 Fixture &x&g Ground Fig The building model with MR dampers Trang 99 Science & Technology Development, Vol 14, No.K4- 2011 &x&2 = A02 + B2 f + E02 The coefficents M, C and K were collected from a 5-storey model at University of = A02 + B2 (h2i2 + D2 ) + E02 Technology, = A02 + B2 h2i2 + B2 D2 + E02 Sydney (UTS) Therefore, = A02 + B2 h2i2 + E2 , according to Equation (2) and (3), when there (39) is an earthquake, the force f will be just where changed in order to reduce the storey displacement While the coefficents M, C and A01 = − m1−1 ((k1 + k ) x1 − k x2 + (c1 + c2 ) x&1 − c2 x& ) K will not change and are often determined based on storey structures For example, if the A02 = −m2−1 ((k1 + k ) x2 − k x1 + (c1 + c2 ) x& − c2 x&1 ) and E1 = B1 D1 + E01 and E2 = B2 D2 + E02 are building structute is storeys, their matrices the first-floor and second-floor disturbances, are as shown in Equations (35), (36) and (37) respectively, in which B1 and B2 are current and if it is a 3-storey building, the coefficents gains M, C and K will be matrices of 3x3 Control parameters are given in Table 1, in Based on Equation (3) and (5), which ρ and γ are the estimated vector norm accelerations &x&1 and &x&2 corresponding to these and the positive constant gain MR dampers installed at the building are &x&1 = A01 + B1 f1 + E01 Table Control parameters = A01 + B1 (h1i1 + D1 ) + E01 (38) = A01 + B1h1i1 + B1 D1 + E01 SMC = A01 + B1h1i1 + E1 , SMC Adaptive SMC ρ ρ γ 650 500 1.5 0.45 [0.1; -0.5] -3 Earthquake: El-Centro x 10 Floor displacement(m) 2 Acc(m/s ) 0.5 -0.5 -1 -2 -3 -4 -1 -5 -6 10 20 30 Time(s) 40 Fig Earthquake record: El-Centro Trang 100 50 60 10 20 30 Time(s) 40 50 60 Fig Floor displacement using SMC-2 MR dampers TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 14, SỐ K4 - 2011 -3 0.01 x 10 0.008 Floor displacement(m) Floor displacement(m) 0.006 0.004 0.002 -0.002 -0.004 -0.006 -2 -4 -6 -0.008 -0.01 -8 10 20 30 Time(s) 40 50 60 Fig Floor displacement-uncontrolled 10 20 30 Time(s) 40 50 60 Fig 10 Floor displacement using ASMC-2 MR dampers -3 First Floor: El-Centro x 10 x 10 Control force(N)- f1 Floor displacement(m) -2 0.5 -0.5 -4 -1 -6 10 20 30 Time(s) 40 50 60 Fig Floor displacement using SMC-1 MR damper 20 30 Time(s) 40 50 60 Fig 11 Control force of MR damper at first-floor -3 10 x 10 Second Floor: El-Centro x 10 Control force(N)- f2 Floor displacement(m) -2 0.5 -0.5 -4 -1 -6 10 20 30 Time(s) 40 50 Fig Floor displacement using ASMC-1 MR damper 60 10 20 30 Time(s) 40 50 60 Fig 12 Control force of MR damper at second-floor Trang 101 Science & Technology Development, Vol 14, No.K4- 2011 Time responses of floor displacements are installed at floor-1 and floor-2 In addition, shown in the Figs 5-12, in which Fig is the Table summarises numerical results of cases El-Centro earthquake record, Fig shows the such as uncontrolled, SMC-1 MR damper, floor displacement without control In Fig ASMC-1 MR damper, in which the SMC-1 and Fig are the floor displacements using MR damper is installed at level-1 and the SMC and adaptive sliding mode control SMC-2 MR damper is of level-2 For (ASMC) methods for one MR damper installed similarity, the ASMC-1 MR damper and the st at the floor, respectively In two cases, the ASMC-2 MR damper can be replaced the floor displacement using the ASMC shows SMC-1 MR damper and the SMC-2 MR better simulation result than that using the damper for the comparison Moreover, the SMC The results of displacements at the different control forces of the first and second second as shown in Fig and Fig 10 using the floors were shown as in Fig 11 and Fig 12 in SMC and the ASMC with MR dampers are order to illustrate that the second floor is less better than that at the first Fig 11 and Fig 12 the displacement than the first floor are control forces f1 , f of the MR dampers Table Floor displacements from different controls Floo r No Uncontrolled SMC-1 damper Max (mm) RMS (mm) Max (mm) RMS (mm) 6.3 9.0 12.0 13.5 13.5 2.2 1.7 2.0 2.2 2.3 3.0 3.8 4.0 5.1 5.1 0.20 0.41 0.38 0.39 0.37 CONCLUSION AND DISCUSSION ASMC-1 damper Max RMS (mm) (mm ) 3.3 0.23 3.4 0.28 3.2 0.27 5.0 0.30 5.0 0.32 SMC-2 dampers Max (mm) RMS (mm) 2.8 3.0 3.3 4.3 4.2 0.40 0.50 0.60 0.60 0.52 ASMC-2 dampers Max RMS (mm) (mm ) 2.5 0.35 3.1 0.45 3.4 0.50 4.2 0.50 4.1 0.47 applying these controllers to a 5-storey model have illustrated the effectiveness of the A sliding mode controller (SMC) has been applied to the control of a building structure using MR dampers installed at each floor A modified controller using adaptive algorithm is proposed for the building structures The stability of the building structure using the adaptive SMC (ASMC) as shown in Fig and Fig 10 is proven based on the Lyapunov function candidate Simulation results when Trang 102 proposed comparison method between In practicular, uncontrolled the and controlled floor displacements as shown in Fig (uncontrolled) and Figs 7-10 (controlled) show that the floors installed with RM dampers using ASMC method will be better than that using SMC method Moreover, Table shows the displacement numbers of the first and second storeys using different cases such as TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 14, SỐ K4 - 2011 uncontrolled, SMC-1 damper, ASMC-1 2, max and RMS values are also shown for the damper, SMC-2 damper and SMC-2 damper, in comparison of the displacements In addition, which amplitudes of controlled methods using numbers show that storeys using ASMC MR SMC damper and ASMC damper are better dampers are more stable than that using SMC than that of uncontrolled method In this Table MR dampers ðIỀU KHIỂN KIỂU TRƯỢT THÍCH NGHI CHO CẤU TRÚC TỊA NHÀ SỬ DỤNG GIẢM XĨC MR Nguyễn Thanh Hải(1), Dương Hoài Nghĩa(2), Lâm Quang Chuyên(3), (1) Trường ðại Học Quốc tế, ðHQG-HCM (2) Trường ðại Học Bách Khoa, ðHQG-HCM (3) Trường Cao ðẳng Cơng Thương, Tp.HCM TĨM TẮT: Trong báo này, ñiều khiển kiểu trượt cho cơng trình xây dựng sử dụng giảm xóc MR (Magnetorheological) ñược ñề xuất cho việc giảm rung tòa nhàkhi có động ðầu tiên, hệ thống điều khiển kiểu trượt gián tiếp cho cấu trúc xây dựng ñược thiết kế Tuy nhiên, ñể giải vấn ñề phi tuyến ñược tạo ñiều khiển gián tiếp, luật thích nghi cho điều khiển kiểu trượt áp dụng để tính tốn bền vững ñiều khiển Tiếp theo, ñiều khiển kiểu trượt thích nghi tính tốn cho ổn định hệ thống dựa vào lý thuyết Lyapunov Cuối cùng, kết mô cho thấy hiệu ñiều kiển kiến nghị REFERENCES Science and Technology Development, Vol 11, Số (2008) [1] Phạm Nhân Hòa, Chu Quốc Thắng, ðánh giá hiệu Của Hệ Cản Ma Sát Biến Thiến Với Cơng Trình Chịu Tải Trọng ðộng ðất, Science and Technology Development, Vol 11, Số 12 (2008) [2] Phạm Nhân Hòa, Chu Quốc Thắng, Các Phương Án Sử Dụng Hệ Cản Ma Sát Biến Thiến Trong Kết Cấu Tầng, [3] Nguyễn Quang Bảo Phúc, Phạm Nhân Hòa, Chu Quốc Thắng, So Sánh Khả Năng Giam Chấn Của Hệ Cản Có ðộ Cứng Thay ðổi Với Hệ Cản Ma Sát Biến Thiến, Science and Technology Development, Vol 12, Số (2009) [4] B F Spenser Jr., S J Dyke, M K Sian and J Phenomenological D Carlson, model for Trang 103 Science & Technology Development, Vol 14, No.K4- 2011 magnetorheological dampers, J of Engineering Mechanics, 230-238 [11] Y K Wen, Method of random vibration of hysteretic systems, Journal of Engineering Mechanics (1997) [5] Nguyễn Minh Hiếu, Chu Quốc Thắng, ðiều Khiển Hệ Cản Bán Chủ ðộng Division, ASCE, Vol 102, 249-263 (1976) RM VớiCác Giải Thuật Khác Nhau [12] S J Dyke, B F Spencer Jr, M K Của Công, Science and Technology Sain and J D Carlson, Modelling and Development, Vol 12, Số (2009) control of magnetorheological Lacis, dampers for seismic J reduction, Smart Material Structure, [6] G Bossis and Magnetorheological S fluids, of Magnetism and Magnetic Materials, response Vol 5, 565-575 (1996) [13] N M Kwok, Q P Ha, T H Nguyen, Vol 252, 224-228 (2002) [7] S L Djajakesukuma, B Samali and J Li and B Samali, A novel hysteretic H Nguyen, Study of a semi-active model for magnetorheological fluid stiffness various dampers and parameter identification earthquake inputs, Earthquake Eng using particle swarm optimization, Structural Dynamics, Vol 31, 1757- Sensors and Actuators A (2006) damper under [14] R A DeCarlo, S H Zak and R A 1776 (2002) [8] T Butz and O von Stryk, Modelling Matthews, Variable structure control and of nonlinear multivariable system: A magnetorheological fluid dampers, tutorial, IEEE, Vol 76, No 3, 212- Applied Mathematics and Mechanics 232 (1988) and simulation of electro- [15] V Utkin, J Guldner, and J Shi, (2002) [9] R Stanway, J L Sproston and N G Sliding Mode Control Stevens, Non-linear identification of electromechanical an and Francis, UK (1999) Electro-rheological vibration systems, in Taylor and [16] C Edwards and S K Spurgeon, System Parameter Estimation, pp Sliding mode control: theory and 195-200 (1985) applications, damper, IFAC Identification [10] R Stanway, J L Sproston and N G Taylor and Francis, London, UK (1998) Stevens, Non-linear modelling of an [17] J N Yang, J C Wu, A K Agrawal electro-rheological vibration damper, and Z Li, Sliding mode control for J Electrostatics, Vol 20, 167-173 seismic-excited linear and nonlinear (1987) civil engineering structures, Technical Report NCEER-94-0017, University Trang 104 TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 14, SỐ K4 - 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ASMC MR SMC damper and ASMC damper are better dampers are more stable than that using SMC than that of uncontrolled method In this Table MR dampers ðIỀU KHIỂN KIỂU TRƯỢT THÍCH NGHI CHO CẤU TRÚC