Position control of a Stewart platform
using inverse dynamics control with
approximate dynamics
Se-Han Lee,Jae-Bok Song *,Woo-Chun Choi,Daehie Hong
Department of Mechanical Engineering,Korea University,5,Anam-dong,Sungbuk-gu,
Seoul 136-701,Korea
Abstract
Con?guration-dependent nonlinear coe?cient matrices in the dynamic equation of a robot manipulator impose computational burden in real-time implementation of tracking control based on the inverse dynamics controller (IDC).However,parallel manipulators such as a Stewart platform have relatively small workspace compared to serial manipulators.Based on the characteristics of small motion range,nonlinear coe?cient matrices can be approximated to constant ones.The modeling errors caused by such approximation are compensated for by H 1controller that treats the error as disturbance.The proposed IDC with approximate dy-namics combined with H 1control shows good tracking performance even for fast tracking control in which computation of full dynamics is not easy to implement.
ó2002Elsevier Science Ltd.All rights reserved.
Keywords:Stewart platform;Inverse dynamics control;H 1control;Approximate inverse dynamics
1.Introduction
Parallel manipulators such as a Stewart platform [1]has some advantages of high rigidity,high accuracy,and high load-carrying capacity over serial manipulators.These manipulators have found a variety of applications in ?ight and vehicle sim-ulators,high-precision machining centers,mining machines,and so on.However,they have some drawbacks of relatively small workspace and di?cult forward ki-nematics problems.
Mechatronics 13(2003)
605–619
*Corresponding author.Tel.:+82-2-3290-3363;fax:+82-2-3290-3757.
E-mail address:jbsong@korea.ac.kr (J.-B.Song).
0957-4158/03/$-see front matter ó2002Elsevier Science Ltd.All rights reserved.
doi:10.1016/S0957-4158(02)00033-8
606S.-H.Lee et al./Mechatronics13(2003)605–619
Generally,forward kinematics of a parallel manipulator is very complicated and di?cult to solve.Liu et al.[2]proposed a numerical algorithm which provided the kinematic solutions based on a set of three nonlinear simultaneous equations.On the other hand,dynamics of a parallel manipulator,which is very important to develop a controller,tends to be very complicated.Most studies on dynamics have been per-formed based on the Lagrangian formulation[3],the Newton–Euler formulation[4] and the principle of virtual work[5].The above-mentioned dynamic equations were accurate by including actuating legs having closed-loop connections to each other in its formulation,but computation of the dynamics was very time-consuming.Even with a high-speed DSP,therefore,real-time calculation was not easy to achieve in the control system.Some literature[3,4]reported simulation-based control analysis which took into account the dynamics of a Stewart platform,but little mention was made regarding the ways of dealing with computational burden in real-time imple-mentation.Fichter[6]assumed that the e?ect of leg inertia was negligible and ob-tained a simple formula for computing actuating forces for a Stewart platform,but su?cient accuracy could not be attained except when the inertia of the load was much larger than that of the actuating leg.In particular,for the case where the platform was used as a tool holder,the e?ect of leg inertia was no longer negligible and thus accurate modeling of dynamics including legs was required for control performance[7].
Parallel manipulators have some drawback of relatively small workspace in comparison with serial manipulators.This characteristic,however,enables the con?guration-dependent coe?cient matrices of the dynamic equations to be ap-proximated to constant ones without introducing large modeling errors.Based on these constant matrices,calculation of the approximated inverse dynamics becomes much simpler than the full inverse dynamics which re?ects every detail varying in time.This approximation may cause some modeling error,and deteriorate tracking performance of the controller based on the inverse dynamics.In this paper,the error caused by such approximation is treated as disturbance,and the H1controller is introduced to cope with this disturbance.Finally,an inverse dynamics controller (IDC)with approximate inverse dynamics combined with the H1controller is proposed as a position controller for a Stewart platform.
This paper presents a brief derivation of the dynamic equations and the ap-proximation process of the Stewart platform under consideration in Section 2. Section3deals with a proposed IDC with approximate dynamics combined with the H1controller.Section4shows the experimental results and compares control per-formance for various controllers including the proposed one.
2.Dynamic equations of a Stewart platform
In this section,the dynamic equations of a Stewart platform under consideration is brie?y derived based on the Newton–Euler approach,and its characteristics are investigated.
S.-H.Lee et al./Mechatronics13(2003)605–619607
2.1.Derivation of dynamic equations
A Stewart platform shown in Fig.1consists of a moving platform,a?xed base, and six actuating legs connecting the platform to the base.The lower?xed part of an actuating leg is connected to the base through a universal joint,while the upper moving part is connected to the platform through a spherical joint.Two actuating legs are connected together to form a spherical joint as shown in Fig.2.The moving platform frame xyz and the?xed base reference frame XYZ are attached to the platform center and the base center,respectively.Force vectors actuating on a leg are shown in Fig.3.Force balance along the leg direction for leg i is given by m u s iáa u i?F itm u s iágàs iáf iei?1;...;6Te1
T
where F i is the actuator force produced by the electric motor and ball-screw mech-anism,m u the moving part mass of the leg,s i the unit vector along the leg,g the acceleration of gravity,a u i is the moving part acceleration,and f i the actuating force acting on the platform.And árepresents the inner product.
Moment balance of the i th leg with the moment center at B i becomes
em d r d i tm u r u i T?g àL i s i ?f i àm d r d i ?a d i àm u r u i ?a u i àeI d i tI u i Ta i
àx i ?eI d i tI u i Tx i ?0e2Twhere m d is the ?xed part mass of the leg,L i is the leg length,r d i and r u i are the position vectors from B i to the mass centers of the ?xed and moving parts,I d i and I u i are the moments of inertia of the ?xed and moving parts about their mass centers,and a i ,x i are the angular velocity and angular acceleration of leg i ,respectively.
On the other hand,the velocity v P ,acceleration a P ,angular velocity x P ,and angular acceleration a P at the platform center are related kinematically to the ve-locity v Tj and acceleration a Tj at the connection points T j (j ?1;2;3)denoted by the position vector b i as follows:
v Tj ?v P tx P ?eRb j T
e3a Ta Tj ?a P ta P ?eRb j Ttx P ?f x P ?eRb j Tg e3b Twhere R is the rotation matrix to describe rotation of the moving frame xyz relative to the reference frame XYZ .Note that v P ,a P ,x P and a P are expressed in the ref-erence frame XYZ and b j is written in the platform frame xyz .Note that Rb i is now expressed in terms of the reference frame.The variables v Tj and a Tj can also be represented in terms of the leg-related variables
v Tj ?_L s i tL x i ?s i e4a T
a Tj ?€L
i s i ta i ?eL i s i Ttx i ?f x i ?eL i s i Tg t2x i ?_L i s i ej ?1for i ?1;2;j ?2for i ?3;4;j ?3for i ?5;6Te4b
T
Fig.3.Free body diagram of platform and moving part of a leg.
608S.-H.Lee et al./Mechatronics 13(2003)605–619
where _L
and €L are the leg elongation velocity and acceleration,respectively.Equating Eqs.3a,3b and 4a,4b,the angular velocity x i and angular acceleration a i of each leg can be described by the platform-related variables v P ,a P ,x P ,and a P .Based on this,the actuating force f i can be described via some matrices Q 1i ,Q 2i ,and Q 3i as follows:
f i ?Q 1i v P x P tQ 2i a P a P
tQ 3i F i e5TUsing the forces f i exerted by the six actuating legs,the following force and moment balances for a Stewart platform are obtained
m P a P ?m P g tX
6i ?1
f i e6TI P a P tx P ?eI P x P T?X 6i ?1?eRb i T?f i
e7T
where m P is the platform mass.Eqs.(6)and (7)may be combined into the following equation in the matrix-vector form
m P I 300I P a P a P ?m P g tP f i àx P ?eI P x P TtP eRb i T?f i
e8Twhere I P is the moment of inertia of the platform and I 3denotes the 3?3identity matrix.Replacing f i on the right-hand side by F i using Eq.(5),and denoting the position,velocity,and acceleration by the single vectors X ,_X ?f v T P x T P g T ,€X ?f a T P a T P g T ,the dynamic equation of a Stewart platform in task space is obtained by
M eX T€X th eX ;_X T?J T F e9T
where M eX Tis the inertia matrix,h eX ;_X
Tis the nonlinear term including Coriolis,centrifugal,and gravity force,and F ?f F 1;...;F 6g T is the actuator force vector,respectively.And J is the Jacobian matrix associated with the relation J _X ?_L ,where _L
?f _L 1;...;_L 6g T is the leg velocity vector.J ?s 1s 2ááás 6Rb 1?s 1Rb 2?s 2áááRb 6?s 6
T e10TIt is noted that J T F represents the actuating force in task space which is converted from the leg force F .
2.2.Characteristics of dynamic equations
The dynamic equation (9)of a Stewart platform has the following characteristics.The inertia matrix M eX Tis dependent only on the con?guration of the platform and the nonlinear term h eX ;_X
Tdepends on both the position and velocity of the platform.Because the workspace of a Stewart platform is relatively small,the S.-H.Lee et al./Mechatronics 13(2003)605–619609
variable X and its function M eX Tvaries in a small range as well.The inertia matrix,therefore,can be assumed to be constant with introduction of some modeling error.
On the other hand,the nonlinear term h ,which includes Coriolis,centrifugal,and gravity force,requires most computational burden in the inverse dynamics calcu-lation.It can be described by [8]
h eX ;_X T?_X T H 1eX T_X ..._X T H 6eX T_X
8><>:9>=>;tG eX Te11Twhere H i eX Tis the 6?6square matrix,and G eX Tis the 6?1gravity force vector.If H i eX Tcan be assumed to be constant as H i eX T%H c i ,h eX ;_X
Tcan be approximated by
h eX ;_X T?^h e_X TtD h ;where ^h e_X T?_X T H c1_X ..._X T H c6_X
8><>:9>=>;tG eX Te12TNote that the gravitational term G eX Tcan be accurately computed since the variable X can be obtained accurately by the high-resolution optical encoder.With this ap-proximation,the complicated inverse dynamics computation is accomplished by relatively simple operations.
The modeling error introduced as a result of this approximation depends on the types of tasks.In general,the larger change in con?guration,the greater error will be generated.Suppose that the platform center is to follow a given circular track (refer to Section 4.1for details).The maximum singular values of H i eX Tin Eq.(11)and the di?erence D H i between H i eX Tand the constant matrix H c i are illustrated in Fig.4.Since the elements of H i eX Trepresent the coe?cients which map the quadratic ve-locities into force or torque,the singular values of H i eX Talso have the same
di-610S.-H.Lee et al./Mechatronics 13(2003)605–619
mension.It is observed that r max eD H i Tis less than 10%of r max eH i eX TT.In Eq.(12),therefore,the nonlinear term requiring most computation time in the inverse dynamics calculation can be reduced to multiplication operations of the constant matrices and the velocities detected by the sensor.
The constant matrix H c i is determined properly depending on the task trajectories.For example,for tracking of a circular trajectory,these matrices can be computed o?-line for the con?guration at the center of the circle and then these matrices are used in real-time calculation.
3.Controller design of a parallel manipulator
3.1.Inverse dynamics controller
The IDC [9],or also called computed-torque controller,which is a popular po-sition controller for a serial manipulator is considered in this research as a main position control scheme.The IDC produces good control performance with accurate modeling of the manipulator.When the modeling is not su?ciently accurate,how-ever,its performance is not generally acceptable.
Fig.5illustrates the IDC based on the dynamic equation (9).As shown in the ?gure,the inner loop computing the inverse dynamics makes the manipulator act as a linear model.The conventional inverse dynamics control law is described by
F ?F c tF h
e13Twhere
F c ?J àT M €X ref tK P eX ref àX TtK D e_X ref à_X TtK I Z eX ref àX Td t
F h ??J àT h eX ;_X
T e14Twhere X ref is the reference trajectory that the platform center is to follow,and K P ,K D ,and K I are the constant controller gain matrices.Note that the term F c is the control force used to track the reference trajectory,while the term F h is used to linearize the plant by canceling nonlinearity.Substitution of Eq.(14)into (9)
yields
S.-H.Lee et al./Mechatronics 13(2003)605–619611
M €X th ?M €X ref tK P eX ref àX TtK D e_X ref à_X TtK I Z eX ref àX Td t
th
e15TThe nonlinear terms h on both sides in Eq.(15)cancel out and thus the following error equation is obtained:€e tK D _e tK P e tK I Z e d t ?0e16Twhere e ?X ref àX represents the error.The matrices K P ,K D ,and K I are determined so that the error vector may approach zero asymptotically.
From a practical point of view,the IDC is hard to implement,since it requires long computation time for the inverse dynamics.If the approximate dynamics are used in which all the coe?cient matrices are assumed to be constant,then the computation time can be reduced drastically with some modeling error introduced.In the case of the DSP running at the 50MHz speed,the proposed approximate dynamics requires less than 1ms,while full dynamics computation needs about 25ms.
3.2.H 1controller
As the approximated model inevitably has some modeling error,stability of the whole control system cannot be guaranteed.Adaptive control [10]and sliding mode control [11]schemes can be employed to cope with the modeling errors.However,the adaptive control scheme also requires computation burden and has to provide persistently exiting signals to the system to identify system parameters.As for the sliding mode control scheme,a sharp change in control input may generate chat-tering and thus induce unnecessary vibration of the system.Although a boundary layer can be introduced to compensate for the chattering problem,slight reduction in performance is unavoidable and the design parameters for the boundary layer is hard to determine.
In this research,the H 1controller is adopted to compensate for the modeling error which is intentionally introduced in the process of approximating the model for a reduction in computation time.Since the range of maximum operating speeds of the parallel manipulator is known,the uncertainty dependent on velocity is also known.The PID controller is employed for tracking in the feedforward manner and the H 1controller is added to compensate for the modeling error.This 2DOF con-troller with the PID and H 1controllers is illustrated in Fig.6.
The H 1controller has a role of attenuating not only the disturbance caused by modeling uncertainty,but also the mismatch error caused by the feedforward PID controller.It is noticed that the feedforward controller part does not a?ect stability of the control system,because it has no feedback.
The dynamic equation (9)can be represented in state space as follows.Substi-tuting of Eq.(13)into (9)and replacing the nonlinear term h of full dynamics by the approximated term ^h on the right-hand side yields
612S.-H.Lee et al./Mechatronics 13(2003)605–619
M eX T€X th eX ;_X T?J T F c t^h e17T
Therefore,the nonlinear terms on both side of Eq.(17)cannot cancel out exactly,thus leading to some mismatch error D h .Substituting Eq.(12)into (17)gives
€X ?M à1J T F c àM à1D h e18T
By introducing a new state vector Z ?f X T _X
T g T ,the following state equation is obtained _Z ?0I 600 Z t0M à1
J T F c à0M à1 D h e19Twhere I 6denotes the 6?6identity matrix.
If the inertia matrix M and Jacobian matrix J are assumed to be constant and D h is considered as disturbance,Eq.(18)can be represented by
_Z ?AZ tBu e20Twhere the matrices A and B correspond to the coe?cient matrices of Eq.(18),u is the actuating force J T F c in task space.
In Fig.7showing the generalized plant,W e es Tand W d es Trepresent the weighting function matrices associated with the tracking error and disturbance,respectively.Because the tracking error should be zero at steady state,the weighting function for the tracking error includes a pure integrator.The disturbance is generated
through
S.-H.Lee et al./Mechatronics 13(2003)605–619613
approximation of the inverse dynamics computation and the operating bandwidth of the parallel manipulator is usually below 10Hz.Taking all these factors into ac-count,the weighting functions are selected as W d ?W d es Tááá0.........0áááW d es T264375;W e ?W e es Tááá0..
.......0áááW e es T
264375;e21Twhere W d es T?d 0=es t20p T,W e es T?e 0=s ,where d 0and e 0are the constants a?ecting tracking performance.The controller K es Tattenuates the closed-loop H 1norm magnitude to less than c via the selected weighting function matrices.W e eI tPK Tà1f àPW d I g 1
Fig.8shows the 6universal-prismatic-spherical Stewart platform designed and built in the laboratory for the experiment.It can operate within the ranges of ?0.2m in the X -and Y -axes,?0.1m in the Z -axis,?25°in roll and pitch,and ?30°in yaw.The controller is divided into two parts;the high-level controller based on PC monitors the platform and performs analysis of the experimental results,while the low-level controller based on the TMS320C31DSP carries out both computation of the inverse dynamics and forward kinematics and implementation of the motor control algorithm.Fig.9shows geometry of the platform and the base of the Stewart platform. 4.1.Inverse dynamics control with full dynamics Fig.8shows the experimental results where the platform center is forced to follow the reference circular trajectory with a radius of 0.02m in the XY plane at a rela-tively slow frequency of 0.2Hz.Two types of controllers are compared;one is the Fig.8.Schematic of experimental setup. 614S.-H.Lee et al./Mechatronics 13(2003)605–619 IDC with full dynamics based on the control law of Eq.(13)and the other is a simple PID controller.The full inverse dynamics computation requires about 25ms,so that the IDC with full dynamics has a long sampling period of 30ms.Since the reference trajectory also has relatively low speed,the tracking performance is not adversely a?ected because of this long sampling period.On the other hand,the simple PID controller that ignores the nonlinear term h eX ;_X Tof the dynamic equations carries out the following control action only with output errors. F ?J àT M €X ref tK P eX ref àX TtK D e_X ref à_X TtK I Z eX ref àX Td t e23T where the integral action in Eq.(23)compensates for ignorance of the nonlinear term to some extent.The two controllers show little di?erence in their responses as shown in Fig. 10. S.-H.Lee et al./Mechatronics 13(2003)605–619615 Fig.11shows the experimental results where the platform center is to track the circular trajectory with a radius of 0.02m in the XY plane at a relatively fast fre-quency of 2.5Hz (12.5times faster than in Fig.10).It is observed that the IDC with full dynamics shows better performance than the simple PID controller which pro-duces a large tracking error.However,even the IDC cannot generate the truly cir-cular trajectory.The reason is that the sampling period of 30ms is not su?ciently shorter than the trajectory period of 400ms,so the control inputs for accurate tracking cannot be provided. 616S.-H.Lee et al./Mechatronics 13(2003)605–619 S.-H.Lee et al./Mechatronics13(2003)605–619617 4.2.Proposed inverse dynamics controller The control scheme proposed in this paper is similar to the IDC with full dy-namics(see Section4.1),but it employs the approximate inverse dynamics together with H1control to compensate for the modeling error.This proposed control scheme will be called the IDC with approximate dynamics below. In the case of slow tracking as in Fig.10,the proposed control scheme shows little di?erence compared to the IDC with full dynamics.In the case of fast tracking as in Fig.11,however,the IDC with approximate dynamics shows better performance than that with full dynamics as illustrated in Fig.12.It is observed in the magni?ed 618S.-H.Lee et al./Mechatronics13(2003)605–619 picture that the IDC with approximate dynamics has much shorter sampling period (5ms)than the IDC with full dynamics and thus generates smoother trajectory. Furthermore,the control signal shown in Fig.13is smoother and has less?uctuation than the IDC with full dynamics. Fig.14shows the experimental results where the platform center is to track the rectangular trajectory at a speed of0.5Hz.It is noted that the rectangular trajectory contains high-frequency components around the corners.It is observed in Fig.14 that the IDC with full dynamics produces generally large tracking error.A partic-ularly large tracking error is generated around the corners,because it cannot faithfully track the corner with high-frequency components due to its long sampling period.On the contrary,the proposed IDC with approximate dynamics shows rel-atively good tracking performance both along the straight-line portion and at the corners.In summary,the proposed controller can track the high-frequency reference command better than the conventional one. 5.Conclusions A Stewart platform has a drawback of small workspace,but this feature enables the con?guration-dependent coe?cient matrices of the dynamic equations to be approximated to constant ones without introducing large modeling errors.By this approximation,the computation time for the inverse dynamics can be signi?cantly reduced. About10%modeling error caused by such approximation can be treated as disturbance,and is compensated for by the H1controller,thus leading to a stable control system.The proposed IDC with approximate dynamics combined with the H1controller shows better responses than that with full dynamics and the simple PID controller as the tracking speed increases.Also it provides better tracking performance for high-frequency reference commands.The proposed controller can be realized on-line in a single DSP running at the50Hz speed.Investigation of the proposed controller is under way for various trajectories and tasks. Acknowledgements This research was supported by the Basic Research Program of the Korea Science and Engineering Foundation(1999-1-304-003). References [1]Stewart D.A platform with six degrees of freedom.Proc of Inst Mech Engr1965;180(1):371–86. [2]Liu K,Fitzgerald J,Lewis FL.Kinematic analysis of a Stewart platform manipulator.IEEE Trans Ind Electron1993;40(2):282–93. S.-H.Lee et al./Mechatronics13(2003)605–619619 [3]Lebret G,Liu K,Lewis FL.Dynamic analysis and control of a Stewart platform manipulator. J Robotic Syst1993;10(5):629–55. [4]Dasgupta B,Mruthyunjaya TS.Closed-form dynamic equations of the general Stewart platform through the Newton–Euler approach.Mech Mach Theory1998;33(7):993–1012. [5]Zhang C,Song S.An e?cient method for inverse dynamics of manipulators based on the virtual work principle.J Robotic Syst1993;10(5):605–27. [6]Fichter EF.A Stewart platform-based manipulator:general theory and practical construction.Int J Robotics Res1986;5(2):157–82. [7]Zhiming J.Study of the e?ect of leg inertia in Stewart platforms.In:International Conference on Robotics and Automation.1993.p.121–6. [8]Craig JJ.Adaptive control of mechanical manipulators.Addison-Wesley;1988. [9]Asada H,Slotine JJE.Robot analysis and control.John Wiley and Sons;1985. [10]Nguyen CC,Antrazi SS,Zhou ZL.Adaptive control of a Stewart platform-based manipulator. J Robotic Syst1993;10(5):657–87. [11]Kim NI,Lee CW.High speed tracking control of Stewart platform manipulator via enhanced sliding mode control.In:International Conference on Robotics and Automation.1998.p.2716–21. 2000年1月大学英语六级考试试题及解答 PartⅠ Listening Comprehension (20 minutes) Section A Directions: In this section, you will hear 10 short conversations. At the end of each conversation, a question will be asked about what was said. Both the conversation and the question will be spoken only once. After each question there will be a pause. During (he pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the centre. Example: You will hear: You will read: A) 2 hours. B) 3 hours. C) 4 hours. D) 5 hours. From the conversation we know that the two are tawe know that the two are talking about some work they will start at 9 o'clock in the morning and have to finish at 2 in the afternoon. Therefore. D) “5 hours”is the correct answer. You should choose ［D］ on the Answer Sheet and mark it with a single line trough the centre. Sample Answer ［A］［B］［C］［D］ 1. A) To cancel his trip. B) To go to bed early. C) To catch a later flight. D) To ask for a wake - up call. 2. A) They have different opinions as to what to do next. B) They have to pay for the house by installments. C) They will fix a telephone in the bathroom. D) The man's attitude is more sensible than the woman's. 3. A) She will save the stamps for the man's sister. B) She will no longer get letters from Canada. C) She can't give the stamps to the man's sister. D) She has given the stamps to the man's roommates. 4. A) Visiting the Brownings. B) Writing a postcard. C) Looking for a postcard. D) Filling in a form. 5. A) The man should work with somebody else. B) The man should meet his partner's needs. C) They should come to a compromise. D) They should find a better lab for the project. 6. A) She can't finish her assignment, either. B) She can't afford a computer right now. C) The man can use her computer. D) The man should buy a computer right away. 7. A) The visiting economist has given several lectures. B) The guest lecturer's opinion is different from Dr. Johnson's. C) Dr. Johnson and the guest speaker were schoolmates. D) Dr. Johnson invited the economist to visit their college. 2015年6月英语六级真题及答案（第三套） Part I Writing (30 minutes) Directions: For this part, you are allowed 30 minutes to write an essay commenting on the saying “If you cannot do great things, do small things in a great way. ’’You can cite examples to illustrate your point of view. You should write at least l50 words but no more than 200 words. 注意: 此部分试题请在答题卡1上作答。 Part II Listening Comprehension (30 minutes) Section A Directions: In this section, you will hear 8 short conversations and 2 long conversations. At the end of each conversation, one or, more questions will be asked about what was said. Both the conversation and the questions will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A, B, C and D and decide which is the best answer. Then mark the corresponding letter on Answer Sheet, with a single line through the centre. 注意: 此部分试题请在答题卡1上作答。 1．A. The man might be able to play in the World Cup. B. The man’s football career seems to be at an end. C. The man was operated on a few weeks. D. The man is a fan of world famous football players. 2．A. Work out a plan to tighten his budget. B. Find out the opening hours of the cafeteria. C. Apply for a senior position in the restaurant. D. Solve his problem by doing a part time job. 3．A.A financial burden. B. A good companion. C. A real nuisance. D.A well trained pet. 4．A. The errors will be corrected soon. B. The woman was mistaken herself. C. The computing system is too complex. D. He has called the woman several times. 5．A. He needs help to retrieve his files. B. He has to type his paper once more. C. He needs some time to polish his paper. D. He will be away for a two-week conference. 6．A. They might have to change their plan. B. He has got everything set for their trip. C. He has a heavier workload than the woman. D. They could stay in the mountains until June 8. 7．A. They have to wait a month to apply for a student loan. B. They can find the application forms in the brochure. C. They are not eligible for a student loan. D. They are not late for a loan application. 洛基英语，中国在线英语教育领导品牌 2003年6月六级试题译文 Passage One 译文 在英国乡间的小村子里还有人记得那些不用想着锁门的美好的老日子。那时根本不用担心犯罪。 令人惊奇的是，这些幸福的时光似乎还在世界最大的社团里与我们同在。一个天才的程序员，丹·法穆用他自称为“撒旦”的自动调查程序所做的一项最新研究表明，万维网一半多的主人建立了不上锁的家。 “撒旦”不用真正闯入就可以试验因特网上黑客的许多臭名昭著的伎俩。法穆把他的程序公开化，使每个人都能得到，这种做法招致了许多批评。居心不良的人可以用它猎取容易闯入行窃的网站。 但是，法穆关心的是，有必要提醒公众注意网络并非安全，到目前为止，事实证明他是对的。与其说“撒旦”制造了新的混乱，倒不如说它警告人们要注意安全。 所以，网络是否越来越安全?远非如此。在早期，当你浏览网站的时候，你的浏览器只注意内容。现在，网络充斥着一些小的程序，当你浏览网页的时候，这些程序会自动下载，然后在你个人的电脑上运行。如果编程者有意，这些程序就会对你的电脑进行各种各样的破坏。 同时，网络中出现了越来越多的蜘蛛、虫子、间谍和其他的一些自动化的动物，它们被预先指定闯入网站，对信息进行查找和分类。所有这些都为那些想进攻弱小的网站并对其造成伤害的反社会的人提供了绝妙的工具。 但是，让我们来看一看光明的一面。如果没有锁，因特网当然是世界上最大的(极端的)没有犯罪的社会。也许，那是因为黑客们从根本上是诚实的。或者，当今没有什么东西好偷。或者，除非你对某一个人有特殊的仇恨，恶意破坏并不是什么好玩的事。 不管是什么原因，让我们在还能享受的时候尽情享受吧。然而，当网络上最有影响力的居民们想出售他们的服务并想要收费时，希望一切会有所改变，那时安全将变成头等重要的事情。 Passage Two 译文 当我离开多年教学的学院和大学时，我坚信扮演角色、表演、改编剧本等都是最成功的教学方式。学生们必须尽可能地被编入或组织到整个教学过程中，成为其中有机的一部分。在大多数的学者看来，认为学习必须包括玩耍并对其进行鼓励的理念近乎愚蠢，但这是事实。曾经是Ezekiel Cheever, 这个马塞诸州海湾殖民地最著名的校长的学生，Cotton Mather 写到，他备的课程能让学生们感觉“上学就像玩一样”，过了大约三百年，Alfred North Whitehead 注意到一个教师必须使他/她的学生“高兴上学”。 由于我们知道在典型的大学里有百分之八十至九十的教学是通过讲座的方式进行的，因此，我们必须给予这样的教育形式以足够的重视。我认为Patricia 1996年1月大学英语六级(CET-6)真题试卷及参考答案 Part I Listening comprehension (20 minutes) Section A Directions: In this section, you will hear 10 short conversations. At the end of each conversation, a question will be asked about what was said. Both the conversation and the question will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the centre. Example: You will hear: You will read: A) 2 hours. B) 3 hours. C) 4 hours. D) 5 hours. From the conversation we know that the two were talking about some work they will start at 9 o’clock in the morning and have to finish at 2 in the afternoon. Therefore, D) “5 hours” is the correct answer. You should choose [D] on the Answer Sheet and mark it with a single line through the center. Sample Answer [A] [B] [C] [D] 1. A) The flight has been canceled. B) The plane is late. C) The plane is on time. D) The tickets for this flight have been sold out. 2. A) He is not to blame. B) It was his fault. C) He will accept all responsibility. D) He will be more careful next time. 3. A) The man is a forgetful person. B) The typewriter is not new. C) The man can have the typewriter later. For investors who desire low riskand guaranteed income,U.S. Government bonds are a secure investment becausethese bonds have the financial backing and full faith and credit of the federalgovernment.Municipal bonds,also secure,are offered by local governmengts andoften have____36______such as tax-free interest.Some may even be____37______.Corportate bonds are a bit more risky. Two questionsoften_____38_____first-time corportate bond investors.The first is”If I purchase a corportate bond,do I have t o hold it until thematueity date?”The answer is no.Bonds are bought and sold daily on____39_____securities exchanges.However,if your bond does not have____40_____that make it attractive to other investors, you may be forced to sell your bondat a____41____i.e., a price less than the bond’s face value. But if your bond is highly valued by otherinvestors, you may be able to sell it at a premium, i.e., a price above itsface value. Bond prices gcncrally____42____ inversely (相反地)with current market interest rates. Asinterest rates go up, bond pnccs tall, and vice versa (反之亦然).Thus, like all investments，bonds have adegree of risk. The second question is “How can I ___43_______ the investment risk of a particular bondissue?” Standard & Poor’s and Moody’s Investors S ervice rate the level of risk of many corporateand government bonds. And ____44______, the higher the market risk of a bond，the higher the interest rate. Investors willinvest in a bond considered risky only if the _____45_____return is highenough. A)advantages I)fluctuate B)assess J)indefinite C)bother K)insured D)conserved L)major E)deduction M)naturally F)discount N)potential G)embarrass 0)simultaneously H)features 36.A advantages 37.K insured 38. C bother 39. L major 40. H features 41. F discount 42. I fluctuate 43. B assess 44. M naturally 45. N potential 2014.6【2】 Fear can be an effective way to change behavior. One study compared the effects of high-tear and low-fear appeals on changes in attitudes and behaviors related to dental hygiene （卫生）. One group of subjects was shown awful pictures of ___36___teeth and diseased gums; another group was shown less frightening materials such as plastic teeth, charts, and graphs. Subjects who saw the frightening materials reported more anxiety and a greater___37___to change the way they took care of their teeth than the low-fear group did. But were these reactions actually___38___into better dental hygiene practices? To answer this important question, subjects were called back to the laboratory on two___39___ (five days and six weeks alter the experiment). They chewed disclosing wafers（牙疾诊断片）that give a red stain to any uncleaned areas of the teeth and thus provided a direct___40___of how well they were really taking care of their teeth. The result showed that the high-fear appeal did actually result in greater and more___41___changes in dental hygiene. That is, the subjects___42___to high-fear warnings brushed their teeth more___43____than did those who saw low-fear warnings. However, to be an effective persuasive device it is very important that the message not be too frightening and that people be given___44___guidelines to help them to reduce the cause of the fear. If this isn’t done, they may reduce their anxiety by denying the message or the___45___of the communicator. If that happens, it is unlikely that either attitude or behavior change will occur. A) accustomed B) carefully C) cautiously D) concrete E) credibility F) decayed G) desire H) dimensions I) eligible J) exposed K) indication L) occasions M) permanent N) sensitivity O) translated 36.F 37.G 38.O 39.L 40.K 41.D 42.J 43.B 44.I 45.E 2000年6月大学英语六级(CET-6)真题试卷 Part I Listening Comprehension (20 minutes) Section A Directions: In this section, you will hear 10 short conversations. At the end of each conversation, a question will be asked about what was said. Both the conversation and the question will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the centre. Example: You will hear: You will read: A) 2 hours. B) 3 hours. C) 4 hours D) 5 hours. From the conversation we know that the two are talking about some work they will start at 9 o’clock in the morning and have to finish at 2 in the afternoon. Therefore, D) “5 hours” is the correct answer. You should choose [D] on the Answer Sheet and mark it with a single a single line through the centre. Sample Answer [A] [B] [C] [D] 1. A) Buy some traveller’s checks. B) Borrow some money from a friend. C) Check the brakes and tires. D) Spend some time travelling. 2. A) He is very forgiving and tolerant. B) He probably has a poor memory. C) He is well liked by his customers. D) He has been introduced to the staff. 3. A) He thinks the book should include more information. B) He doesn’t think it necessary to provide the answers. C) The answers will be added in a later edition. D) The book does include the answers. 最牛英语口语培训模式：躺在家里练口语，全程外教一对一，三个月畅谈无阻！ 洛基英语，免费体验全部在线一对一课程：https://www.doczj.com/doc/404947390.html,/ielts/xd.html（报名网址）Section B Passage One There are some serious problems in the Biramichi River. The local Chamber of Commerce, which represents the industries in the area, hired me as a consultant to do a one-year study on fishing in the Biramichi River and write a report for them. This is my report. One of the major problems in the Biramichi River, is that the level of the oxygen in the water is too low. Several chemicals have displaced the oxygen. This chemical pollution has two sources: The factories which dump polluted water directly into the river and the local community, which dumps untreated human wastes into the river. The local town government has already spent 2 million dollars on waste water treatment projects. But it would cost another 27 million to complete the projects. It would take at least 15 years for the town to collect enough revenue from taxes to complete these projects. The factories here employed 17 000 people, and in the area where there is very little alternative employment, it is not economically practical to close or relocate the factories. Also, the factories can not afford to finance chemical treatment plants by themselves. Another problem is that the members of the Biramichi fishing cooperative are overfishing. Fishes are caught when they are on the way upstream to lay eggs. Consequently, not enough fish are left to reproduce in large numbers. The members of the cooperative say that they have already reduced their annual catch by 60 percent. However, my study indicates that they took fewer fish because there were fewer fish to catch, not because they were trying to preserve fishes. Passage Two Everybody has to die someday. But nobody likes to think about it. Even so, at some time in their lives most people manage to think about the question of how to make a will. If you have already made yours, it's probably just a few pages of wring, stating that you wish to leave everything to your family. That's the kind of will that the majority of people make. However, there are plenty of ways to make your will more interesting if you want to. To begin with, you don't have to write it on paper. One man wrote his will on an envelope, another on a door, and the third on an egg. For some people, the most important part of their will is the part that says how they want to be buried. Mrs . Sundrew West, a rich widow from Texas, decided that she wanted to be buried with her favorite car. In 1973, Mr. Green, a dentist from England, left most of his money to the nurse who worked for him if, in 5 years, she wouldn't wear any kind of make-up or jewelry or go out with men. Finally, let's hope that your will is not like that of Dr. Wagner, who lived in America 2015年6月大学英语6级真题(三套全) 2015年6月大学英语六级考试真题（第一套） Part II Listening Comprehension (30 minutes) Section A 1. A) Prepare for his exams. B) Catch up on his work. C) Attend the concert. D) Go on a vacation. 2. A) Three crew members were involved in the incident. B) None of the hijackers carried any deadly weapons. C) The plane had been scheduled to fly to Japan. D) None of the passengers were injured or killed. 3. A) An article about the election. B) A tedious job to be done. C) An election campaign. D) A fascinating topic. 4. A) The restaurant was not up to the speakers' expectations. B) The restaurant places many ads in popular magazines. C) The critic thought highly of the Chinese restaurant. D) Chinatown has got the best restaurant in the city. 5. A) He is going to visit his mother in the hospital. B) He is going to take on a new job next week. 2002年6月大学英语六级(CET-6)真题试卷及答案 试卷一 Part I Listening Comprehension (20 minutes) Section A Directions: In this section, you will hear 10 short conversations. At the end of each conversation, a question will be asked about what was said. Both the conversation and the question will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the centre. Example: You will hear: You will read: A) 2 hours. B) 3 hours. C) 4 hours. D) 5 hours. From the conversation we know that the two are talking about some work they will start at 9 o’clock in the morning and have to finish at 2 in the afternoon. Therefore, D)“5 hours”is the correct answer. Y ou should choose [D] on the Answer Sheet and mark it with a single line through the centre. Sample Answer [A] [B] [C] [D] 1. A) Registering for courses. B) Getting directions. C) Buying a new computer. D) Studying sociology. 2. A) The man will probably have to find a roommate. B) The man is unlikely to live in the suburbs. C) The man will probably have to buy a car. D) The man is unlikely to find exactly what he desires. 3. A) Painting a picture. B) Hosting a program. 2000年1月大学英语六级CET6真题及答案 Part I Listening Comprehension (20 minutes) Section A Directions: In this section, you will hear 10 short conversations. At the end of each conversation, a question will be asked about what was said. Both the conversation and the question will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the center. Example: You will hear: You will read: A) 2 hours. B) 3 hours. C) 4 hours. D) 5 hours. From the conversation we know that the two were talking about some work they will start at 9 o’clock in the morning and have to finish at 2 in the afternoon. Therefore, D) “5 hours” is the correct answer. You should choose [D] on the Answer Sheet and mark it with a single line through the center. Sample Answer [A] [B] [C] [D] 1. A) To cancel his trip. B) To go to bed early. C) To catch a later flight. D) To ask for a wake-up call. 2. A) They have different opinions as to what to do next. B) They have to pay for the house by installments. C) They will fix a telephone in the bathroom. D) The man’s attitude is more sensible than the woman’s. 3. A) Sh e will save the stamps for the man’s sister. B) She will no longer get letters from Canada.2000年1月大学英语六级考试试题及解答
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