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.     

An Active Suspension with Optimal Linear State Feedback

SUMMARY

In this paper modern optimal control theory is applied to the design of an active suspension system for a motor vehicle. The road profile is assumed to be continuous and random with a power spectral density (P.S.D.) which varies inversely with the square of the frequency. The quadratic integral type performance index employed is a weighted sum of the integral squares of body acceleration, dynamic tyre deflection and relative body-to-axle displacement. A solution is obtained for the infinite time case which is both computationally and physically realizable as an active suspension in which the only continuous measurements required are the body absolute velocity and the body displacement relative to the road. The performance is compared with that of a conventional type passive suspension and found to be significantly better in practically all respects.     

An Active Suspension with Optimal Linear State Feedback

In this paper modern optimal control theory is applied to the design of an active suspension system for a motor vehicle. The road profile is assumed to be continuous and random with a power spectral density (P.S.D.) which varies inversely with the square of the frequency. The quadratic integral type performance index employed is a weighted sum of the integral squares of body acceleration, dynamic tyre deflection and relative body-to-axle displacement. A solution is obtained for the infinite time case which is both computationally and physically realizable as an active suspension in which the only continuous measurements required are the body absolute velocity and the body displacement relative to the road. The performance is compared with that of a conventional type passive suspension and found to be significantly better in practically all respects.     

Designing H∞/GH 2 static-output feedback controller for vehicle suspensions using linear matrix inequalities and genetic algorithms

This paper presents an approach to design the H_∞/GH ₂ static-output feedback controller for vehicle suspensions by using linear matrix inequalities (LMIs) and genetic algorithms (GAs). Three main performance requirements for an advanced vehicle suspension are considered in this paper. Among these requirements, the ride-comfort performance is optimized by minimizing the H_∞ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road-holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H₂ (GH ₂) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH ₂ norm as well. A four-degree-of-freedom half-car model with active suspension system is applied in this paper. Several kinds of H_∞/GH ₂ static-output feedback controllers, which use the available sprung mass velocities or the suspension deflections as feedback signals, are obtained by using the GAs to search for the possible control gain matrices and then resolving the LMIs together with the minimization optimization problem. These designed H_∞/GH ₂ static-output feedback controllers are validated by numerical simulations on both the bump and the random road responses which show that the designed H_∞/GH ₂ static-output feedback controllers can achieve similar or even better active suspension performances compared with the state-feedback control case in spite of their simplicities.     

汽车主动悬架的单神经元自适应控制

在1/4汽车动力学模型的基础上,设计了汽车主动悬架的自适应神经元控制器。以车辆的行驶平顺性为主要控制目标,车身垂直加速度、悬架动挠度、车轮动位移为具体评价参数,研究了系统在随机路面激励条件下的时域响应,计算了振动响应的均方根值,考察了在变参数条件下控制器的鲁棒性。仿真结果表明,该控制器能有效改善车辆的综合性能,尤其是平顺性和舒适性,并且具有较好的鲁棒性,对模型参数的变化有一定的适应性。     

Optimisation of active suspension control inputs for improved performance of active safety systems

A collocation-type control variable optimisation method is used to investigate the extent to which the fully active suspension (FAS) can be applied to improve the vehicle electronic stability control (ESC) performance and reduce the braking distance. First, the optimisation approach is applied to the scenario of vehicle stabilisation during the sine-with-dwell manoeuvre. The results are used to provide insights into different FAS control mechanisms for vehicle performance improvements related to responsiveness and yaw rate error reduction indices. The FAS control performance is compared to performances of the standard ESC system, optimal active brake system and combined FAS and ESC configuration. Second, the optimisation approach is employed to the task of FAS-based braking distance reduction for straight-line vehicle motion. Here, the scenarios of uniform and longitudinally or laterally non-uniform tyre–road friction coefficient are considered. The influences of limited anti-lock braking system (ABS) actuator bandwidth and limit-cycle ABS behaviour are also analysed. The optimisation results indicate that the FAS can provide competitive stabilisation performance and improved agility when compared to the ESC system, and that it can reduce the braking distance by up to 5% for distinctively non-uniform friction conditions.     

Optimal Linear Active Suspensions with Multivariable Integral Control

In this paper, an optimal suspension system is derived for a quarter-car model using multivariable integral control. The suspension system features two parts. The first part is an integral control acting on suspension deflection to ensure zero steady-sate offset due to body and maneuvering forces as well as road inputs. The second is a proportional control operating on the vehicle system states for vibration control and performance improvement. The optimal ride performance of the active suspensions based on linear full-state feedback control laws with and without integral control together with the performance of passive suspensions are compared.     

Designing H ∞/GH 2 static-output feedback controller for vehicle suspensions using linear matrix inequalities and genetic algorithms

This paper presents an approach to design the H _∞/GH ₂ static-output feedback controller for vehicle suspensions by using linear matrix inequalities (LMIs) and genetic algorithms (GAs). Three main performance requirements for an advanced vehicle suspension are considered in this paper. Among these requirements, the ride-comfort performance is optimized by minimizing the H _∞ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road-holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H ₂ (GH ₂) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH ₂ norm as well. A four-degree-of-freedom half-car model with active suspension system is applied in this paper. Several kinds of H _∞/GH ₂ static-output feedback controllers, which use the available sprung mass velocities or the suspension deflections as feedback signals, are obtained by using the GAs to search for the possible control gain matrices and then resolving the LMIs together with the minimization optimization problem. These designed H _∞/GH ₂ static-output feedback controllers are validated by numerical simulations on both the bump and the random road responses which show that the designed H _∞/GH ₂ static-output feedback controllers can achieve similar or even better active suspension performances compared with the state-feedback control case in spite of their simplicities.     

DISCUSSION NOTE on Karnopp's article “Active Damping in Road Vehicle Suspension Systems”

SUMMARY

In this paper, an optimal suspension system is derived for a quarter-car model using multivariable integral control. The suspension system features two parts. The first part is an integral control acting on suspension deflection to ensure zero steady-sate offset due to body and maneuvering forces as well as road inputs. The second is a proportional control operating on the vehicle system states for vibration control and performance improvement. The optimal ride performance of the active suspensions based on linear full-state feedback control laws with and without integral control together with the performance of passive suspensions are compared.     

汽车在对开路面上的制动稳定性研究

以汽车动力学模型和汽车制动稳定性控制原理为基础,通过分析汽车两侧车轮在路面附着系数相差较大的对开路面上的紧急制动状况进行理论分析,提出运用主动转向技术控制汽车的方向稳定性,并使汽车在制动驶偏后能快速通过转向控制恢复到正确的行驶车道。     

汽车爆胎特性建模与主动制动控制策略

为了提高汽车在突发爆胎事故时的稳定性,对爆胎汽车主动制动控制策略进行了研究。根据车轮爆胎时间与压力变化的关系,在UniTire模型基础上建立了爆胎模型;根据电子稳定性控制系统中横摆角速度及质心侧偏角对汽车稳定性影响的关系,基于二自由度汽车动力学模型,通过计算汽车横摆角速度及质心侧偏角实际值与理想值的偏差,并基于线性二次型调节器最优控制方法决策出最优附加横摆力矩,从而修正爆胎后汽车的运动状态。最后通过计算机仿真对所提策略的有效性进行了验证。结果表明：主动制动控制策略可以保证爆胎过程中汽车的行驶稳定性和安全性。     

Utilisation of optimisation solutions to control active suspension for decreased braking distance

This work deals with how to utilise active suspension on individual vehicle wheels in order to improve the vehicle performance during straight-line braking. Through numerical optimisation, solutions have been found as regards how active suspension should be controlled and coordinated with friction brakes to shorten the braking distance. The results show that, for the studied vehicle, the braking distance can be shortened by more than 1?m when braking from 100?km/h. The applicability of these results is studied by investigating the approach for different vehicle speeds and actuator stroke limitations. It is shown that substantial improvements in the braking distance can also be found for lower velocities, and that the actuator strokes are an important parameter. To investigate the potential of implementing these findings in a real vehicle, a validated detailed vehicle model equipped with active struts is analysed. Simplified control laws, appropriate for on-board implementation and based on knowledge of the optimised solution, are proposed and evaluated. The results show that substantial improvements of the braking ability, and thus safety, can be made using this simplified approach. Particle model simulations have been made to explain the underlying physical mechanisms and limitations of the approach. These results provide valuable guidance on how active suspension can be used to achieve significant improvements in vehicle performance with reasonable complexity and energy consumption.     

用于电子稳定程序的汽车模型和控制策略

电子稳定程序(ElectronicStabilityProgram)是行驶车辆的一种主动安全系统,它综合了制动防抱死系统,驱动力控制系统和横摆力矩控制系统,使行驶车辆的安全性得到很大的提高。本文首先建立用于电子稳定程序的汽车模型,包括车身模型、悬架模型、转向模型、轮胎模型、制动系统模型、发动机模型和传动系模型。然后建立了主动横摆控制的控制逻辑,通过加入制动防抱死系统和牵引力控制系统,构成了电子稳定程序的控制逻辑。最后对移线运动、紧急转向、制动转向、驱动转向4个典型的工况进行仿真,从而验证了电子稳定程序控制逻辑的正确性。     

Vehicle dynamic stability improvements through gain-scheduled steering and braking control

This paper is concerned with the synthesis of a robust gain-scheduled ?_∞ MIMO vehicle dynamic stability controller (VDSC) involving both steering and rear braking actuators. This VDSC aims at improving automotive vehicle yaw stability and lateral performances. The aim of this work is to provide a methodology to synthesise such a controller while taking into account the braking actuator limitations and use the steering actuator only if it is necessary. These objectives are treated in an original way by the synthesis of a parameter-dependent controller built in the LPV framework and by the solution of an LMI problem. The proposed solution is coupled with a local ABS strategy to guarantee slip stability and make the solution complete. Nonlinear time and frequency domain simulations on a complex full vehicle model (which has been validated on a real car), subject to critical driving situations, show the efficiency and robustness of the proposed solution.     

智能汽车自动紧急转向避撞的跟踪控制方法对比研究

为了提高智能汽车的主动安全性,提出3种不同的自动紧急转向避撞跟踪控制方法。首先建立汽车避撞简化模型,对制动、转向及两者相结合的3种不同避撞方式进行对比分析。其次,为深入研究汽车避撞过程中的实际响应,建立包含转向、制动及悬架3个子系统耦合特性的底盘18自由度统一动力学模型,并进行相关试验验证。随后构建智能汽车自动紧急转向避撞控制框架,对五次多项式参考路径和七次多项式参考路径的横摆角速度和横摆角加速度进行对比分析。接着以线性2自由度转向动力学模型为参考对象,对最优控制四轮转向、最优控制前轮转向、前馈与反馈控制相结合的前轮转向3种不同的跟踪控制系统分别进行设计。最后,以汽车底盘18自由度统一动力学模型为研究对象,对上述3种避撞控制系统进行仿真试验对比分析。研究结果表明：与制动避撞相比而言,转向避撞所需的纵向距离有较大降低,随着车速的增加和路面附着系数的越低,效果越明显;七次多项式参考路径比五次多项式参考路径的避撞过渡过程更为平缓,当实际车速与控制器所用车速不一致时,前者避撞性能表现更优;最优四轮转向控制系统在高、低2种不同附着路面都具有较好的避撞效果,最优前轮转向控制系统次之,而前馈与反馈相结合的前轮转向控制系统在低附着路面上则表现出严重的失稳。     

A Pitch-Plane Model of a Vehicle with Controlled Suspension

A vehicle model incorporating front and rear wheel suspensions and seat suspension is presented. The suspension control includes algorithms to provide both dynamic and steady state (levelling) control. Vehicle response to (a) vertical inputs due to ground disturbances at the wheels and (b) longitudinal inputs due to the inertial forces during braking and accelerating, are investigated. It is shown that the static (self-levelling) control causes a slight deterioration in dynamic performance. The active ride control produces improvements of ride comfort under dynamic conditions compared to an equivalent passively suspended vehicle. In steady state the proposed control eliminates the error heave of the body caused by tilting of the vehicle with active suspension.     

Optimal Active Suspension Design Using a Frequency-shaping PID Filter

By the incorporation of frequency-shaping into the linear quadratic methods used in active suspension design it is possible to achieve improvements in both body frequency response and road-holding. The use of a PID filter for this purpose also leads to robustness of the system to disturbance forces. Zero steady-state deflections are achieved for applied body loads by the integral action with excellent attenuation of the transient response. The resulting system consists of a hydraulic actuator in parallel with a body spring of arbitrary stiffness and is optimal with equivalent full state feedback.     

Performance of Low-bandwidth, Semi-active Damping Concepts for Suspension Control

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.     

电液主动悬架滤波输出反馈控制器的设计及仿真实现

基于1／2车辆模型和非线性电液作动器，提出并详细设计了主动悬架滤波输出反馈控制器。整个主动悬架系统分解为内、外两个回路，外回路采用滤波输出反馈控制，大幅度衰减了车辆在高低频范围内的起伏和俯仰运动，提高了车辆的乘坐舒适性。内回路基于非线性作动器模型，采用传统的PI控制器，较好地跟踪输出了控制系统需要的作用力。此外，还对作动系统的摩擦力进行了详细建模。频域和时域仿真结果演示了主动悬架的良好性能并验证了结论。     

Performance of Low-bandwidth,Semi-active Damping Concepts for Suspension Control

Abstract

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.