An analytical design approach for self-powered active lateral secondary suspensions for railway vehicles

In this paper, an analytical design approach for the development of self-powered active suspensions is investigated and is applied to optimise the control system design for an active lateral secondary suspension for railway vehicles. The conditions for energy balance are analysed and the relationship between the ride quality improvement and energy consumption is discussed in detail. The modal skyhook control is applied to analyse the energy consumption of this suspension by separating its dynamics into the lateral and yaw modes, and based on a simplified model, the average power consumption of actuators is computed in frequency domain by using the power spectral density of lateral alignment of track irregularities. Then the impact of control gains and actuators’ key parameters on the performance for both vibration suppressing and energy recovery/storage is analysed. Computer simulation is used to verify the obtained energy balance condition and to demonstrate that the improved ride comfort is achieved by this self-powered active suspension without any external power supply.     

Development of Preview Active Suspension Control System and Performance Limit Analysis by Trajectory Optimization

The main role of the suspension system is to achieve ride comfort by reducing vibrations generated by the road roughness. The active damper is getting much attention due to its reduced cost and ability to enhance ride comfort especially when the road ahead is measurable by an environment sensor. In this study a preview active suspension control system was developed in order to improve ride comfort when the vehicle is passing over a speed bump. The control system consists of a feedback controller based on the skyhook logic and a feedforward controller for canceling out the road disturbance. The performance limit for the active suspension control system was computed via trajectory optimization to provide a measure against which to compare and validate the performance of the developed controller. The simulation results indicated that the controller of this study could enhance ride comfort significantly over the active suspension control system employing only the skyhook feedback control logic. Also the developed controller, by displaying similar control pattern as the trajectory optimization during significant time portions, proved that its control policy is legitimate.     

Designing a non-linear tracking controller for vehicle active suspension systems using an optimization process

In this paper, a new non-linear tracking controller for vehicle active suspension systems is analytically designed using an optimization process. The proposed scheme employs a realistic non-linear quarter-car model, which is composed of a hardening spring and a quadratic damping force. The control input is the external active suspension force and is determined by minimizing a performance index defined as a weighted combination of conflicting objectives, namely ride quality, handling performance and control energy. A linear skyhook model with standard parameters is used as the reference model to be tracked by the controller. The robustness of the proposed controller in the presence of modeling uncertainties is investigated. The performed analysis and the simulation results indicate that both vehicle ride comfort and handling performance can be improved using the minimum external force when the proposed non-linear controller is engaged with the model. Meanwhile, a compromise between different objectives and control energy can easily be made by regulating their respective weighting factors, which are the free parameters of the control law.     

Adaptive sliding control of active suspension systems with uncertain hydraulic actuator dynamics

An adaptive sliding controller is proposed in this article to control the active suspension systems of a quarter-car model with hydraulic actuator. The highly nonlinear actuator dynamics is assumed to have some time-varying uncertainties with unknown bounds. Owing to its time-variant nature, traditional adaptive designs are not feasible. As the variation bounds are not given, the conventional robust controllers cannot be applied either. In this article, we use the function approximation technique to represent the uncertainties with finite combinations of some basis functions, and the Lyapunov method is employed to find update laws for the coefficients of the approximating series. The actuator force can track the desired force generated from the skyhook dynamics with ultimately bounded performance. If a sufficient number of basis functions are used and the approximation error can be ignored, asymptotic convergence performance can be proved. If the bound of the approximation error is available, asymptotic convergence of the output error still can be obtained with some modifications of the proposed control law. Simulation results show that the controller proposed can give significant improvement of ride comfort when compared with the performance of its passive counterpart.     

汽车辅助驾驶系统上位控制方法研究

在建立两辆汽车组成的动力学系统模型基础上，应用线性二次型最优理论及时间－能量最优理论研究了汽车辅助驾驶系统上位控制方法。针对现有方法存在的问题，将LQ法及时间－能量最优法相结合，提出了一种改进的上位系统控制方法。理论分析及仿真试验结果表明，新的控制方法在满足安全性和舒适性要求的同时，显著降低了系统的响应时间。     

A new active variable stiffness suspension system using a nonlinear energy sink-based controller

This paper presents the active case of a variable stiffness suspension system. The central concept is based on a recently designed variable stiffness mechanism which consists of a horizontal control strut and a vertical strut. The horizontal strut is used to vary the load transfer ratio by actively controlling the location of the point of attachment of the vertical strut to the car body. The control algorithm, effected by a hydraulic actuator, uses the concept of 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 at a relatively lower cost compared to the traditional active suspension using the skyhook concept. 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.     

New insights from fractional order skyhook damping control for railway vehicles

Active suspensions for railway vehicles have been a topic of research for a number of decades and while their applications in service operation are limited, it seems clear that they will in due course see widespread adoption. Railway suspension design is a problem of compromise on the non-trivial trade-off of ride quality versus track following (guidance), and the skyhook damping control approach has been paramount in illustrating the potential benefits. Since skyhook damping control, various advanced control studies appeared contributing to redefine the boundaries of the aforementioned trade-off. Yet there is no study on the impact of fractional order (FO) methods in the context of skyhook railway active suspensions and in particular related to skyhook damping control. This is the area to which this paper strongly contributes. We present findings from a current project on FO controllers for railway vehicles active suspensions, in particular work on the effect of FO methods in basic skyhook damping control schemes, i.e. pure and intuitively based skyhook. First, we present a brief review of conventional skyhook damping control and then proceed to a rigorous investigation of the impact of FO on the ride quality/track following trade-off. The relevant benefits from FO methods are appraised and new insights highlighted.     

基于SIMULINK的车辆主动悬架LQG控制仿真研究

通过建立1／4车辆模型,应用最优控制理论进行了车辆主动悬架的LQG(Linear Quadratic Gaussian)控制器的设计,并在Matlab／Simulink环境中建立系统模型并进行仿真,将仿真结果与被动悬架仿真结果进行对比分析。仿真结果表明,具有LQG控制器的主动悬架对车辆行驶平顺性和乘坐舒适性的改善有良好的效果。     

A novel neuro-fuzzy controller to enhance the performance of vehicle semi-active suspension systems

This paper proposes a neuro-fuzzy (NF) strategy to implement semi-active suspension in passenger vehicles. The proposed method is composed of two parts: a NF controller (NFC), to establish an efficient controller strategy to improve ride comfort and road handling (RCH), and an inverse mapping to estimate the semi-active suspension current. To effectively estimate the current needed to control the semi-active damper, an inverse mapping based on neural network, modified back-propagation (MBP) is presented. The inverse mapping is incorporated into the FC to enhance RCH. Given the relative velocity between the mass and the base and also the absolute acceleration of the mass, the FC computes the optimum damping coefficient. The fuzzy logic rules are extracted based on expert knowledge encapsulated in skyhook and groundhook. A quarter-car model was adopted for the purpose of simulating and experimenting with the proposed NFC. To verify the performance of the FC, two sets of results are reported. First, an experimental analysis was performed to demonstrate the effectiveness of the FC in comparison with the benchmark skyhook and Rakheja–Sankar controllers. Furthermore, a random input was considered to examine the robustness of the NFC in comparison with the other adopted controllers. It was shown that the developed NFC control enhances the performance of the quarter-car system significantly, in terms of both ride comfort and handling characteristics. Second, four FCs with the same control strategies were implemented on a full-vehicle model to demonstrate the effectiveness of the proposed control strategy in reducing the propensity to rollover. It was concluded that the developed FC enhances the RHC and also has the potential to increase the stability of vehicles.     

Comparison between different sets of suspension parameters and introduction of new modified skyhook control strategy incorporating varying road condition

This study examines the uncertainties in modelling a quarter car suspension system caused by the effect of different sets of suspension parameters of a corresponding mathematical model. To overcome this problem, 11 sets of identified parameters of a suspension system have been compared, taken from the most recent published work. From this investigation, a set of parameters were chosen which showed a better performance than others in respect of peak amplitude and settling time. These chosen parameters were then used to investigate the performance of a new modified continuous skyhook control strategy with adaptive gain that dictates the vehicle's semi-active suspension system. The proposed system first captures the road profile input over a certain period. Then it calculates the best possible value of the skyhook gain (SG) for the subsequent process. Meanwhile the system is controlled according to the new modified skyhook control law using an initial or previous value of the SG. In this study, the proposed suspension system is compared with passive and other recently reported skyhook controlled semi-active suspension systems. Its performances have been evaluated in terms of ride comfort and road handling performance. The model has been validated in accordance with the international standards of admissible acceleration levels ISO2631 and human vibration perception.     

汽车磁流变半主动悬架自适应模糊控制研究

针对汽车磁流变半主动悬架存在非线性及不确定性等因素而难以控制的问题,提出采用自适应模糊控制策略并进行了研究。在分析磁流变减振器输入输出特性的基础上,针对1/4车辆悬架模型设计了自适应模糊控制器并进行了仿真分析。以某微型车为试验用车,搭建了平顺性道路试验系统,进行了不同车速、不同控制策略(自适应模糊控制和天棚控制)下的随机路面试验,试验结果与仿真结果相吻合,说明将自适应模糊策略应用于半主动控制是可行的,能够抑制车身的垂直振动,提高乘坐的舒适性,且控制效果要优于天棚控制。     

Level and attitude control of the active suspension system with integral and derivative action

A 7-DOF full-car model with optimal active control suspension is utilized to evaluate the vehicle dynamic performances which are achieved through proposed controllers. The optimal controller, which includes the integral action for the suspension deflection, considerably improves the attitude control of a vehicle because the rolling and pitching motion in cornering and braking maneuvers are reduced, respectively. In the viewpoint of level control, the integral control acting on the suspension deflection results in the zero steady-state deflection in response to static body forces and ramp road input. The dynamic characteristics of the suspension control system are evaluated in terms of time domain and frequency domain. The simulations in the time domain demonstrate the advantages of the active suspension system obtained by penalizing the integral and derivative of suspension deflections and the derivative of roll and pitch angles in the performance index. The frequency characteristic curves obtained by simulations regarding integral action or derivative action show the increase of both ride comfort and road-holding performances by maximizing the use of suspension deflections. The potential of derivative control is shown by the performances of the car traveling over a bump and braking.     

Level and attitude control of the active suspension system with integral and derivative action

A 7-DOF full-car model with optimal active control suspension is utilized to evaluate the vehicle dynamic performances which are achieved through proposed controllers. The optimal controller, which includes the integral action for the suspension deflection, considerably improves the attitude control of a vehicle because the rolling and pitching motion in cornering and braking maneuvers are reduced, respectively. In the viewpoint of level control, the integral control acting on the suspension deflection results in the zero steady-state deflection in response to static body forces and ramp road input. The dynamic characteristics of the suspension control system are evaluated in terms of time domain and frequency domain. The simulations in the time domain demonstrate the advantages of the active suspension system obtained by penalizing the integral and derivative of suspension deflections and the derivative of roll and pitch angles in the performance index. The frequency characteristic curves obtained by simulations regarding integral action or derivative action show the increase of both ride comfort and road-holding performances by maximizing the use of suspension deflections. The potential of derivative control is shown by the performances of the car traveling over a bump and braking.     

State observer-based sliding mode control for semi-active hydro-pneumatic suspension

This paper proposes an improved virtual reference model for semi-active suspension to coordinate the vehicle ride comfort and handling stability. The reference model combines the virtues of sky-hook with ground-hook control logic, and the hybrid coefficient is tuned according to the longitudinal and lateral acceleration so as to improve the vehicle stability especially in high-speed condition. Suspension state observer based on unscented Kalman filter is designed. A sliding mode controller (SMC) is developed to track the states of the reference model. The stability of the SMC strategy is proven by means of Lyapunov function taking into account the nonlinear damper characteristics and sprung mass variation of the vehicle. Finally, the performance of the controller is demonstrated under three typical working conditions: the random road excitation, speed bump road and sharp acceleration and braking. The simulation results indicated that, compared with the traditional passive suspension, the proposed control algorithm can offer a better coordination between vehicle ride comfort and handling stability. This approach provides a viable alternative to costlier active suspension control systems for commercial vehicles.     

基于免疫算法的汽车主动悬架控制研究

应用免疫算法理论,以车身垂直加速度、悬架动行程和车轮动载为控制目标,设计了基于汽车1/4模型的主动悬架控制策略。该算法利用信息熵作为评价抗体亲和力的指标,具有多样识别能力、强鲁棒性和免疫记忆功能。仿真结果表明,基于免疫控制器的主动悬架对汽车的平顺性和操纵稳定性有较明显的改善。     

汽车转向与悬架系统的集成控制研究

在建立了汽车转向与悬架系统的综合模型的基础上,运用一种具有扩展的调节器结构LQG控制方法,设计了 主动悬架控制器,实现对车身横摆角速度、车身垂直加速度、车身侧倾角和俯仰角的集成控制,从而显著提高汽车的 平顺性、操纵稳定性和安全性。     

电磁主动悬架的设计及仿真研究

基于电磁学原理,利用电磁铁作为主动悬架的作动器,构造出电磁作动器的一般结构。在1/4汽车悬架的基础上,建立了电磁主动悬架的非线性模型,并应用现代控制理论设计了该模型的次优控制器,对该模型进行分析、仿真。模拟结果表明,电磁悬架能够实现一般主动悬架的功能,满足车辆平顺性的要求,可以适用于汽车的悬架系统。     

Semi-active control of tracked vehicle suspension incorporating magnetorheological dampers

In past years, the application of magnetorheological (MR) and electrorheological dampers in vehicle suspension has been widely studied, mainly for the purpose of vibration control. This paper presents theoretical study to identify an appropriate semi-active control method for MR-tracked vehicle suspension. Three representative control algorithms are simulated including the skyhook, hybrid and fuzzy-hybrid controllers. A seven degrees-of-freedom tracked vehicle suspension model incorporating MR dampers has been adopted for comparison between the performance of the three controllers. The model differential equations are derived based on Newton's second law of motion and the proposed control methods are developed. The performance of each control method under bump and sinusoidal road profiles for different vehicle speeds is simulated and compared with the performance of the conventional suspension system in time and frequency domains. The results show that the performance of tracked vehicle suspension with MR dampers is substantially improved. Moreover, the fuzzy-hybrid controller offers an excellent integrated performance in reducing the body accelerations as well as wheel bounce responses compared with the classical skyhook and hybrid controllers.     

电液主动悬架的H_∞控制研究

对用流量伺服阀构成的电液主动悬架进行了系统分析,并将其简化为H_∞标准问题,设计了基于干扰抑制指标的H_∞控制器。仿真和实验结果表明,设计出的H_∞最优控制器有良好的控制效果,同时可以对系统的总体性能进行优化,是一种适合主动悬架控制多目标特点的控制器。     

汽车主动悬架自调整模糊控制试验

以汽车操纵稳定性及行驶平顺性为控制目标,提出一种在线可调整的模糊控制算法,其模糊控制规则表可以用解析的方法进行计算。针对简化的汽车模型,为控制悬架系统的振动设计了自调整模糊控制器。与自适应控制主动悬架系统相比较,在两自由度悬架系统试验台架上进行了对比试验研究,结果表明该算法对汽车的振动控制具有明显效果,进一步说明提出的算法对汽车悬架系统的振动控制具有较好的适应性。