Semi-active Inerter Research Articles

Design and Experimental Analysis of an Operational Amplifier Circuit-Based Mechatronic Semiactive Inerter

A novel mechatronic semi-active inerter (MSAI) by using an operational amplifier (OPA) circuit-based adjustable capacitor (OPA-CC) is proposed in this study to address the realization challenge of fast-responding semi-active inerters. The fast-responding ability, inertance-directly controlled capability, and sensor-less regulation characteristic are distinctive advantages of the proposed MSAI. To implement a pure controlled capacitor and a pure capacitive motor load (the internal resistance of the motor is canceled), two different types of OPA circuits are designed. Tuned inerter damper (TID) and tuned viscous mass damper (TVMD), as two typical MSAI-based configurations, are established and tested. It is found that the proposed MSAI can modify the inertance quickly (in the microsecond time scale) and reliably, and good congruence between theoretical and experimental results is obtained.

Performance improvement study of nonlinear bionic suspension based on inerter and on–off control strategy

How to improve the dynamic performance of nonlinear suspension systems is a focus of attention. The combination of inerter and on–off control strategy can effectively improve the dynamic performance of linear suspension systems, but it will also bring some adverse effects. This paper puts forward a nonlinear suspension system performance enhancement scheme based on semi-active on–off control strategies of inerter to eliminate the adverse effects of the introduction of the inerter and to enhance the dynamic performance of nonlinear suspension systems. This paper takes the nonlinear double-diamond bionic kangaroo leg suspension system as an example and adopts the above scheme to carry out dynamic modeling, time–frequency domain dynamic characteristics analysis, and control characteristics research. The results show that the dynamic performance of the proposed nonlinear suspension system with passive inerter is partially better than that of the original suspension system in time–frequency domain, while the overall dynamic performance of the proposed nonlinear suspension system with semi-active inerter is better than that of the original suspension system. The proposed nonlinear suspension system with semi-active inerter shows good stability and adaptability under different working conditions, and the proposed control strategies can eliminate the adverse effects of passive inerter. The above results indicate the correctness of the proposed scheme and the effectiveness of the control strategies.

A versatile semi-active magnetorheological inerter with energy harvesting and active control capabilities

Semi-active devices typically adjust the system’s damping coefficient to control vibration, offering advantages such as excellent performance and low power consumption. However, the output force of the traditional variable damping (VD) device can only be opposite to the relative motion direction of the device’s two terminals, which limits the vibration control performance. This paper introduces a versatile semi-active magnetorheological (MR) inerter with three operating modes, the VD, energy harvesting, and active control modes, to break through the performance bottleneck of traditional semi-active devices. The MR inerter combines two MR dampers and a flywheel, acting as the controllable units and energy sink. The built prototype is tested, and its parameters are identified. When the innovative semi-active inerter works with a corresponding control strategy to regulate the current in two MR dampers, it can achieve vibration energy storage and release. The harvested energy can help to reduce the high dependency of the semi-active output force on external inputs. The proposed semi-active inerter has excellent potential in the future applications.

Comfort-Oriented Semi-Active Suspension Configuration with Inerter-Based Network Synthesis

This paper presents a comfort-oriented semi-active suspension system composed of a network-synthesized passive section and a controllable section based on a semi-active inerter. Firstly, the semi-active suspension system is divided into a passive part and a controllable part. For the passive part, first-order and second-order robust positive real controllers are designed. The problem with H2 cost is considered, and the bilinear matrix inequalities (BMI) are solved using an iterative method to obtain two admittance functions. The admittance functions are physically realized as two mechanical networks composed of mechanical passive elements such as inerter, spring, and damper (ISD). Then, the parameters of these mechanical elements in those networks are optimized by Particle Swarm Optimization (PSO). Secondly, a semi-active inerter based on Sky-hook control is introduced for the semi-active part of the suspension system. Finally, the semi-active ISD suspension structure is verified by a quarter vehicle model. The simulation results show that the first-order and second-order suspension systems optimize the RMS of the spring mass acceleration by 14.2% and 23.9%, respectively, as compared to traditional suspension systems. Furthermore, frequency-domain analysis also shows that both suspension systems effectively reduce the value of spring mass acceleration in the low-frequency band.

Inherent stability analysis for multibody systems with semi-active inerters

Inherent stability reflects the reliability performance of a semi-active control system, where for “active” semi-active inerter-based systems, the inherent stability problem has not been studied. The motivation of this paper is to present sufficient conditions that ensure inherent stability for such systems. The absolute stability theory is adopted, and the general multibody system with semi-active inerters is formulated in a Lurè form. Sufficient conditions are derived based on the circle criterion for three different cases including the case with only one semi-active inerter, the case with several semi-active inerters without common connection points, and the case with several semi-active inerters where the ground is the common connection point. Extensive numerical examples based on low-degree-of-freedom systems are provided to show the effectiveness of the derived conditions.

Lever-Based Semiactive Inerter and Its Application in Vibration Absorbers

In this paper, a lever structure is proposed to enlarge the range of inertances of existing semiactive inerters. A semiactive inerter with the lever structure would be called lever-based semiactive inerter. The transmission ratio of the lever-based semiactive inerter can be changed by setting a different ratio of the arm of force of the lever, and then the range of inertance of the lever-based semiactive inerter can be enlarged. This paper also presents the mechanical model of the proposed lever-based semiactive inerter. The lever-based semiactive inerter is applied to an adaptive tuned vibration absorber. The frequency-tracker-based control algorithm is derived to maximize vibration reduction of the absorber. It can be shown that the vibration absorber with the lever-based semiactive inerter can adapt to a broader range of frequencies of vibration compared with that of the classical semiactive inerter.

Mem-inerter: a passive nonlinear element equivalent to the semi-active inerter performing initial-displacement-dependent inertance control strategy

Mem-inerter: a passive nonlinear element equivalent to the semi-active inerter performing initial-displacement-dependent inertance control strategy

Design and testing of a semi-active inerter with magneto-rheological fluid valve

This paper presents a novel semi-active inerter with magneto-rheological fluid valve (SAI-MRFV) for improving semi-active system performances in low-frequency domain. The proposed device is composed of a driver element and two driven elements. Driven element 1 contains a hydraulic motor and a plate. Driven element 2 contains a cylinder, two piston rods, two floating pistons and a MR valve. The two driven elements are connected in parallel. The area between the floating pistons is filled with MR fluid, while other areas of SAI-MRFV are filled with hydraulic oil. With the motion of driver piston, the hydraulic oil will be circulated in driver element and driven elements. The flow rate distribution of hydraulic oil in two driven elements can be changed by controlling the pressure drop of driven element 2. Along with the changing of the hydraulic oil flow rate in hydraulic motor, the inertance and damping can be tuned simultaneously. A novel compact annular-radial-orifice flow MR valve is proposed to provide controllable pressure drop in driven element 2. Besides, a theoretical model was established to describe the characteristics of variable inertance and damping force. Based on the conceptual design and theoretical analysis, a prototype was designed, fabricated and tested. The characteristics of single inerter, single MR valve and SAI-MRFV were obtained by a series of experimental tests. The experimental results show that the inertance and damping can be controlled by the changing current of MR valve.

Application of semi-active inerter in a two-body point absorber via force tracking

In this paper, a self-reaction point absorber (PA) wave energy converter is studied, where wave energy is collected by the relative motion of the on-board plate and the buoy. The purpose of this study is to increase the relative displacement to obtain the maximum power. A semi-active inerter (SAI) is applied in the system, which is controlled by a force-tracking (FT) strategy. Two parts are required in the FT strategy: a target active control law; and a proper control law to adjust the inertance to track the active force (AF). The target control law is obtained by the full-state feedback of the state-space model of a two-body PA . The control law to adjust the inertance is to saturate the AF between the maximal and minimal semi-active force of an SAI. Both linear time-invariant system and linear time-varying system are studied. Power absorption is improved in both two systems by the application of SAIs. Moreover, the influence of dimensionless parameters on the ratio of power absorption improvement in the considered linear time-varying system is studied. Numerical simulation shows that the ratio of power absorption improvement is most sensitive to the changes of mass ratio of the on-board plate and the buoy.

A controllable mechanical motion rectifier-based semi-active magnetorheological inerter for vibration control

The conventional semi-active variable damping (VD) device can only dissipate the vibration energy, which inherently limits its performance in vibration control. This paper proposes a novel semi-active inerter concept and develops a prototype with magnetorheological (MR) dampers, which can store the vibration energy in a flywheel and then release it to suppress vibration. The new idea is inspired by a variable inertance (VI) device, which has a VD device and a passive inerter in serial, and a passive mechanical motion rectifier (MMR), which can convert the reciprocating input into a unidirectional output. The controllable MMR (CMMR) applies two VD devices to replace the two one-way roller clutches in the MMR. By equipping the CMMR, the semi-active inerter gets more controllability than the original VI device because it can switch the torque and motion transmitting routes between the device terminals and the flywheel in it. The frequency-domain analysis validates the versatile of the semi-active inerter, which can work in VD and VI modes. The test results of the semi-active MR inerter prototype are used to identify the device parameters, which are applied for the control simulation. The semi-active MR inerter in CMMR mode has the best torque tracking performance with a given test condition, and it has a 20.13% improvement than in the VD mode. Then, a seat suspension with the semi-active MR inerter is applied to validate the effectiveness of the device in vibration control. The results show that the vibration reduction of the seat suspension in the CMMR mode is 39.3% higher than in the VD mode, which indicates a significant improvement of ride comfort. The new concept of the semi-active device has excellent potential in vibration control and is promising in practical applications.

Integrated Shock Absorber With Both Tunable Inertance and Damping

Inerter is a two-terminal mass element and the applied force is proportional to the relative acceleration between the terminals. According to the second class of mechanical-electrical analogy, the inerter corresponds exactly to the capacitor in the electric network. Aiming at improving the limited vibration isolation performance using constant inertance of conventional inerter, a new semi-active inerter based on smart material, magnetorheological (MR) fluid, is proposed in this paper. Further, according to the design concept of “functional integration”, the MR inerter, an MR damper and a spiral spring are integrated to realize a new integrated inerter-spring-damper (IISD) with both adjustable inertance and damping characteristics. The MR inerter consists of a ball screw, an MR clutch, MR fluid, excitation coils, an excitation shell, a flywheel, a flywheel shell, a connector, upper and lower covers, bearings and seals. The tunable inertance is achieved by adjusting the excitation current in the excitation coils to change the operating state of the MR clutch. The MR damper and the spiral spring provide variable damping and constant stiffness, respectively. The mathematical model of the IISD is established. The adjustment principle of inertance is verified by numerical simulation, and the mechanical output characteristics of the IISD are analyzed. Besides, the 1/4 vehicle suspension model based on the proposed IISD is built by using MATLAB/SimMechanics. The frequency response and unit impulse response characteristics of the suspension are obtained via the comfort-oriented virtual experiment. The simulation results show that the suspension with the IISD has a 23.0% higher performance than the conventional suspension in vehicle body acceleration, and the suspension deflection and dynamic tire load are also improved.

Averaging analysis on a semi-active inerter–based suspension system with relative-acceleration–relative-velocity control

The semi-active inerter–based suspension system with a semi-active inerter is proposed in this article to improve the dynamic performance of the passive one. The fluid inerter is used to implement the semi-active inerter and has two adjustable inertances: the maximum and minimum inertances. Based on the relative acceleration and relative velocity between the unsprung mass and sprung mass of the suspension system, and combined with the mechanical property of the semi-active inerter, the relative-acceleration–relative-velocity control strategy is proposed and has two different types: relative-acceleration–relative-velocity+− and relative-acceleration–relative-velocity−+ control strategies, respectively. The relative-acceleration–relative-velocity+− control strategy means adjusting the inertance of the semi-active inerter to the maximum one when the signs of relative acceleration and relative velocity are the same, and to the minimum one when the signs are the opposite, and the meaning of relative-acceleration–relative-velocity−+ control strategy does the reverse. The dynamic response of the semi-active inerter–based suspension system with the relative-acceleration–relative-velocity control strategy is obtained using the averaging method, and its dynamic performance is evaluated using three performance indices: vehicle body acceleration, dynamic tire load, and suspension system stroke. The results show that the semi-active inerter–based suspension system with the relative-acceleration–relative-velocity+− control strategy can have a better dynamic performance for the dynamic tire load and suspension system stroke in which the low-frequency and high-frequency resonance peaks can be smaller, but is poor for the vehicle body acceleration in which the high-frequency resonance peak can be significantly larger; whereas the relative-acceleration–relative-velocity−+ control strategy does the reverse. For smaller maximum and minimum inertances, the relative-acceleration–relative-velocity+− and relative-acceleration–relative-velocity−+ control strategies can achieve the corresponding better performance indices, with a small degeneration for the other performance indices.

Principle Study of a Semi-active Inerter Featuring Magnetorheological Effect

Inerters are a two-terminal mass element, and the forces applied at their two terminals are proportional to the relative acceleration between the two terminals. The volume and weight of inerters are much smaller than those of any conventional mass element providing a same generated force, which is beneficial to engineering applications. The inerter in mechanical system is completely corresponding to the capacitor in electrical system, which makes it more convenient to do related investigations based on mechanical-electrical analogies. A semi-active inerter (SAI) featuring magnetorheological (MR) effect with tunable inertance is proposed, designed and investigated to enhance the performance of the passive inerters. The proposed SAI consists of a flywheel, a flywheel housing, a ball screw, a connection sleeve, bearings, upper and lower covers, excitation coils and MR fluid. MR fluid fulfilled in the flywheel housing of the SAI is energized by the excitation coils with applied current, and correspondingly the mechanical characteristics of the SAI is tunable via the applied current. The mathematical model and the mechanical performance of the SAI is established and tested, respectively. The nonlinearity of the experimental results is analyzed and the nonlinear model of the SAI is further established. The preliminary principle verification of the continuous adjustment of the equivalent inertance of the SAI is conducted using the nonlinear model. Moreover, a compensator is proposed to address the problem of the phase difference between the controllable force and the real output force of the SAI, and continuous inertance adjustment of the SAI with a compensator is realized and analyzed.

Analytical research on the dynamic performance of semi-active inerter-based vibration isolator with acceleration-velocity-based control strategy

A semi-active inerter-based vibration isolator with semi-active inerter is presented in this paper; the inertance of the semi-active inerter is hierarchically adjusted between two values: the maximum inertance and minimum inertance. On the basis of the mechanical property of the semi-active inerter, two acceleration–velocity-based control strategies are proposed, which are the relative-acceleration–relative-velocity (RARV) control strategy and the relative-acceleration–absolute-velocity (RAAV) control strategy. The dynamic responses of the semi-active inerter-based vibration isolator with the two control strategies are obtained using the averaging method and further checked by the numerical results. Four performance indices are defined to evaluate the isolation performance of the semi-active inerter-based vibration isolator: maximum dynamic displacement, maximum transmissibility, isolation frequency band, and transmissibility in the higher isolation frequency band. The solving process to determine the four performance indices is investigated in detail in the paper. The results show that for the semi-active inerter-based vibration isolator, the maximum dynamic displacement and transmissibility are smaller than the passive one; the latter two performance indices fall in between the value when the maximum inertance and minimum inertance are achieved for the passive one. In addition, the isolation performance of the semi-active inerter-based vibration isolator with the two control strategies are compared based on the four performance indices.

Comfort-oriented vehicle suspension design with skyhook inerter configuration

This paper is concerned with the comfort-oriented vehicle suspension design problem by using a skyhook inerter configuration. The rationale of the skyhook inerter is to use a grounded inerter to virtually increase the sprung mass of a vehicle, as it is analytically demonstrated that increasing the sprung mass can always improve the ride comfort performance. Semi-active means to realize the skyhook inerter configuration are investigated by using semi-active inerters. Three control laws, that is the on-off control, the anti-chatter on-off control, and the continuous control, are proposed for the semi-active inerter to approximate the skyhook inerter. Numerical simulations are performed to demonstrate the effectiveness and performances of these control laws. It is shown that the semi-active realizations of the skyhook inerter by using the proposed control laws can achieve over 10% improvement compared with the traditional strut, and similar performances are obtained for these control laws, with slight differences with respect to different static stiffnesses of the suspension system.

Semiactive Inerter and Its Application in Adaptive Tuned Vibration Absorbers

This brief presents a novel framework to realize the semiactive inerter, and proposes a novel semiactive-inerter-based adaptive tuned vibration absorber (SIATVA). The proposed semiactive inerter can be realized by replacing the fixed-inertia flywheel in the existing flywheel-based inerters with a controllable-inertia flywheel. Then, by using the proposed semiactive inerter, an SIATVA is constructed, and two control methods, that is, the frequency-tracker-based (FT) control and the phase-detector-based (PD) control, are derived. The experimental results show that both the FT control and the PD control can effectively neutralize the vibration of the primary mass, although the excitation frequency may vary. The proposed SIATVA can also tolerate the parameter variation of the primary system. As a result, it can be applied to a variety of primary systems without resetting the parameters. The performance degradation by the inherent damping is also demonstrated.

Application of Semi-Active Inerter in Semi-Active Suspensions Via Force Tracking

This paper investigates the application of semi-active inerter in semi-active suspension. A semi-active inerter is defined as an inerter whose inertance can be adjusted within a finite bandwidth by online control actions. A force-tracking approach to designing semi-active suspension with a semi-active inerter and a semi-active damper is proposed in this paper. Two parts are required in the force-tracking strategy: a target active control law and a proper algorithm to adjust the inertance and the damping coefficient online to track the target active control law. The target active control law is derived based on the state-derivative feedback control methodology in the “reciprocal state-space” (RSS) framework, which has the advantage that it is straightforward to use the acceleration information in the controller design. The algorithm to adjust the inertance and the damping coefficient is to saturate the active control force between the maximal and the minimal achievable suspension forces of the semi-active suspension. Both a quarter-car model and a full-car model are considered in this paper. Simulation results demonstrate that the semi-active suspension with a semi-active inerter and a semi-active damper can track the target active control force much better than the conventional semi-active suspension (which only contains a semi-active damper) does. As a consequence, the overall performance in ride comfort, suspension deflection, and road holding is improved, which effectively demonstrates the necessity and the benefit of introducing semi-active inerter in vehicle suspension.

Semi-active suspension with semi-active inerter and semi-active damper

This paper investigates the application of semi-active inerter in semi-active suspension. A semi-active inerter is defined as an inerter whose inertance can be adjusted within a finite bandwidth by on-line control actions. A force-tracking approach to designing semi-active suspension with a semi-active inerter and a semi-active damper is proposed, where the target active control force derived by LQR control in the “Reciprocal State-Space” (RSS) framework is tracked by controlling the semi-active damping coefficient and semi-active inertance. One of the advantages of the proposed method is that it is straightforward to use the acceleration information in the controller design. Simulation results demonstrate that the semi-active suspension with a semi-active inerter and a semi-active damper can track the target active control force much better than the conventional semi-active suspension (which only contains a semi-active damper) does. As a consequence, the overall performance in ride comfort, suspension deflection and road holding is improved, which effectively demonstrates the necessity and the benefit of introducing semi-active inerter in vehicle suspension.