Skyhook Damper Research Articles

Dynamic modelling and analysis of a physics-driven strategy for vibration control of railway vehicles

This work introduces a new control strategy that prioritises low computational load and ease of implementation, with the objective of enhancing the vertical suspension performance of railway vehicles. The vibration isolation technology that leverages the interaction and combination of structure, device, and control is discussed. The advantage of the combination of structure and control is investigated. The phase–frequency relationship of the control strategy and the dynamic response under various physical structural configurations are analyzed. Furthermore, a physics-driven control strategy is presented, in which the optimised structure can enhance the control effect. To verify the proposed physics-driven strategy, the fundamental mechanism between the control strategy and the physical structure is investigated, and the performance of the physics-driven strategy based on inertial suspensions is verified under modified track irregularity with periodic roughness. The results indicate that the proposed physics-driven strategy can significantly improve the vibration isolation quality. For example, the acceleration of a car body is over 10% lower than that realised with the traditional suspension. Furthermore, the physics-driven control strategy maintains the simplicity of the conventional skyhook damper control. This work proposes a new design principle for vibration control systems that has significant potential for practical applications.

Experimental study on the double-skyhook controls of semi-active suspension with variable inertance and damping

As a conventional control approach, the skyhook damping control algorithm can respond to changes in road circumstances but not to those in load circumstances. The skyhook inertance control algorithm, a newly developed control approach, may adapt to changes in load circumstances rather than in road circumstances. The recent introduction of double-skyhook control algorithms has allowed vehicle suspension systems to accomplish both load and road adaptation. This paper presents an experimental investigation contrasting the performance of the double-skyhook configuration to that of the traditional skyhook damper configuration and the skyhook inerter configuration. By integrating the double-skyhook control strategy with semi-active devices with variable inertance and damping, the paper proposes two strategies for coordinating skyhook inertance and skyhook damping control. A controller using the double-skyhook control strategy is designed to employ the Development to Production rapid control prototyping platform. The controller mode is adjusted using MotoTune software to implement control methods. Three tests were conducted under various road conditions, load conditions, and impact conditions for semi-active suspension. Test results indicate that the double-skyhook configuration considerably enhances driving comfort compared to the single-skyhook configuration. Moreover, the greater the deterioration of road conditions and the decrease in load, the more pronounced the enhancement.

Energy-saving robust control of active suspension system based on bioinspired reference model

This paper proposes an energy-saving robust tracking control method for active suspension systems with a bio-inspired reference model and nonlinear extended state observer (NLESO). According to the principle of cheetah running biology, a bionic structure with nonlinear quasi-zero stiffness is designed, which also has ideal Sky-hook damping and vibration-absorbing mass. An NLESO is designed to estimate the total uncertain disturbance and the state of sprung mass in the suspension system, and then an energy-saving robust tracking controller is proposed. The controller consumes less control energy while isolating the vibration of the sprung mass, thus improving the riding comfort of vehicles and saving energy. The simulation results show that, compared with the reference control method, the vertical acceleration of the sprung mass is reduced by 80.68% and 92.42% respectively in the class C road and bump road conditions and the control energy is decreased by 31.71% and 30.50%, respectively. The control effect of the proposed controller for the active suspension system is verified.

Bifurcation and stability analysis of a high-speed rail vehicle with active yaw dampers

Active yaw dampers (AYDs) show promise in addressing the carbody and bogie hunting issues of high-speed rail vehicles. However, the bifurcation behaviour under active control and the control law for hunting instability still require investigation. This study presents a comprehensive description of the linear control law, which can be simplified to various schemes, including skyhook damping, groundhook stiffness, modal, and blended schemes. The bifurcation behaviour under active control was analysed using a simplified lateral-dynamics-intended seven DOFs vehicle model and verified using a 3D full DOFs model in SIMPACK. Besides the well-known Hopf bifurcation, results also revealed a branching point (BP) and two new stable asymmetric equilibria. Although the asymmetric equilibria born through BP are stable, BP bifurcation should still be avoided for wheel flange contact and derailment concerns. Possible control laws are explored for two hunting scenarios: carbody hunting and bogie hunting. For carbody hunting cases, the control force can be either a linear function of bogie yaw displacement or a linear weighting function of bogie lateral and carbody roll velocity. The dominant frequency of the actuated force falls below 2 Hz, with a peak of 1.6 kN, and the allowable time delay is 70 ms. For bogie hunting cases, the control force can be a linear function of either bogie yaw displacement or velocity. In other words, both the groundhook stiffness and damping strategy are applicable. However, the actuated force contains several relatively high-frequency components (6∼13 Hz), which poses challenges to the control system and actuators, and the allowable time delay is relatively small.

Design, analysis and testing of an inerter-based passive sky-hook damper

The benefits of the sky-hook damper have been intentionally introduced to reduce the resonance peak while maintaining performance in the high-frequency band. However, few results have been reported on passive methods to realize the sky-hook damper effect. This paper proposes a novel inerter-based vibration isolation system exhibiting a passive sky-hook damper effect, i.e., suppressing resonance while ensuring high-frequency attenuation performance without utilizing inertial velocity sensors. Firstly, the mechanism and the structure of the proposed inerter-based sky-hook damper (IPSD) are introduced. Then, the influences of parameters on the performance of the IPSD are studied, including the inertance, the rotational friction, and the magnet pitch. Finally, an IPSD prototype is designed, fabricated, and tested. The experiment results demonstrate that the IPSD can reduce 69% of the peak value of the transmissibility while maintaining a roll-off of −40 dB/Dec in the high-frequency band. This work presents a new approach to realize passive sky-hook damping in a compact way and provides guidelines for designing and analyzing the inerter-based vibration isolator.

Ride Behaviour of Three-Wheel Vehicle using Semi-Active Suspension using Skyhook Control Strategy

This paper analyses the ride behaviour of a 2 degrees of freedom model of three-wheel vehicle subjected to bounce and pitch velocity inputs. This paper also demonstrates the isolation properties of semi-active suspension using skyhook dampers. The results show semi-active suspension can provide isolation near resonance as compared with passive suspension when subjected to bounce and pitch velocity inputs. Below and beyond the resonating frequencies, the behaviour of passive and semi-active suspension is identical for all damping values.

Generalized Skyhook-Groundhook Hybrid Strategy and Control on Vehicle Suspension

This piece of research aims to design and evaluate an impedance-based control for vehicle suspension on the basis of the proposed generalized skyhook-groundhook hybrid strategy. Different from classical impedance control, the proposed impedance-based control optimizes and generalizes the skyhook-groundhook structure from the perspective of complex domain mechanical impedance. A controllable inerter is designed and its nonlinearity is identified based on the bench experiment to realize the proposed impedance-based control. The hybrid weighting coefficient of the skyhook and groundhook in impedance-based control is determined via the 95th percentile aggregate fourth-power force. The numerical analysis demonstrates that the proposed impedance-based control in the ideal model and the nonlinear model can both enhance the suspension performance in ride comfort and road friendly significantly. Furthermore, the impedance-based control can be surprisingly simple as the traditional skyhook damper control and much easier for realization than the feedback-based control strategies. In addition, the influence of nonlinearity and sprung mass on suspension performance verifies that the designed suspension can maintain stability under different working conditions. In conclusion, the impedance-based control manifests a great prospect in vibration control and provides a new design principle for the vibration control system.

Passivity‐based control of nonlinear active dynamic vibration absorber

AbstractIn this article, a nonlinear active dynamic vibration absorber based on passivity‐based energy shaping control is proposed. Using the proposed method, the vibrations that are excited by force and velocity disturbances simultaneously can be controlled. The control law only uses the relative displacement and velocity of the vibration system, which can be easily measured by sensors. The numerical solutions to the partial differential equations are not required in our proposed method. The main idea of the controller's parameters design is to convert a plant system with a nonlinear dynamic vibration absorber into a desired system with multiple virtual skyhook dampers. We also derive the parameters' selection guidelines for the proposed controller. The global asymptotical stability is guaranteed through passivity‐based control theory, although the parameter design is based on linearization. We verify the effectiveness of the proposed controller by some simulations on a cart‐pendulum system.

A Multi-Hook Control Strategy for a Semi-Active Device Combining an Adjustable Inerter and Damper

Neither the separate skyhook damping nor the skyhook inertance control strategy can adapt to the variations of both road and load conditions simultaneously. To address this issue, this work proposed a novel ideal multi-hook system by combining the skyhook inerter and hybrid damper, with both of their coefficients optimized. The proposed system can achieve road holding without sacrificing ride comfort. Depending on whether the inerter and damper were adjusted independently or together, this ideal multi-hook was realized semi-actively in two different control models with three different control strategies, i.e., independent, inertance-based and damping-based control. The effects of these strategies were compared and analyzed. The simulation results show that compared with passive suspension, the root mean square value of body acceleration of the three kinds of multi-hook suspension decreases by more than 40% under different loads and by more than 28% on the roads of Classes A, B and C. Compared with the skyhook damping suspension, the dynamic wheel load of the multi-hook suspensions is reduced by more than 27.5%, proving that the semi-active suspension system with multi-hook control guarantees handling stability under various road and load conditions while ensuring ride comfort.

Semi-active control of crankshaft skyhook based on magnetorheological torsional damper

The purpose of this study was to solve the problem that the damping of rubber or silicone oil torsional dampers used in crankshafts is not adjustable and cannot effectively control torsional vibration at different resonant frequencies. Based on the controlled rheological properties of magnetorheological (MR) smart materials, this study designed a new type of variable damping MR torsional damper (MRTD) and proposed a semi-active control method to effectively control the torsional vibration of the crankshaft under multiple harmonic resonances. First, a mechanical model of the MRTD and a lumped parametric mass model of the crankshaft system were developed, and the resonance frequency harmonic range of the crankshaft system operation was determined by the torsional vibration characteristics analysis. Then a semi-active skyhook control method for the MRTD was proposed, and a joint control simulation analysis was performed using Amesim and Matlab software. The torsional vibration control effects of the crankshaft system with no damper, MRTD with different damping coefficients, and MRTD with skyhook control under acceleration and uniform speed conditions were comprehensively investigated. The simulation results indicated that the skyhook damping control significantly reduced the torsional vibration amplitude under both acceleration and uniform speed conditions, verifying the effectiveness of the skyhook-based control strategy for MRTD.

Hybrid Mass Damper: Theoretical and Experimental Power Flow Analysis

Abstract In this paper, a hybrid mass damper (HMD) and its hyperstability due to a power flow approach are studied. The HMD proposed combines an active control system with an optimal passive device. The initial passive system is an electromagnetic tuned mass damper (TMD) and the control law is a modified velocity feedback with a phase compensator. The resulting hybrid controller system is theoretically hyperstable and ensures fail-safe behavior. Experiments are performed to validate the numerical simulation and provide good results in terms of vibration attenuations. Both excitation from the bottom in the frequency domain and shock response in the time domain are tested and analyzed. The different power flows in terms of active and reactive powers are estimated numerically and experimentally on the inertial damper (passive and active) and on the HMD. Moreover, through a mechanical analogy of the proposed system, it is shown that this hybrid device can be seen as an active realization of an inerter based tuned-mass-damper associated with a sky-hook damper. Observations and analysis provide insight into the hyperstable behavior imposed by the specific control law.

COMBINED CONTROL OF VEHICLE SUSPENSION WITH FRACTIONAL-ORDER MAGNETORHEOLOGICAL FLUID DAMPER MODEL

The fractional-order Bingham model of magnetorheological fluid damper has simple structure and can better describe the hysteretic characteristics of the system. The vibration control of a nonlinear vehicle suspension system with magnetorheological fluid damper under harmonic excitation is studied, where the single-degree-of-freedom 1/4 vehicle suspension system with fractional-order Bingham model of magnetorheological fluid damper is considered. The primary resonance response of suspension system with fractional-order Bingham model under sky-hook damping semi-active control is analyzed, and the approximate analytical solution is obtained by means of averaging method. The amplitude-frequency response equation of the steady-state solution of the suspension system is obtained, and the stability condition of the suspension system is also obtained according to Lyapunov’s stability theory. By comparing the amplitude-frequency response curves of the numerical solution and approximate analytical solution, the accuracy of the approximate analytical solution has been verified. The influence of semi-active control on the ride comfort of the vehicle is illustrated by the root mean square values of acceleration of the sprung mass in the vertical direction, it is found that the semi-active control strategy of sky-hook damping can not improve the ride comfort of vehicle in low frequency excitation region of road. Therefore, a combined control strategy of passive control and semi-active control is proposed, and the influence of semi-active control parameter on the vibration control effect is analyzed. The results show that the combined control strategy can not only improve the ride comfort of the vehicle, but also effectively suppress the primary resonance vibration amplitude of suspension system.

Vibration control of superconducting electro-dynamic suspension train with electromagnetic and sky-hook damping methods

The superconducting electrodynamic suspension (EDS) train, which has reached a manned speed of 603 km/h in 2015, and is therefore regarded as one of the most attractive technologies for the higher speed train. In the superconducting EDS train, the discrete layout of ground null-flux coils causes the additional electromagnetic ripples towards the bogies, making the vibration control more essential to ensure the running performance. In this work, a fourteen-degree-of-freedom dynamics model of superconducting EDS train, was established to explore the effective strategy for vibration reduction. This model uses the time domain wave of track irregularity spectrum as the input of vehicle system. MATLAB/Simulink and "Zhai’s method" are both adopted to solve the vehicle dynamic model and validate the model. Using these models, the effectiveness of the proportional force and maximum force for the primary suspension was examined. The results show that the maximum force strategy has advantage over the proportional force strategy in terms of energy consumption and vibration sensitiveness. However, the electromagnetic damping control can only suppress the vibration of bogie. To achieve an overall vibration control, the "ON-OFF" sky-hook damping was further introduced to the secondary suspension to suppress the vibration of car body. We find that, the control effect is preferable with the damping value being between 5 kN·s/m and 10 kN·s/m. Therefore, the cooperative control, considering both the primary and secondary suspensions, is necessary to meet the Urban Tracked Aircushion Vehicle Standard and provide theoretical supports for the suspension design of superconducting EDS train.

Central Non-Linear Model-Based Predictive Vehicle Dynamics Control

Considering automated driving, vehicle dynamics control systems are also a crucial aspect. Vehicle dynamics control systems serve as an important influence factor on safety and ride comfort. By reducing the driver’s responsibility through partially or fully automated driving functions, the occupants’ perception of safety and ride comfort changes. Both aspects are focused even more and have to be enhanced. In general, research on vehicle dynamics control systems is a field that has already been well researched. With regard to the mentioned aspects, however, a central control structure features sufficient potential by exploiting synergies. Furthermore, a predictive mode of operation can contribute to achieve these objectives, since the vehicle can act in a predictive manner instead of merely reacting. Consequently, this contribution presents a central predictive control system by means of a non-linear model-based predictive control algorithm. In this context, roll, self-steering and pitch behavior are considered as control objectives. The active roll stabilization demonstrates an excellent control quality with a root mean squared error of 7.6953×10−3 rad averaged over both validation maneuvers. Compared to a vehicle utilizing a conventional control approach combined with a skyhook damping, pitching movements are reduced by 19.75%. Furthermore, an understeering behavior is maintained, which corresponds to the self-steering behavior of the passive vehicle. In general, the central predictive control, thus, increases both ride comfort and safety in a holistic way.

Vibration Damping Control for Mobile Scaffolding Device Based on Skyhook Damper Theory

Vibration Damping Control for Mobile Scaffolding Device Based on Skyhook Damper Theory

Hybrid skyhook mass damper

The objective of this study is to increase the efficiency of an initial passive Tuned Mass Damper (TMD) by adding an active control unit. A critical issue in many engineering domains is the design of fail-safe active systems. The proposed hybrid system aims to address this issue and realizes the said objective. It emulates the behavior of a skyhook damper parallel to a passive TMD. Skyhook dampers acts like viscous dampers connected to the ground, reducing the vibration amplitudes without any overshoot. It can be difficult to design a specific control law to obtain a desired dynamical behavior. The paper presents two ways to understand and design the hyperstable control law for Hybrid Mass Damper (HMD) (also called Active TMD), using the power flow formulation or the mechanical impedance analysis. These approaches are illustrated through the synthesis of this hybrid device and the emulation of the Skyhook damper. It is shown that a well-designed control law for this kind of system may result in high damping performance, ensuring stability and a fail-safe behavior. In addition, the amplitude of the primary system’s response is reduced over the entire frequency range which is not the case for the usual active or hybrid systems. Robustness is analyzed and compared to that of the classical active mass damper, and an experimental set up validates the proposed hybrid system.

A Passive Vibration Isolator Integrated a Skyhook Damper or a Groundhook Damper

Presented in this paper is a passive vibration isolator integrated a skyhook damper or groundhook damper. The dynamic behavior of the isolator supporting a lumped mass is investigated using force and displacement transmissibility of the isolator. Force and displacement transmissibility are derived by modelling the new isolator a two-degree-of-freedom system. Numerical simulation and parameter studies of the isolator were performed. It reveals that the new isolator is a passive linear isolator, without any non-linear elements, spring or damper. However, it can bear a large static load and, at the same time, achieve greatly improved vibration isolation without employing high damping element, which is difficult to achieve in practices. Moreover, the implementation of such an isolator in practice is convenient. All these make the isolator attractive for engineering application.

Lateral-vertical coupled active suspension on railway vehicle and optimal control methods

Plenty of studies focused on single-direction active suspensions on railway vehicles; at least four actuators per vehicle are needed forconventional active secondary suspensions in both lateral and vertical directions, leading to a sharp increase in costs and reduction inreliability. This paper proposes a novel configuration, lateral-vertical coupled (LVC) active secondary suspension, with only two actuators and two accelerometers per vehicle. To deal with the coupled dynamics, linear quadratic Gaussian (LQG) method and optimal skyhook damping (OSD) method are developed for achieving optimal control. OSD method has similar advantages as LQG method and is easier to implement. Then, linearised vehicle dynamics is modelled to design the controllers and observer, and a more complete nonlinear simulation model is established for verification. Theoretical analysis and simulation results show that LVC active suspension reduces car body vibration in one direction at the cost of negative effects in the other. LQG control fails to provide satisfying performance compared with passive suspensions, whereas OSD control can effectively improve lateral and vertical vibration and ride comfort by applying reasonable actuator forces. Besides, actuator dynamics is important to the effectiveness of LVC active suspension, and OSD controller is robust to measurement noise and model errors to some extent.

An active hybrid control approach with the Fx-RLS adaptive algorithm for active-passive isolation structures

With improvements in the performance of optical equipment on spacecraft, the requirements for vibration isolation have become increasingly stringent. An efficient and reliable active hybrid control (AHC) approach used for an active-passive isolation single strut (APISS) is proposed in this paper. The APISS adopts an active-passive architecture in series as one single leg of the Stewart platform. To improve performance, the AHC approach includes a modified proportional integration force (PIF) feedback control algorithm and an improved filtered-x recursive least squares (Fx-RLS) adaptive feedforward control algorithm. The PIF is applied to establish a sky-hook damping and variable mass matrix system, and Fx-RLS is employed to compensate the vibration error caused by the base platform to the payload platform. Then, a single-DOF vibration isolation system consisting of a real-time active control system and a spectrum testing and analysis system is adopted to verify the proposed approach. The experimental results indicate that the AHC approach can effectively reduce the natural frequency by 5.02 Hz. Additionally, the resonance amplitude of the natural frequency decreases by 41.84 dB, the vibration attenuation rate reaches 99.2%, and the amplitude of the mid-frequency band is further attenuated. The experimental results highlight the effectiveness of the proposed method.

Optimal response of half car vehicle model with sky-hook damper using LQR with look ahead preview control

This paper addresses the problem of determining the optimal parameters of a sky-hook damper type suspension in the control of the stationary random response of half car vehicle models traversing a rough road with constant velocity. The feedback control scheme is realized by approximating the sky-hook damper strategy, and the optimal parameters of the sky-hook damper are obtained by equating the sky-hook damper suspension force with that of a fully active suspension force using linear quadratic regulator with preview control (LQR with preview control). Results show that the overall performance of the sky-hook damper approximately 99% matches with performance of LQR with preview control (look ahead preview control) over a specified vehicle velocity range.