The Response of Active and Semi-active Suspensions to Realistic Feedback Signals

SUMMARY

A simple vehicle model is presented incorporating passive, active, and semi-active suspensions. When the desired feedback variables are ideally available, the system response is well understood and excellent sprung mass isolation results. More often than not, the measured variables must be signal processed in some manner prior to their use in some control algorithm. This paper presents the expected response of a simple vehicle with an active and/or semi-active suspension, subject to non-ideal feedback information.     

Optimal Linear Active Suspensions with Derivative Constraints and Output Feedback Control

In optimally controlled active suspensions with either full or incomplete state feedback there is tradeoff between system performance and overall stiffness. It is sought to remove this limitation by incorporating integral action which results in a system with infinite stiffness towards static loading, but which is soft with respect to road inputs. The system is also able to eliminate the steady state deflections due to step and (potentially) ramp type inputs at the wheel. Optimality is retained at the cost only of a derivative constraint and the system can be physically realised using output feedback control.     

Achievable Dynamic Response for Automotive Active Suspensions *

A complete set of constraints is derived for the road disturbance transfer functions in a quarter car model of an automotive active suspension, for typical choices of measured outputs. It is shown that any road disturbance responses which are achievable using “full state feedback” can be achieved, to within an arbitrary small tolerance, using a dynamic compensator measuring suspension deflection only. Also considered are the disturbance responses to loads acting on the sprung mass, and a complete set of constraints is derived for these. It is shown that road disturbance and load disturbance responses can be determined independently if suspension deflection and sprung mass velocity are measured. Indeed, any responses achievable separately with “full measurements” can be approximated together to an arbitrary small tolerance. Certain integral relationships are shown to follow from the derived transfer function constraints. These relationships imply fundamental limitations for certain responses (e.g. tyre deflection) no matter what measurements are available for feedback.     

Optimal Linear Active Suspensions with Vibration Absorbers and Integral Output Feedback Control

The bandwidth of the body response to a road input in an active suspension may be considerably reduced if the axle motions are independently controlled and if, at the same time, the effects of static and dynamic loads are counteracted by integral action in the body force control system. The paper presents a further application of the Ferguson-Rekasius method, leading to optimal output control with incomplete state feedback. To achieve narrow bandwidth body response the support springs are replaced by hydraulic actuators, and vibration absorbers or active wheel dampers are employed for the control of the axle motions. Active wheel damping is the more effective and gives good results. Proportional-plus-integral control action is shown to reduce the transient body displacements due to external forces.     

Optimal Linear Active Suspensions with Vibration Absorbers and Integral Output Feedback Control

SUMMARY

The bandwidth of the body response to a road input in an active suspension may be considerably reduced if the axle motions are independently controlled and if, at the same time, the effects of static and dynamic loads are counteracted by integral action in the body force control system. The paper presents a further application of the Ferguson-Rekasius method, leading to optimal output control with incomplete state feedback. To achieve narrow bandwidth body response the support springs are replaced by hydraulic actuators, and vibration absorbers or active wheel dampers are employed for the control of the axle motions. Active wheel damping is the more effective and gives good results. Proportional-plus-integral control action is shown to reduce the transient body displacements due to external forces.     

Active Control of Non-stationary Response of Vehicles with Nonlinear Suspensions

Active control of non-stationary response of a single degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteresis type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.     

Active Control of Non-stationary Response of Vehicles with Nonlinear Suspensions

SUMMARY

Active control of non-stationary response of a single degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteresis type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.     

Anti-Roll and Active Roll Suspensions

Full car roll model is used to show an anti-roll control like that in Citroen's Xantia Activa and the proposed active roll with an in-series active suspension. Computed responses to pulse-shaped anti-phase road unevenness as well as to lateral acceleration in comparison with passive suspension are given in the paper. Also stability values for all parameters can be found.     

Anti-Roll and Active Roll Suspensions

Full car roll model is used to show an anti-roll control like that in Citroen's Xantia Activa and the proposed active roll with an in-series active suspension. Computed responses to pulse-shaped anti-phase road unevenness as well as to lateral acceleration in comparison with passive suspension are given in the paper. Also stability values for all parameters can be found.     

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.     

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.     

主动悬架的参数估计自校正控制

本文采用二自由度的单轮模型，运用衰减记忆递推最小二乘法参数估计算法和广义加权最小方差自校正控制算法，通过控制律隐式结构直接估计控制器参数，再综合得到控制律，从而实现了主动悬架的参数估计自校正控制。经实例计算和数值仿真，证明了该控制方法的有效性和可行性。     

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

SUMMARY

Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.     

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.     

An Active Pantograph with Shaped Frequency Response Employing Linear Output Feedback Control

In pantographs used for current collection on high speed electric trains it is desirable to minimise the fluctuations in the contact force between the collector head and the catenary. A simple two-mass linear model is employed for the pantograph and the design of the proposed control system is based on the input admittance at low frequencies. Frequency shaping is incorporated in the performance index, and a simple dynamic controller is employed to achieve optimality in an equivalent transformed system, while minimising the number of feedback quantities to be measured. A significant reduction in the average contact force appears possible.     

An Active Pantograph with Shaped Frequency Response Employing Linear Output Feedback Control

SUMMARY

In pantographs used for current collection on high speed electric trains it is desirable to minimise the fluctuations in the contact force between the collector head and the catenary. A simple two-mass linear model is employed for the pantograph and the design of the proposed control system is based on the input admittance at low frequencies. Frequency shaping is incorporated in the performance index, and a simple dynamic controller is employed to achieve optimality in an equivalent transformed system, while minimising the number of feedback quantities to be measured. A significant reduction in the average contact force appears possible.     

主动底盘系统的发展趋向（下）

本文论述“主动底盘系统”范畴内两个最现实的问题:悬架减振及四轮转向。关于悬架减振,首先探讨传统悬架的规律,然后阐述主动和半主动悬架系统对悬架可能作出的改进。对所谓“悬空阻尼”系统,着重作了介绍。四轮转向方面首先论述了比例四轮转向、质心侧偏角补偿和可调节的四轮转向等几种基本型式的理论基础。接着介绍了现有的四轮转向系统。     

Active Railway Suspensions: Implementation Status and Technological Trends

The paper provides a comprehensive survey of active railway suspensions, covering both basic concepts and significant practical implications around the world. A critical review of technological opportunities, both current and future, is included, and the final section takes a speculative look at long term trends.     

Fuzzy Logic Active and Semi-Active Control of Off-Road Vehicle Suspensions

For off-road vehicles, minimizing the absorbed power is the main objective of suspension control. The primary cause of increase in the absorbed power in off-road vehicles driven at high speeds on harsh courses is the exhaustion of the suspension travel. Fuzzy-logic approach to active and semi-active off-road vehicle suspension control, with the goal of improving the speed of the vehicle over rough terrains are developed. The ride metric used for quantifying improvements is the absorbed power of the sprung mass. Particular attention is paid to the proper modeling of the suspension using both the full kinematic constraints and the more convenient two degree of freedom linear model of the quarter vehicle suspension. The nonlinearities due to the kinematic constraints on motion are accounted for by modifying the stiffness and damping coefficients of the suspension spring and dashpot in the linear model. The control laws are developed using the less complex model and demonstrated in the fully constrained environment. Nonlinearities of the suspension, including tire stiffness/damping and bumpstops are included at all stages of controller development.