Статті в журналах з теми "6-DOF vibration isolation"

The inevitable vibration caused by normal operation of the spacecraft in orbit will interfere sensitive instruments, such as space telescope, reconnaissance camera, space interferometer. Serious vibrations affect the accuracy and reliability of the sensitive instruments, even cause flight mission failed. This paper presents a hybrid 6-DOF vibration isolation platform (HVIP) with six degree-of-freedom for active vibration isolation of the space sensitive instruments. The HVIP is composed of three orthogonal vibration isolation module, which composed of the active piezoelectric actuator and passive rubber isolator. The dynamic model of the HVIP is established based Lagrange equation approach. Finally, the numerical simulations are performed to verify the vibration isolation effect of the HVIP.

Multi-degree-of-freedom isolator with low stiffness is a fair prospect in engineering application. In this paper, a novel 6-DOF QZS vibration isolation platform based on leaf spring structure is presented. Its bearing capacity is provided through four leaf springs, and the quasi-zero-stiffness is realized by the force balance between the central spring and the suspension spring. 6-DOF vibration isolation is realized by the ball-hinge fixed design of a leaf spring. Through static and dynamic analysis, the following conclusions are brought. The stiffness of the leaf spring and the deformation of the central spring under static load are directly proportional to the bearing capacity of the isolation table. Besides, in order to ensure that the stiffness of the system is close to zero, the stiffness of the suspension spring and the inner spring should be as similar as possible. The vertical and horizontal displacement transmissibility tests of the isolation platform are carried out, in which the jumping phenomenon in the QZS vibration isolation platform is analyzed. By improving the damping of the structure and the length of the suspension spring, the dynamic vibration isolation process of the system can be more stable, the transmissibility can be reduced, and the vibration isolation effect can be enhanced.

This paper proposes a novel control strategy for six degrees-of-freedom active vibration isolation tables. In these systems, the most challenging issue is to suppress the external vibrations and isolate the internal interactions while still preserving the system’s robustness when facing uncertainties. A noninteracting controller is designed to tackle these problems. The resulting control system is completely decoupled in the sense that each system output is independently controlled to follow the corresponding reference signal. In this paper, the model of an active vibration isolation table is firstly derived. Conditions for system stability and decoupled performance are then discussed. The control law is formulated using the linear matrix inequality approach, which results in optimal control gains for the control objectives. With the proposed controller, complex system characteristics can be handled more efficiently such that an effective system is designed to obtain good control performance. Finally, simulations and comparison studies were conducted, and the results validate the efficiency of the proposed scheme.

In this paper a 6-DOF(Degree of Freedom) vibration isolation platform with structural configuration of 3CPS (3 Cylindrical-Prismatic-Spherical)-1UPS (1 Universal-Prismatic-Spherical) parallel mechanism is proposed. Firstly, the dynamic model is developed through virtual work principle. The transfer function and the complex frequency response function were obtained from the dynamical equation. Then, 36 amplitude frequency diagrams are obtained from the frequency response function. By analyzing the 36 amplitude frequency diagrams, 10 vibration coupling terms were chosen. The range of the spring stiffness coefficient and the range of the damping coefficient of the magneto-rheological damper are determined by analyzing the acceleration transmissibility of the 10 vibration coupling terms. At last, an integrated optimization combining structural and controller optimization is developed. The optimal parameters of the parallel mechanism are obtained through Genetic Algorithm (GA). This work is significant for the prototype design and verification of the vibration isolator.

Micro vibrations, produced by reaction flywheels, coolers, driving motors and other moving parts in spacecrafts, will result in jitters and performance degradation of sensitive optical payloads, such as laser communication platforms, space telescopes and staring cameras. In this paper, one hexapod platform with flexible ball joints is employed to suppress vibrations and steer the payload in 6-degree-of-freedom (DOF). At first, dynamic modeling of the flexible hexapod platform with two-stage hybrid isolation struts is derived. Then, a composite control strategy is proposed for vibration isolation and precision tracking. Finally, the simulation study is presented to validate the proposed control strategy.

In order to study the vibration isolation and positioning performance of the noncontact 6-DOF platform in the space microgravity environment, this paper presented a cosimulation model of a virtual prototype. Based on the model driven by biaxial noncontact Lorentz force actuators (NLFAs), an equivalent dynamic model has been established. In the meanwhile, the 6-DOF sliding mode robust controller with exponential convergence disturbance observer is developed. The mechanical system simulation model was designed using ADAMS, and the corresponding 6-DOF decoupling control system and disturbance observer programs were developed using MATLAB/Simulink. According to the mechatronics simulation results, the system can enable the floating platform to achieve micron-level posture positioning within 0.5 s. In vibration isolation simulation, the disturbance observer can predict the external disturbance input and compensate the control force more accurately so that the floating platform can effectively suppress low-frequency disturbance and step disturbance under the control of the sliding mode controller. And the displacement of the floating platform under the disturbance of 1–100 Hz frequency sweep is less than 1 μm.

A mathematical model of a six-degree-of-freedom (6-DOF) hexapod system for vibration isolation was derived in the discrete-time domain on the basis of the experimental data obtained from a satellite. Using a Box–Jenkins model structure, the transfer functions between six piezoelectric actuator input voltages and six geophone sensor output voltages were identified empirically. The 6×6 transfer function matrix is symmetric, and its off-diagonal terms indicate the coupling among different input/output channels. Various multi-input multi-output (MIMO) control techniques such as Linear Quadratic Gaussian and H∞ were proposed for active vibration isolation in the broadband up to 100 Hz. The simulation results using these controllers obtain 13 and 8 dB vibration attenuation at 25 and 35 Hz, respectively.

Micro-vibration has been a dominant factor impairing the performance of scientific experiments which are expected to be deployed in a micro-gravity environment such as a space laboratory. The micro-vibration has serious impact on the scientific experiments requiring a quasi-static environment. Therefore, we proposed a maglev vibration isolation platform operating in six degrees of freedom (DOF) to fulfill the environmental requirements. In view of the noncontact and large stroke requirement for micro-vibration isolation, an optimization method was utilized to design the actuator. Mathematical models of the actuator's remarkable nonlinearity were established, so that its output can be compensated according to a floater's varying position and a system's performance may be satisfied. Furthermore, aiming to adapt to an energy-limited environment such as space laboratory, an optimum allocation scheme was put forward, considering that the actuator's nonlinearity, accuracy, and minimum energy-consumption can be obtained simultaneously. In view of operating in 6-DOF, methods for nonlinear compensation and system decoupling were discussed, and the necessary controller was also presented. Simulation and experiments validate the system's performance. With a movement range of 10 × 10 × 8 mm and rotations of 200 mrad, the decay ratio of −40 dB/Dec between 1 and 10 Hz was obtained under close-loop control.

The 6-DOF vibration isolation platform (VIP) is used to isolate vibration in the processing and manufacturing of semiconductor chips, especially electric vehicle chips. The 6-DOF VIP has the characteristics of high position accuracy, fast dynamic response, and short motion travel. In this paper, a novel four-quadrant Lorentz force motor (FQLFM) applied on the 6-DOF VIP is proposed. The structure of this LFM has a high force density, low force fluctuation, and low coupling force. First, the basic structure and operating principle of the proposed FQLFM are presented. Secondly, the expressions of the magnetic field and electromagnetic force are obtained based on an equivalent current model and the permanent magnet mirror-image method (PMMIM). Thirdly, the magnetic field and electromagnetic force characteristics of the proposed FQLFM and an LFM with a traditional bilateral structure are analyzed and compared. The relationship between the force and displacement of the FQLFM is investigated. Moreover, the PMMIM is verified by a 3D finite element analysis (FEA). Finally, the experimental platform for a force test is built and the above results are validated by an experiment.

This paper presents a novel magnetically levitated (maglev) stage developed to meet the ever-increasing precise positioning requirements in nanotechnology. This magnetic levitator has 6 independent linear actuators necessary and sufficient to generate all 6-degree-of-freedom (6-DOF) motions. This minimum-actuator design concept led to a compact, 200 g lightweight moving part and the power consumption less than of a Watt, thereby reducing the thermal-expansion error drastically. The analysis and sizing of the magnetic linear actuators and the working principle of the maglev stage are presented. We designed and implemented stabilizing controllers for 6-DOF motion control with the dynamic model based on the actuator analysis. Test results showed nanoscale step responses in all six axes with 2nmrms horizontal position noise. A noise propagation model and analysis identified the capacitance sensor noise and the floor vibration as the dominant noise sources in the vertical and horizontal dynamics, respectively. A comparison of noise performances with controllers closed at 25, 65, and 90 Hz crossover frequencies illustrated how the selection of the control bandwidth should be made for nanopositioning. Experimental results including a 250μm step response, sinusoidal and square-wave trajectories, and spherical motion generation demonstrated the three-dimensional (3D) nanoscale motion-control capability of this minimum-actuator magnetic levitator. Potential applications of this maglev stage include manufacture of nanoscale structures, atomic-level manipulation, assembly and packaging of microparts, vibration isolation for delicate instruments, and seismic motion detection.

The optical reference cavity in an ultrastable laser is sensitive to vibrations; the microvibrations in a space platform affect the accuracy and stability of such lasers. In this study, an active vibration isolation controller is proposed to reduce the effect of vibrations on variations in the cavity length and improve the frequency stability of ultrastable lasers. Based on the decentralized control strategy, we designed a state-differential feedback controller with a linear quadratic regulator (LQR) and added a disturbance observer (DOB) to estimate the source noise. Experiments were conducted using an active vibration isolation system; the results verified the feasibility and performance of the designed controller. The accelerations along the axis (Z-, X-, Y-) directions were suppressed in the low-frequency band within 200 Hz, and the root-cumulative power spectral densities (PSDs) declined to 1.17 × 10−5, 7.16 × 10−6, and 8.76 × 10−6 g. This comprehensive vibration met the requirements of an ultrastable laser.

This study proposes a novel handheld vibrotactile display (T-hive) to provide a human operator with spatial and directional information. The proposed design is composed of a spherical knob with a vibrotactile surface and a moving base that allows 6-DOF motion. To isolate vibrotactile stimuli provided by multiple actuators, the spherical knob is divided into 13 vibrotactile modules. Each vibrotactile module consists of a vibration motor, a patch of spherical surface, and a vibration isolator. By coordinating the vibrotactile modules, the vibrotactile display delivers spatial and directional information based on phantom sensation and sensory saltation. Through experiments, we evaluated the effectiveness of the spatial and directional information perceived on the palm and fingers of the operator's hand. The experimental results confirm that vibrotactile feedback is useful for object control by providing intuitive information.

Abstract. With the development of motor control technology, the electrically driven Stewart platform (EDSP), equipped with a ball screw or lead screw, is being widely used as a motion simulator, end effector, and vibration isolator. The motor drives the lead screw on each driven branch chain to realize 6-DOF motion of the moving platform. The control loop of the EDSP adopts the rotor position as a feedback signal from the encoder or resolver on the motor. When the moving platform of the EDSP performs translational or rotational motion, the lead screw on each driven branch chain passively generates a relative rotation between its screw and nut in addition to its original sliding motion. This type of passive rotation (PR) of the lead screw does not disturb the motor; hence, it cannot be detected by the position sensor attached to the corresponding motor. Thus, the driven branch chains cause unexpected length changes because of PR. As a result, the PR generates posture errors on the moving platform during operation. In our research, the PR on the EDSP was modeled and analyzed according to the geometry configuration of EDSP. Then, a control method to compensate for the posture errors caused by the PR was proposed. Finally, the effectiveness of the analysis process and compensation control method were validated; the improvement in pose accuracy was confirmed both by simulation and experiments.

For improving the generality, expandability and accuracy, the general embedded intelligent monitoring system of tower crane is developed. The system can be applied to different kinds of tower cranes running at any lifting ratio, can be initialized using U disk with the information of tower crane, and fit the lifting torque curve automatically. In dangerous state, the system can sent out alarm signals with sounds and lights, and cut off power by sending signals to PLC through communication interface RS485. When electricity goes off suddenly, the system can record the real-time operating information automatically, and store them in a black box, which can be taken as the basis for confirming the accident responsibility.In recent years, tower cranes play a more and more important role in the construction of tall buildings, in other construction fields are also more widely used. For the safety of tower cranes, various monitors have been developed for monitoring the running information of crane tower [1-8]. These monitors can’t eliminate the errors caused by temperature variations automatically. The specific tower crane’s parameters such as geometric parameters, alarming parameters, lifting ratio, lifting torque should be embedded into the core program, so a monitor can only be applied to a specific type of tower crane, lack of generality and expansibility.For improving the defects of the existing monitors, a general intelligent monitoring modular system of tower crane with high precision is developed, which can initialize the system automatically, eliminate the temperature drift and creep effect of sensor, and store power-off data, which is the function of black box.Hardware design of the monitoring systemThe system uses modularized design mode. These modules include embedded motherboard module, sensor module, signal processing module, data acquisition module, power module, output control module, display and touch screen module. The hardware structure is shown in figure 1. Figure 1 Hardware structure of the monitoring systemEmbedded motherboard module is the core of the system. The motherboard uses the embedded microprocessor ARM 9 as MCU, onboard SDRAM and NAND Flash. Memory size can be chosen according to users’ needs. SDRAM is used for running procedure and cache data. NAND Flash is used to store embedded Linux operating system, applications and operating data of tower crane. Onboard clock with rechargeable batteries provides the information of year, month, day, hour, minute and second. This module provides time tag for real-time operating data. Most interfaces are taken out by the plugs on the embedded motherboard. They include I/O interface, RS232 interface, RS485 interface, USB interface, LCD interface, Audio interface, Touch Screen interface. Pull and plug structure is used between all interfaces and peripheral equipments, which not only makes the system to be aseismatic, but also makes its configuration flexible. Watch-dog circuit is designed on the embedded motherboard, which makes the system reset to normal state automatically after its crash because of interference, program fleet, or getting stuck in an infinite loop, so the system stability is improved greatly. In order to store operating data when power is down suddenly, the power-down protection circuit is designed. The saved data will be helpful to repeat the accident process later, confirm the accident responsibility, and provide the basis for structure optimization of tower crane.Sensor module is confirmed by the main parameters related to tower crane’s security, such as lifting weight, lifting torque, trolley luffing, lifting height, rotary angle and wind speed. Axle pin shear load cell is chosen to acquire lifting weight signals. Potentiometer accompanied with multi-stopper or incremental encoder is chosen to acquire trolley luffing and lifting height signals. Potentiometer accompanied with multi-stopper or absolute photoelectric encoder is chosen to acquire rotary angle signals. Photoelectric sensor is chosen to acquire wind speed signals. The output signals of these sensors can be 0~5V or 4~20mA analog signals, or digital signal from RS485 bus. The system can choose corresponding signal processing method according to the type of sensor signal, which increases the flexibility on the selection of sensors, and is helpful for the users to expand monitoring objects. If the acquired signal is analog signal, it will be processed with filtering, isolation, anti-interference processing by signal isolate module, and sent to A/D module for converting into digital signals, then transformed into RS485 signal by the communication protocol conversion device according to Modbus protocol. If the acquired signal is digital signal with RS485 interface, it can be linked to RS485 bus directly. All the acquired signals are sent to embedded motherboard for data processing through RS485 bus.The data acquisition module is linked to the data acquisition control module on embedded motherboard through RS485 interface. Under the control of program, the system inquires the sensors at regular intervals, and acquires the operating data of crane tower. Median filter technology is used to eliminate interferences from singularity signals. After analysis and processing, the data are stored in the database on ARM platform.Switch signal can be output to relay module or PLC from output control module through RS485 bus, then each actuator will be power on or power off according to demand, so the motion of tower crane will be under control.Video module is connected with motherboard through TFT interface. After being processed, real-time operating parameters are displayed on LCD. The working time, work cycle times, alarm, overweight and ultar-torque information will be stored into database automatically. For meeting the needs of different users, the video module is compatible with 5.7, 8.4 or 10.4 inches of color display.Touch screen is connected with embedded motherboard by touch screen interface, so human machine interaction is realized. Initialization, data download, alarm information inquire, parameter modification can be finished through touch screen.Speaker is linked with audio interface, thus alarm signals is human voice signal, not harsh buzz.USB interface can be linked to conventional U disk directly. Using U disk, users can upload basic parameters of tower crane, initialize system, download operating data, which provides the basis for the structural optimization and accident analysis. Software design of the monitoring systemAccording to the modular design principle, the system software is divided into grading encryption module, system update module, parameter settings module, calibration module, data acquisition and processor module, lifting parameters monitoring module, alarm query module, work statistics module.Alarm thresholds are guarantee for safety operation of the tower crane. Operating data of tower crane are the basis of service life prediction, structural optimization, accident analysis, accident responsibility confirmation. According to key field, the database is divided into different security levels for security requirements. Key fields are grade encryption with symmetrical encryption algorithm, and data keys are protected with elliptic curve encryption algorithm. The association is realized between the users’ permission and security grade of key fields, which will ensure authorized users with different grades to access the equivalent encrypted key fields. The user who meets the grade can access equivalent encrypted database and encrypted key field in the database, also can access low-grade encrypted key fields. This ensures the confidentiality and integrity of key data, and makes the system a real black box.The system is divided into operating mode and management mode in order to make the system toggle between the two states conveniently. The default state is operating mode. As long as the power is on, the monitoring system will be started by the system guide program, and monitor the operating state of the tower crane. The real-time operating data will be displayed on the display screen. At the dangerous state, warning signal will be sent to the driver through voice alarm and light alarm, and corresponding control signal will be output to execution unit to cut off relevant power for tower crane’s safety.By clicking at the mode switch button on the initial interface, the toggle can be finished between the management mode and the operating mode. Under the management mode, there are 4 grades encrypted modes, namely the system update, alarm query, parameter setting and data query. The driver only can browse relevant information. Ordinary administrator can download the alarm information for further analysis. Senior administrator can modify the alarm threshold. The highest administrator can reinitialize system to make it adapt to different types of tower crane. Only browse and download function are available in the key fields of alarm inquiry, anyone can't modify the data. The overload fields in alarm database are encrypted, only senior administrator can browse. The sensitive fields are prevented from being tampered to the great extent, which will provide the reliable basis for the structural optimization and accident analysis. The system can be initialized through the USB interface. Before initialization, type, structural parameters, alarm thresholds, control thresholds, lifting torque characteristics of tower crane should be made as Excel files and then converted to XML files by format conversion files developed specially, then the XML files are downloaded to U disk. The U disk is inserted into USB interface, then the highest administrator can initialize the system according to hints from system. After initialization, senior administrator can modify structural parameters, alarm thresholds, control thresholds by clicking on parameters setting menu. So long as users can make the corresponding excel form, the system initialization can be finished easily according to above steps and used for monitoring. This is very convenient for user.Tower crane belongs to mobile construction machinery. Over time, sensor signals may have some drift, so it is necessary to calibrate the system regularly for guaranteeing the monitoring accuracy. Considering the tower is a linear elastic structure, sensors are linear sensors,in calibration linear equation is used:y=kx+b (1)where x is sample value of sensor, y is actual value. k, b are calibration coefficients, and are calculated out by two-points method. At running mode, the relationship between x and y is:y=[(y1-y0)/(x1-x0)](x-x0)+y0 (2)After calibration, temperature drift and creep can be eliminated, so the monitoring accuracy is improved greatly.Lifting torque is the most important parameter of condition monitoring of tower crane. Comparing the real-time torque M(L) with rated torque Me(L), the movement of tower crane can be controlled under a safe status.M (L)= Q (L)×L (3)Where, Q(L)is actual lifting weight, L is trolley luffing. Me(L) = Qe(L)×L (4)Where, Q e(L) is rated lifting weight. The design values of rated lifting weight are discrete, while trolley luffing is continuous. Therefore there is a rated lifting weight in any position. According to the mechanical characteristics of tower crane, the rated lifting weight is calculated out at any point by 3 spline interpolation according to the rated lifting weight at design points.When lifting weight or lifting torque is beyond rated value, alarm signal and control signal will be sent out. The hoist motor with high, medium and low speed is controlled by the ratio of lifting weight Q and maximum lifting weight Qmax,so the hoisting speed can be controlled automatically by the lifting weight. The luffing motor with high and low speed is controlled by the ratio of lifting torque M and rated lifting torque Me. Thus the luffing speed can be controlled by the lifting torque automatically. The flow chart is shown in figure 2. Fig. 2 real-time control of lifting weight and lifting torqueWhen accidents take place, power will be off suddenly. It is vital for identifying accident liability to record the operating data at the time of power-off. If measures are not taken to save the operating data, the relevant departments is likely to shirk responsibility. In order to solve the problem, the power-off protection module is designed. The module can save the operating data within 120 seconds automatically before power is off suddenly. In this 120 seconds, data is recorded every 0.1 seconds, and stores in a 2D array with 6 rows 1200 columns in queue method. The elements of the first line are the recent time (year-month-day-hour-minute-second), the elements of the second line to sixth line are lifting weight, lifting torque, trolley luffing, lifting height and wind speed in turn. The initial values are zero, when a set of data are obtained, the elements in the first column are eliminated, the elements in the backward columns move frontwards, new elements are filled into the last column of the array, so the array always saves the operating data at the recent 120 seconds. In order to improve the real-time property of the response, and to extend the service life of the nonvolatile memory chip EEPROM-93C46, the array is cached in volatile flip SDRAM usually. So long as power-off signal produces, the array will be shift to EEPROM, at once.In order to achieve the task, the external interruption thread and the power-off monitoring thread of program is set up, the power-off monitoring thread of program is the highest priority. These two threads is idle during normal operation. When power is off, the power-off monitoring thread of program can be executed immediately. When power-off is monitored by power-off control circuit, the external interruption pins produces interrupt signal. The ARM microprocessor responds to external interrupt request, and wakes up the processing thread of external interruption, then sets synchronized events as informing state. After receiving the synchronized events, the data cached in SDRAM will be written to EEPROM in time.ConclusionThe general intelligence embedded monitoring system of tower crane, which can be applicable to various types of tower crane operating under any lifting rates, uses U disk with the information of the tower crane to finish the system initialization and fits the lifting torque curve automatically. In dangerous state, the system will give out the voice and light alarm, link with the relay or PLC by the RS485 communication interface, and cut off the power. When power is down suddenly, the instantaneous operating data can be recorded automatically, and stored in a black box, which can be taken as the proof for identifying accident responsibility. The system has been used to monitor the "JiangLu" series of tower cranes successfully, and achieved good social and economic benefits.AcknowledgementsThe authors wish to thank China Natural Science Foundation(50975289), China Postdoctoral Science Foundation(20100471229), Hunan science & technology plan, Jianglu Machinery & Electronics Co. Ltd for funding this work.Reference Leonard Bernold. Intelligent Technology for Crane Accident Prevention. Journal of Construction Engineering and Management. 1997, 9: 122~124.Gu Lichen,Lei Peng,Jia Yongfeng. Tower crane' monitor and control based on multi-sensor. Journal of Vibration, Measurement and Diagnosis. 2006, 26(SUPPL.): 174-178.Wang Ming,Zhang Guiqing,Yan Qiao,et, al. Development of a novel black box for tower crane based on an ARM-based embedded system. Proceedings of the IEEE International Conference on Automation and Logistics. 2007: 82-87.Wang Renqun, Yin Chenbo, Zhang Song, et, al. Tower Crane Safety Monitoring and Control System Based on CAN Bus. Instrument Techniques and Sensor. 2010(4): 48-51.Zheng Conghai,Li Yanming,Yang Shanhu,et, al. Intelligent Monitoring System for Tower Crane Based on BUS Architecture and Cut IEEE1451 Standard. Computer Measurement & Control. 2010, 18, (9): 1992-1995.Yang Yu,Zhenlian Zhao,Liang Chen. Research and Design of Tower Crane Condition Monitoring and Fault Diagnosis System. 2010 Proceedings of International Conference on Artificial Intelligence and Computational Intelligence. 2010: 405-408.Yu Yang, Chen Liang, Zhao Zhenlian. Research and design of tower crane condition monitoring and fault diagnosis system. International Conference on Artificial Intelligence and Computational Intelligence, 2010, 3: 405-408.Chen Baojiang, Zeng Xiaoyuan. Research on structural frame of the embedded monitoring and control system for tower crane. 2010 International Conference on Mechanic Automation and Control Engineering. 2010: 5374-5377.

Micro-vibrations generated by rotating machinery could influence the working performance of the precise instruments equipped in industrial facilities, aircraft, ships, etc. Isolation systems are thus essential for preventing the high-sensitive instruments from being disturbed. In this work, a 6 degrees-of-freedom (DOF) micro-vibration isolation platform is proposed based on the quasi-zero-stiffness (QZS) isolator. The structure of the isolation platform is a conventional Stewart mechanism equipped with the QZS isolators in each leg. To analyze the stiffness of the leg, the static analysis is carried out. Afterwards, the stiffness of the platform in six directions are also discussed. Moreover, the dynamical equations of the isolation platform are formulated by the Lagrange Equation. Finally, the dynamic response of the proposed model is investigated and compared with the linear case whose stiffness of the leg is linear. The results show that the newly designed QZS platform in this work has a good isolation performance, which can attenuate the external vibrations significantly within a broad frequency band. Parametric analysis shows that the structure parameters, damping and excitation amplitude have a great influence on the isolation performance of the QZS platform. Delightfully, the result of indicates that, (a) the newly designed QZS platform is able to provide an excellent isolation performance in all the six DOFs, which advances the dynamic study of multi-dimensional QZS vibration isolation; (b) The multi-dimensional vibration isolation platform is innovatively designed using geometric nonlinear technology, there is no influence of the magnetic sources to the precision instruments when compared with the previous designs; (c) the regulation mechanism of the structure parameters of the QZS isolation platform on the dynamic transmission characteristics of the system is revealed, which indicates that the platform is particularly suitable for micro-vibration isolation whose vibration magnitude and frequency are quite low.

With the development of aerospace technology, more and more scientific activities are carried out in the universe. Due to the microgravity environment of space, the control of the 6-DOF platform is different from those on the earth. First, a virtual prototype model of the 6-DOF non-contact platform was built in ADAMS. The dynamics model was developed based on the Newton–Euler method. Then, the 6-DOF backstepping sliding mode controller and disturbance observer were designed in MATLAB/Simulink. Finally, by combining the virtual prototype model in ADAMS and the control system in MATLAB, the co-simulation model was proposed. According to the simulation results, the 6-DOF backstepping sliding mode controller can well complete the positioning, 3D trajectory tracking, and vibration isolation tasks of non-contact 6-DOF platform. Quantitatively, the spatial error of backstepping sliding mode controller’s 3D trajectory tracking is only 50% of the ordinary sliding mode control and it is 20% of the nonlinear propotional-derivative-integral.