Semi-active Variable Stiffness Research Articles

AN INTELLIGENT ISOLATION SYSTEM BASED-ON LONG SHORT-TERM MEMORY MODULE MODEL FOR GROUND MOTION CHARACTERISTICS PREDICTION

An intelligent control system based on a semi-active variable stiffness isolation system and the Long Short-Term Memory (LSTM) is proposed in this study. In the field of semi-active control, the design of control laws relies on the measurement and feedback of the structural response when an earthquake occurs. The optimal control parameters should be determined in real time to achieve the performance-oriented control target by identifying the ground motion characteristics, which have a great influence on the control performance in the early stage. To deploy the optimal control parameters, a LSTM-based module for predicting ground motion characteristics is first proposed. In addition, a sensitivity analysis using the world-wide ground motion database is also conducted, and the representative cases are selected to optimize the fuzzy inference surface for the Leverage-type Stiffness Controllable Isolation System (LSCIS). Numerical simulation indicates, by using the proposed GA-LSTM control system, prominent effect of suppressing the isolation displacement and superstructure acceleration for near-fault and far-field ground motions can be achieved respectively. Series of shaking table tests was also conducted to verify the actual control performance of the proposed system. Both numerical and experimental results have demonstrated that the proposed intelligent control system has high efficiency and reliability to protect the structures from earthquakes of all types of ground motion characteristics.

A Computational Gait Model With a Below-Knee Amputation and a Semi-Active Variable-Stiffness Foot Prosthesis.

Simulations based on computational musculoskeletal models are powerful tools for evaluating the effects of potential biomechanical interventions, such as implementing a novel prosthesis. However, the utility of simulations to evaluate the effects of varied prosthesis design parameters on gait mechanics has not been fully realized due to the lack of a readily-available limb loss-specific gait model and methods for efficiently modeling the energy storage and return dynamics of passive foot prostheses. The purpose of this study was to develop and validate a forward simulation-capable gait model with lower-limb loss and a semi-active variable-stiffness foot (VSF) prosthesis. A seven-segment 28-DoF gait model was developed and forward kinematics simulations, in which experimentally observed joint kinematics were applied and the resulting contact forces under the prosthesis evolved accordingly, were computed for four subjects with unilateral below-knee amputation walking with a VSF. Model-predicted resultant ground reaction force (GRFR) matched well under trial-specific optimized parameter conditions (mean R2: 0.97, RMSE: 7.7% body weight (BW)) and unoptimized (subject-specific, but not trial-specific) parameter conditions (mean R2: 0.93, RMSE: 12% BW). Simulated anterior-posterior center of pressure demonstrated a mean R2 = 0.64 and RMSE = 14% foot length. Simulated kinematics remained consistent with input data (0.23 deg RMSE, R2 > 0.99) for all conditions. These methods may be useful for simulating gait among individuals with lower-limb loss and predicting GRFR arising from gait with novel VSF prostheses. Such data are useful to optimize prosthesis design parameters on a user-specific basis.

A semi-active variable equivalent stiffness and inertance device implemented by an electrical network

Semi-active devices have been widely investigated and applied due to their advantages in control systems. However, for satisfying complicated applications, some semi-active devices need to be capable of controlling multiple mechanical properties, which is hard to implement with a mechanical network considering the space limitation. In this paper, a semi-active variable equivalent stiffness and inertance (VESI) device is developed by an electrical network and an electromagnetic device instead of a mechanical system. Due to that the inerter and spring can store energy, the dynamic control of their mechanical properties without the external power to compensate the stored energy will cause the system discontinuity, which will affect the control performance. Therefore, the variable damping (VD) device is applied to connect with spring or inerter in series to obtain variable equivalent stiffness or inertance properties. Then, according to the force-current analogy, an electrical “VESI” network is designed to simulate the mechanical VESI network. An electromagnetic device equips with the variable electrical system can achieve the VESI mechanical properties, which is validated with experiments. The imaginary part of the admittance of the proposed device can vary to the positive phase and also the negative phase by controlling two resistors. The application of VESI device in the vehicle is investigated and analysed. A semi-active control strategy is designed for vibration control and rollover prevention of vehicles with VESI suspensions. According to the simulation result, the proposed semi-active system can significantly improve the vibration reduction performance at both vertical and roll directions; also, it can decrease the roll angel when vehicles in the cornering maneuver. Besides, the semi-active VESI device with an electrical network has the advantages in installation and maintenance. It has great potential in practical applications.

An Electromagnetic Variable Stiffness Device for Semiactive Seat Suspension Vibration Control

This article introduces a rotary semiactive variable stiffness (VS) device, including its system design and model validation. A variable damping (VD) device and springs can form mechanical networks with specific topologies, and the VD device can control the equivalent stiffness of the network by varying its damping. The proposed rotary electromagnetic VS device consists of an electromagnetic VD device and a torsion spring, which are in series, while a planetary gear reducer is used to amplify the torque output of the VS device. The models of the electromagnetic VD and VS devices are both built and validated with tests. Then, a seat suspension applies the VS device by installing the device in the center of its scissors structure. Bump and random vibration experiments are implemented to validate the effectiveness of the proposed VS system for seat suspension vibration control. The new system has merits in controllability and energy efficiency. It is easier to design the controller than the conventional one with magnetorheological damper due to the linear damping of the electromagnetic VD device. Besides, the system energy consumption is low and has energy harvesting capability. The proposed semiactive electromagnetic VS device also has potential in other practical applicationss.

Research on semi-active vibration isolation system based on electromagnetic spring

This paper proposes a semi-active variable stiffness vibration isolation system based on electromagnetic spring for the low-frequency vibration isolation of mass-varying objects. It is achieved by four straight leaf springs in parallel to an electromagnetic spring system composed of a single electromagnet and a permanent magnet. The equivalent magnetic circuit method is used to compute electromagnetic force of the electromagnetic spring system, and mathematical model of the semi-active vibration isolation system is established according to Maxwell's equations. The nonlinear mathematical model is linearized at the equilibrium point by using the Taylor series expansion theorem to establish linear state-space representation of the system, and then using the traditional PID control method, a double closed-loop feedback control system of the inner current loop and outer location loop is designed. By controlling the current in the coil, the equivalent stiffness and electromagnetic force of the system are variable to achieve semi-active control. Furthermore, the control block diagram of the semi-active vibration isolation system is built based on Simulink software, then make a simulation analysis to the vibration isolation performance of the system and compare the effects of vibration isolation with inner current loop control and without inner current loop control, respectively. Finally, the experiments prove the correctness of the theory. It concludes that this semi-active vibration isolation system is a vibration isolation system with broad application prospects, which has fast current response, high vibration isolation efficiency, and an excellent vibration isolation effect for the low-frequency disturbance of mass-varying objects.

Design and Validation of a Semi-Active Variable Stiffness Foot Prosthesis.

This paper presents the design and validation of a novel lower limb prosthesis called the variable stiffness foot (VSF), designed to vary its forefoot stiffness in response to user activity. The VSF is designed as a semi-active device that adjusts its stiffness once per stride during swing phases, in order to minimize size, mass, and power consumption. The forefoot keel is designed as an overhung composite beam, whose stiffness is varied by moving a support fulcrum to change the length of the overhang. Stiffness modulation is programmed in response to the gait characteristics detected through foot trajectory reconstruction based on an embedded inertial sensor. The prototype VSF has a mass of only 649 g including the battery, and a build height of 87 mm. Mechanical testing demonstrated a forefoot stiffness range of 10-32 N/mm for the prototype, a threefold range of stiffness variation. The stiffness range can be altered by changing the keel material or geometry. Actuation testing showed that the VSF can make a full-scale stiffness adjustment within three strides, and tracks moderate speed-driven variations within one swing phase. Human subjects testing demonstrated greater energy storage and return with lower stiffness settings. This capability may be useful for the modulating prosthesis energy return to better mimic human ankle function. Subjective feedback indicated clear perception by the subjects of contrasts among the stiffness settings, including interpretation of scenarios for which different settings may be beneficial. Future applications of the VSF include adapting stiffness to optimize stairs, ramps, turns, and standing.

Developing a smart structure using integrated DDA/ISMP and semi-active variable stiffness device

Recent studies integrating vibration control and structural health monitoring (SHM) use control devices and control algorithms to enable system identification and damage detection. In this study real-time SHM is used to enhance structural vibration control and reduce damage. A newly proposed control algorithm, including integrated real-time SHM and semi-active control strategy, is presented to mitigate both damage and seismic response of the main structure under strong seismic ground motion. The semi-active independently variable stiffness (SAIVS) device is used as semi-active control device in this investigation. The proper stiffness of SAIVS device is obtained using a new developed semi-active control algorithm based on real-time damage tracking of structure by damage detection algorithm based on identified system Markov parameters (DDA/ISMP) method. A three bay five story steel braced frame structure, which is equipped with one SAIVS device at each story, is employed to illustrate the efficiency of the proposed algorithm. The obtained results show that the proposed control algorithm could significantly decrease damage in most parts of the structure. Also, the dynamic response of the structure is effectively reduced by using the proposed control algorithm during four strong earthquakes. In comparison to passive on and off cases, the results demonstrate that the performance of the proposed control algorithm in decreasing both damage and dynamic responses of structure is significantly enhanced than the passive cases. Furthermore, from the energy consumption point of view the maximum and the cumulative control force in the proposed control algorithm is less than the passive-on case, considerably.

Investigation of Geographical impact on Power Dissipation during simulation of Electronics Design on 28nm FPGA

In this paper, an optimal control matrix, based on the modified differential equation of Riccati, will be formulated, for the active isolation analysis of structures subjected to earthquakes, and a passive mechanical isolator device which is will be also proposed. The combination of the active and the passive isolators compose a Semi-Active Variable Stiffness and Friction Isolator (SAVSFI) model which proposed for the nonlinear analysis of structures subjected to earthquakes. The active feedback gain is determined in terms of the optimal control matrix for which with the passive device model present indeed, new propositions to reduce actively and semi-actively the effect of earthquakes on the responses of civil engineering structures. Three examples of structures (two buildings and a bridge) have been analyzed for the three uncontrolled, active-controlled and semi-active-controlled cases and subjected to a strong earthquake. The results obtained either displacements or stresses for the active and the semi-active cases, show good and excellent reductions, in comparison with those deducted for the uncontrolled cases. This good reduction of the effect of such strong earthquake would be turns to the good formulation of the optimal active feedback gain computed and to the good passive mechanical model proposed.

Vibration control of platform structures with magnetorheological elastomer isolators based on an improved SAVS law

This paper presents a study on the vibration control of platform structures with magnetorheological elastomer (MRE) isolators. Firstly, a novel MRE isolator design is put forward based on the mechanical properties of MREs, and subsequently a single-degree-of-freedom (SDOF) dynamic model and a multiple-degree-of-freedom (MDOF) dynamic model for platform systems incorporating such isolators are developed. In order to overcome the shortcomings of the conventional on–off control law, an improved semi-active variable stiffness (SAVS) control law is proposed. The proposed SAVS scheme makes full use of the continuously variable stiffness of MREs, and it takes into account the influence of the sampling interval such that the field-dependent restoring force is made to do negative work during the whole sampling interval as far as possible. The results of numerical simulations demonstrate that the improved SAVS control law can achieve better vibration-control effectiveness than the on–off control law. The comparative results are discussed through examining the mechanisms of these two control laws in light of the power spectral density and the energy input. For an MDOF platform a simplified approach is proposed to combine the local response signals with an equivalent SDOF representation to generate the control parameters for individual isolators, and the effectiveness of such a scheme is also verified through numerical simulation.

Seismic protection of the horizontally curved bridge with semi-active variable stiffness damper and isolation system

Seismic vibration due to earthquake can damage the curved bridges that are the main interconnecting component for traffic separation structures of the urban highway system. Failure of bridges during and after a seismic event is vulnerable as bridges are lifeline structures. This work investigates the application of semi-active variable stiffness damper for a seismic control of the horizontally curved bridge isolated with different passive devices. The main objectives of the study are to investigate the effectiveness of the hybrid system and to find the optimum hybrid system for the seismic control of the curved bridge with different control laws of a damper. The selected bridge is a three-span continuous concrete box girder supported on pier and rigid abutment. The bridge deck is modeled as a single spine beam and the supporting pier is modeled as linear lumped mass system. The bridge is excited with four different ground motions having different ground motion characteristics with all three-ground motion components (horizontal as well as vertical). The results of the analysis demonstrate that the use of semi-active variable stiffness damper with different isolators is very effective in controlling the response of the curved bridge. The combination of semi-active variable stiffness damper and lead rubber bearing can provide an effective way for overall seismic control of the curved bridge. The use of modified switching control law for damper is as effective as switching control law with less number of sensors.

A New Semiactive Variable Stiffness Suspension System Using Combined Skyhook and Nonlinear Energy Sink-Based Controllers

This paper presents the semiactive case of a variable stiffness suspension system. The central concept is based on a recently designed variable stiffness mechanism that consists of a horizontal strut and a vertical strut, both of which are semiactively controlled by magnetorheological (MR) dampers. The vertical MR damper force is designed to track a skyhook damper force, while the horizontal strut is used is to vary the load transfer ratio by semiactively controlling the location of the point of attachment of the vertical strut to the car body. The control algorithm, effected by the horizontal MR damper, uses the concept of a nonlinear energy sink (NES) to effectively transfer the vibrational energy in the sprung mass to a control mass, thereby reducing the transfer of energy from road disturbance to the car body. The analyses and simulation results show that a better performance can be achieved by subjecting the point of attachment of a suspension system, to the chassis, to the influence of a horizontal NES system.

Seismic response of torsionally coupled building with passive and semi-active stiffness dampers

The seismic response of single-storey, one-way asymmetric building with passive and semi-active variable stiffness dampers is investigated. The governing equations of motion are derived based on the mathematical model of asymmetric building. The seismic response of the system is obtained by numerically solving the equations of motion using state-space method under different system parameters. The switching and resetting control laws are considered for the semi-active devices. The important parameters considered are eccentricity ratio of superstructure, uncoupled lateral time period and ratio of uncoupled torsional to lateral frequency. The effects of these parameters are investigated on peak lateral, torsional and edge displacements and accelerations as well as on damper control forces. The comparative performance is investigated for asymmetric building installed with passive stiffness and semi-active stiffness dampers. It is shown that the semi-active stiffness dampers reduce the earthquake-induced displacements and accelerations significantly as compared to passive stiffness dampers. Also, the effects of torsional coupling on effectiveness of passive dampers in reducing displacements and accelerations are found to be more significant to the variation of eccentricity as compared to semi-active stiffness dampers.

LQR Control of Wind Excited Benchmark Building Using Variable Stiffness Tuned Mass Damper

LQR control of wind induced motion of a benchmark building is considered. The building is fitted with a semiactive variable stiffness tuned mass damper adapted from the literature. The nominal stiffness of the device corresponds to the fundamental frequency of the building and is included in the system matrix. This results in a linear time-invariant system, for which the desired control force is computed using LQR control. The control force thus computed is then realized by varying the device stiffness around its nominal value by using a simple control law. A nonlinear static analysis is performed in order to establish the range of linearity, in terms of the device (configuration) angle, for which the control law is valid. Results are obtained for the cases of zero and nonzero structural stiffness variation. The performance criteria evaluated show that the present method provides displacement control that is comparable with that of two existing controllers. The acceleration control, while not as good as that obtained with the existing active controller, is comparable or better than that obtained with the existing semiactive controller. By using substantially less power as well as control force, the present control yields comparable displacement control and reasonable acceleration control.

Response of piping system with semi-active variable stiffness damper under tri-directional seismic excitation

Seismic loads on piping system due to earthquakes can cause excessive vibrations, which can lead to serious instability resulting in damage or complete failure. In this paper, semi-active variable stiffness dampers (SAVSDs) have been studied to mitigate seismic response and vibration control of piping system used in the process industries, fossil and fissile fuel power plant. The SAVSD changes its stiffness depending upon the piping response and accordingly adds the control forces in the piping system. A study is conducted on the performance of SAVSD due to variation in device stiffness ratios in the switching control law and modified switching control law, which plays an important role in the present control algorithm of the damper. The effectiveness of the SAVSD in terms of reduction in the responses, namely, displacements, accelerations and base shear of the piping system is investigated by comparing uncontrolled responses under four different artificial earthquake motions with increasing amplitudes. The analytical results demonstrate that the SAVSDs under particular optimum parameters are very effective and practically implementable for the seismic response mitigation, vibration control and seismic requalification of piping systems.

Study on the Application of Semi-Active Variable Stiffness Fuzzy Control System to a Residential Building

Based on a steel concrete building, this paper presents a study on the fuzzy control of building vibration. The building structure is simplified into layer model and is applied with a fuzzy control. Three membership functions, Gaussian, triangel and π shap, are used for the simulation. Three earthquake waves, El_centro, Taft and Tianjinghuanhe, are utilized as well. Nine operating modes are proposed for fuzzy control. A series of fuzzy control rules are designed with ground acceleration and mass point displacement being regarded as firstly important components. The simulation results show the control ratio of decreased displacement to the maximum displacement without control varies from 12.67% of Mode I to 36.33% of Mode G. The average control ratio is 23.99%. The fuzzy control system has a quite good control effect on building vibration.

Study on the Application of Semi-Active Variable Stiffness Fuzzy Control System to a Residential Building

Based on a steel concrete building, this paper presents a study on the fuzzy control of building vibration. The building structure is simplified into layer model and is applied with a fuzzy control. Three membership functions, Gaussian, triangel and π shap, are used for the simulation. Three earthquake waves, El_centro, Taft and Tianjinghuanhe, are utilized as well. Nine operating modes are proposed for fuzzy control. A series of fuzzy control rules are designed with ground acceleration and mass point displacement being regarded as firstly important components. The simulation results show the control ratio of decreased displacement to the maximum displacement without control varies from 12.67% of Mode I to 36.33% of Mode G. The average control ratio is 23.99%. The fuzzy control system has a quite good control effect on building vibration.

Semi-active variable stiffness vibration control of vehicle seat suspension using an MRelastomer isolator

This paper presents a study on continuously variable stiffness control of vehicle seatsuspension using a magnetorheological elastomer (MRE) isolator. A concept design for anMRE isolator is proposed in the paper and its behavior is experimentally evaluated. Anintegrated seat suspension model, which includes a quarter-car suspension and a seatsuspension with a driver body model, is used to design a sub-optimal controller for an active isolator. The desired control force generated by this active isolatoris then emulated by the MRE isolator through its continuously variable stiffness propertywhen the actuating condition is met. The vibration control effect of the MRE isolator isevaluated in terms of driver body acceleration responses under both bump andrandom road conditions. The results show that the proposed control strategyachieves better vibration reduction performance than conventional on–off control.

A Novel Semiactive Variable Stiffness Device and Its Application in a New Semiactive Tuned Vibration Absorber

An innovative design for a semiactive variable stiffness (SAVS) device is presented in this paper. This beamlike device is capable of altering its stiffness in a smooth manner between minimum and maximum levels by using the variations of moment of inertia of an area as it rotates around a normal axis passing through its centroid. Analytical expressions for the stiffness of the proposed device have been derived. As an application of the SAVS device in engineering, a semiactive tuned vibration absorber (SATVA) is developed that is capable of real-time retuning and operates effectively in broadband frequency excitations. A single-degree-of-freedom (SDOF) system coupled with the SATVA is considered. The excitation force is assumed to arise from a rotating unbalance whose frequency varies with a constant acceleration and then reaches a steady-state operating condition. The absorber stiffness is varied to tune the absorber’s natural frequency to the forcing frequency in real time. The effectiveness of SATVA is evaluated by comparing the system’s responses with those of the system with passive vibration absorber. The results show the salient features of the proposed SATVA in transient response reduction compared with the traditional passive vibration absorber.

Adaptive passive, semiactive, smart tuned mass dampers: identification and control using empirical mode decomposition, hilbert transform, and short-term fourier transform

Tuned mass dampers (TMD), active mass dampers (AMD) and hybrid mass dampers (HMD) have been widely applied for vibration control of tall buildings and bridges in the past decade. Recently, the author and his coworkers have developed semiactive or smart tuned mass dampers (STMD) using semiactive variable stiffness systems. STMD's are superior than TMD's in reducing the response of the primary structure. In case the fundamental frequency of the primary structure changes due to damage or deterioration, then the TMD will be off-tune; hence, it will lose its effectiveness significantly, whereas the STMD is robust against such changes as it is always tuned. The author and his coworkers have shown that STMD can provide performance similar to AMD/HMD, but with an order of magnitude less power consumption. In this paper, new adaptive length pendulum STMD's are introduced. The concept of adaptive passive tuned mass dampers (APTMD) is introduced. APTMD is a TMD in which a tuning parameter such as frequency is adjusted passively based on some local mechanical feedback (displacement, velocity, rotation, etc.), but without associated sensing and computer feedback needed in a STMD. Also, the concept of STMD is further developed in this paper and practical STMD's and APTMD's implementation in USA, Japan, and China is presented. Systems with semiactive variable stiffness devices and STMD/APTMD are linear time varying systems (LTV); hence, algorithms are needed for their identification and control. Recently, the author and his coworkers have developed instantaneous frequency tracking control algorithms. In this paper new system identification algorithms based on time frequency methods, such as Empirical Mode Decomposition (EMD), Hilbert Transform (HT), and short time Fourier transform (STFT), are developed. New real time tuning algorithms that identify the instantaneous frequency of the LTV system and tune the STMD are developed based on EMD, HT, and STFT. Systems with STMD subjected to stationary (harmonic, sinsweep, and white-noise) and nonstationary (earthquake) excitations are investigated. The effectiveness of the STMD systems and the new identification and control algorithms is demonstrated by means of numerical simulations and experimental validation. Copyright © 2009 John Wiley & Sons, Ltd.

Effect of Geometrical Nonlinearity on the SAVIS Device

The excessive stroke of semi-active variable stiffness-tuned mass damper (SATMD) which causes large distortion is common in practice. The effects of the geometrical nonlinearity of the semi-active variable stiffness (SAVIS) device have been investigated and are described in this paper. An expression which includes the stiffness nonlinearity of the device is obtained. A cubic polynomial model of the equivalent stiffness is approximately obtained using the least squares interpolation method. First, the simplified coupled nonlinear equations with no forcing and no damping are approximately solved using the multiple scale method. The results show that the vibration frequency of the primary system can be modulated by the nonlinearity of the SAVIS device, and the 1:1, 1:3 and 3:1 internal resonance may occur in some conditions. Second, using the Runge-Kutta method, the iteration results are obtained under a full period sine-wave pulse and under the El Centro seismic record. Standard deviation (STD) responses and peak responses of the system are calculated for different damping ratios and different local frequency ratios. The power spectra distribution (PSD) of the response of a nonlinear system shows that the local frequency will be shifted, and the effect on the vibration control of the main structure is much better for a nonlinear case than for a linear case as the frequency ratio is less than one under both the sine-wave pulse and the El Centro seismic excitation.