Generalized magnetorheological (MR) damper model and its application in semi-active control of vehicle suspension system

In this paper, analytical characterization of the magneto-rheological (MR) damper is done using a new modified algebraic model. Algebraic model is also more preferable because of its low computational expenses compared to differential Bouc-Wen’s model which is highly computationally demanding. This model along with the obtained model parameters is used as a semi-active suspension device in a quarter car model and the stationary response of the vehicle traversing on a rough road is obtained. The control part consists of two nested controllers. One of them is the system controller which generates the desired damping force and the other is the damper controller which adjusts the voltage level to MR damper so as to track the desired damping force. For the system controller a model reference skyhook Sliding Mode Controller (SMC) is used and for the damper controller a continuous state algorithm is built to determine the input voltage so as to gain the desired damping force. The analytical model is subsequently used in the quarter car vehicle model and the vehicular responses are studied. A simulation study is performed to prove the effectiveness and robustness of the semi-active control approach. Results show that the semi-active controller can achieve compatible performance as that of active suspension controller except for a little deterioration.     

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.     

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.     

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.     

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.     

The Development and Implementation of Adaptive Semi-Active Suspension Control*

Using adjustable shock absorbers within vehicle suspension systems, it is possible to improve ride comfort significantly when a control strategy is applied based on the so-called skyhook principle. However, the drawback is a poorly damped wheel-hop mode which makes the road holding ability worse. Using adaptive semi-active suspension control based on the tire load variations as introduced in this paper, the trade-off between road holding and ride comfort can be relaxed. Implementation of adaptive skyhook control requires the determination of a number of important and difficult to measure states of the vehicle. This can either be accomplished by several sensors and filters or by a state estimator in combination with less sensors and an internal model of the vehicle. Both methods are discussed. Finally some preliminary test results are discussed.     

Preview suspension control for a full tracked vehicle

In this study, preview control algorithms for the active and semi-active suspension systems of a full tracked vehicle (FTV) are designed based on a 3-D.O.F model and evaluated. The main issue of this study is to make the ride comfort characteristics of a fast moving tracked vehicle better to keep an operator’s driving capability. Since road wheels almost trace the profiles of the road surface as long as the track doesn’t depart from the ground, the preview information can be obtained by measuring only the absolute position or velocity of the first road wheel. Simulation results show that the performance of the sky-hook suspension system almost follows that of full state feedback suspension system and the on-off semi-active system carries out remarkable performance with the combination of 12 on-off semi-active suspension units. The results simulated with 1^st and 2^nd weighting sets mean that the suspension system combined with the soft type of inner suspension and hard type of outer suspension can carry out better ride comfort characteristics than that with identical suspensions. The full tracked vehicle (FTV) system is uncontrollable and the system is split into controllable and uncontrollable subspace using singular value decomposition transformation. Frequency response curves to four types of inputs, such as heaving, pitching, rolling, and warping inputs, also demonstrate the merits of preview control in ride comfort. All the frequency characteristic responses confirm the continuous time results.     

The Development and Implementation of Adaptive Semi-Active Suspension Control*

SUMMARY

Using adjustable shock absorbers within vehicle suspension systems, it is possible to improve ride comfort significantly when a control strategy is applied based on the so-called skyhook principle. However, the drawback is a poorly damped wheel-hop mode which makes the road holding ability worse. Using adaptive semi-active suspension control based on the tire load variations as introduced in this paper, the trade-off between road holding and ride comfort can be relaxed. Implementation of adaptive skyhook control requires the determination of a number of important and difficult to measure states of the vehicle. This can either be accomplished by several sensors and filters or by a state estimator in combination with less sensors and an internal model of the vehicle. Both methods are discussed. Finally some preliminary test results are discussed.     

一种引入行驶状态识别的半主动悬架PID控制修正算法

基于车辆不同行驶状态（路面不平度和车速）下悬挂质量垂向加速度和悬架动挠度响应不相同的客观事实,针对半主动悬架PID控制器无自适应能力的局限,以悬挂质量垂向加速度和悬架动挠度响应作为车辆行驶状态的识别判据．建立起一种引入行驶状态识别的半主动悬架PID控制修正算法,进而以某型轿车为对象,采用MATLAB／Simulink建立起半主动悬架PID控制的仿真模型,针对不同行驶状态计算出PID控制算法修正前、后的车辆平顺性响应并加以对比,表明所提出的PID控制修正算法是有效的。     

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.     

Development of a systematic and practical methodology for the design of vehicles semi-active suspension control system

In this paper, a novel systematic and practical methodology is presented for design of vehicle semi-active suspension systems. Typically, the semi-active control strategies developed to improve vehicle ride comfort and stability have a switching nature. This makes the design of the controlled suspension systems difficult and highly dependent on an extensive trial-and-error process. The proposed methodology maps the discontinuous control system model to a continuous linear region, where all the time and frequency design techniques, established in the conventional control system theory, can be applied. If the semi-active control system is designed to satisfy some ride and stability requirements, an inverse mapping offers the ultimate control law. At the end, the entire design procedure is summarised in six steps. The effectiveness of the proposed methodology in the design of a semi-active suspension system for a Cadillac SRX 2005 is demonstrated with road tests results. Real-time experiments confirm that the use of the newly developed systematic design method reduces the required time and effort in real industrial problems.     

Adaptive Control of Vehicle Suspension

An adaptive control scheme for a two-degree-of-freedom vehicle model with active suspension is proposed. The performance goal is to minimize the variance of vehicle body acceleration under inequality constraints imposed on the variance of either tire or suspension deflection. An active suspension is adapted to the changes in vehicle velocity and the type of road (or terrain) surface which is assumed to be reconstructable from the accelerometer measurements. The control gain factors are obtained by the iterative method taking advantage of stochastic linear control theory. The performance of the system is evaluated and compared to that of an active system with constant gain factors and a passive system with adjustable parameters.     

轿车悬架阻尼二阶最优控制设计方法研究

本文以半动悬架与二阶最优控制理论为基础，通过被动悬架阻尼的主动力表示，结合对最优控制力的分解以及最优评价指标，振动加速功率谱密函数与系统振动阻尼之间的关系的研究，建立了多自由度汽车振动系统在随机输入下以振动加速度功率谱密度函数极小为目标的悬架最优减振器阻尼参数的方法，并给出了７自由汽车振动最优减振器阻尼设计实例。     

New model and simulation of Macpherson suspension system for ride control applications

The main purpose of this paper is to propose a new nonlinear model of the Macpherson strut suspension system for ride control applications. The model includes the vertical acceleration of the sprung mass and incorporates the suspension linkage kinematics. This two-degree-of-freedom (DOF) model not only provides a more accurate representation of the Macpherson suspension system for control applications in order to improve the ride quality, but also facilitates evaluation of the suspension kinematic parameters, such as camber, caster and king-pin angles as well as track alterations on the ride vibrations. The performances of the nonlinear and linearised models are investigated and compared with those of the conventional model. Besides, it is shown that the semi-active force improves the ride quality better than active force, while the opposite is true in terms of improving the performance of the kinematic parameters. The results of variations of the kinematic parameters based on the linear model subject to road disturbances are compared with those of a virtual prototype of Macpherson suspension in ADAMS software. The analytical results in both cases are shown to agree with each other.     

On the achievable performance using variable geometry active secondary suspension systems in commercial vehicles

There is a need to further improve driver comfort in commercial vehicles. The variable geometry active suspension offers an interesting option to achieve this in an energy efficient way. However, the optimal control strategy and the overal performance potential remains unclear. The aim of this paper is to quantify the level of performance improvement that can theoretically be obtained by replacing a conventional air sprung cabin suspension design with a variable geometry active suspension. Furthermore, the difference between the use of a linear quadratic (LQ) optimal controller and a classic skyhook controller is investigated. Hereto, an elementary variable geometry actuator model and experimentally validated four degrees of freedom quarter truck model are adopted. The results show that the classic skyhook controller gives a relatively poor performance while a comfort increase of 17–28% can be obtained with the LQ optimal controller, depending on the chosen energy weighting. Furthermore, an additional 75% comfort increase and 77% energy cost reduction can be obtained, with respect to the fixed gain energy optimal controller, using condition-dependent control gains. So, it is concluded that the performance potential using condition-dependent controllers is huge, and that the use of the classic skyhook control strategy should, in general, be avoided when designing active secondary suspensions for commercial vehicles.     

Inverse neuro-fuzzy MR damper model and its application in vibration control of vehicle suspension system

In this paper, a magneto-rheological (MR) damper-based semi-active controller for vehicle suspension is developed. This system consists of a linear quadratic Gauss (LQG) controller as the system controller and an adaptive neuro-fuzzy inference system (ANFIS) inverse model as the damper controller. First, a modified Bouc–Wen model is proposed to characterise the forward dynamic characteristics of the MR damper based on the experimental data. Then, an inverse MR damper model is built using ANFIS technique to determine the input current so as to gain the desired damping force. Finally, a quarter-car suspension model together with the MR damper is set up, and a semi-active controller composed of the LQG controller and the ANFIS inverse model is designed. Simulation results demonstrate that the desired force can be accurately tracked using the ANFIS technique and the semi-active controller can achieve competitive performance as that of active suspension.     

电流变智能半主动悬架模糊PID控制

对带有电流变液智能阻尼器的半主动汽车悬架系统设计了一种模糊PID控制器。将半主动悬架簧载质量的位移及其导数作为模糊控制器的输入，PID控制器的3个增益参数作为其输出，利用电流变液智能阻尼器的阻尼力可随电压变化的特性来使车身的振动降为最小。仿真实验给出了最优被动悬架、固定参数PID控制智能半主动悬架和模糊PID控制智能半主动悬架在不同路面激励情况下的响应曲线。     

Skyhook and H8 Control of Semi-active Suspensions: Some Practical Aspects

Summary This paper deals with single-wheel suspension car model. We aim to prove the benefits of controlled semi-active suspensions compared to passive ones. The contribution relies on H 8 control design to improve comfort and road holding of the car under industrial specifications, and on control validation through simulation on an exact nonlinear model of the suspension. Note that we define semi-active suspensions as control systems incorporating a parallel spring and an electronically controlled damper. However, the type of damper used in automotive industry can only dissipate energy. No additional force can be generated using external energy. The control issue is then to change, in an accurate way, the damping (friction) coefficient in real-time. This is what we call semi-active suspension. For this purpose, two control methodologies, H 8 and Skyhook control approaches, are developed, using a linear model of the suspension, and compared in terms of performances using industrial specifications. The performance analysis is done using the control-oriented linear model first, and then using an exact nonlinear model of the suspension incorporating the nonlinear characteristics of the suspension spring and damper.     

Adaptive Control of Vehicle Suspension

SUMMARY

An adaptive control scheme for a two-degree-of-freedom vehicle model with active suspension is proposed. The performance goal is to minimize the variance of vehicle body acceleration under inequality constraints imposed on the variance of either tire or suspension deflection. An active suspension is adapted to the changes in vehicle velocity and the type of road (or terrain) surface which is assumed to be reconstructable from the accelerometer measurements. The control gain factors are obtained by the iterative method taking advantage of stochastic linear control theory. The performance of the system is evaluated and compared to that of an active system with constant gain factors and a passive system with adjustable parameters.