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.     

主动汽车悬架的非线性控制

本文采用１／４车模型对天棚阻尼器和主动悬架的动力学性能进行分析，针对执行器的非线性特性，探讨了微分几何法和反馈法线必互法在主动悬架控制中的应用，在系统控制设计中采用了离散滑模法，仿真结果显示非线性控制律能有效地改善主动悬架的隔振特性。     

Design of Nonlinear Controllers for Active Vehicle Suspensions Using Parameter-Varying Control Synthesis

Nonlinear suspension controllers have the potential to achieve superior performance compared to their linear counterparts. A nonlinear controller can focus on maximizing passenger comfort when the suspension deflection is small compared to its structural limit. As the deflection limit is approached, the controller can shift focus to prevent the suspension deflection from exceeding this limit. This results in superior ride quality over the range of road surfaces, as well as reduced wear of suspension components. This paper presents a novel approach to the design of such nonlinear controllers, based on linear parameter-varying control techniques. Parameter-dependent weighting functions are used to design active suspensions that stiffen as the suspension limits are reached. The controllers use only suspension deflection as a feedback signal. The proposed framework easily extends to the more general case where all the three main performance metrics, i.e., passenger comfort, suspension travel and road holding are considered, and to the design of road adaptive suspensions.     

Design of Nonlinear Controllers for Active Vehicle Suspensions Using Parameter-Varying Control Synthesis

Nonlinear suspension controllers have the potential to achieve superior performance compared to their linear counterparts. A nonlinear controller can focus on maximizing passenger comfort when the suspension deflection is small compared to its structural limit. As the deflection limit is approached, the controller can shift focus to prevent the suspension deflection from exceeding this limit. This results in superior ride quality over the range of road surfaces, as well as reduced wear of suspension components. This paper presents a novel approach to the design of such nonlinear controllers, based on linear parameter-varying control techniques. Parameter-dependent weighting functions are used to design active suspensions that stiffen as the suspension limits are reached. The controllers use only suspension deflection as a feedback signal. The proposed framework easily extends to the more general case where all the three main performance metrics, i.e., passenger comfort, suspension travel and road holding are considered, and to the design of road adaptive suspensions.     

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.     

Stochastic Optimal Control of Highway Tractors with Active Suspensions

Stochastic optimal control and estimation theories are used to design an active suspension system for a cab ride in a tractor-semitrailer vehicle. A discrete-continuous vehicle model with eleven degrees of freedom is augmented by a stochastic road excitation model and a human perception of vibration shape filter. Both perfect measurement and estimated state cases are considered. The impact of the measurement noise on the design of the optimal controller is demonstrated. The performance of the optimally controlled system is compared with an optimal passive system. It is shown that significant improvements in ride comfort can be achieved through the use of actively controlled cab suspensions.     

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.     

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。     

Active Roll Control of Articulated Vehicles

This paper describes an investigation into active roll control of articulated vehicles. The objective is to minimise lateral load transfer using anti-roll bars incorporating low bandwidth hydraulic actuators. Results from handling tests performed on an articulated vehicle are used to validate a nonlinear yaw/roll model of the vehicle. The methodology used to design lateral acceleration controllers for vehicles equipped with active anti-roll bars is developed using a simplified linear articulated vehicle model. The hardware limitations and power consumption requirements of the active elements are studied. The controller is then implemented in the validated articulated vehicle model to evaluate the performance of an articulated lorry with active anti-roll bars. The simulation results demonstrate the possibility of a significant improvement in transient roll performance of the vehicle, using a relatively low power system (10 kW), with low bandwidth actuators (5 Hz).     

An Optimal Continuous Time Control Strategy for Active Suspensions with Preview

A continuous time control strategy for an active suspension with preview, based on optimal control theory, is presented. No approximation is needed to model the time delay between the excitation of the front and the rear wheels. The suspension is applied to a two DOF model of the rear side of the tractor of a tractor-semitrailer. The purpose of the suspension is to reduce either the required suspension working space or the maximum absolute acceleration of the sprung mass, without an increase of the dynamic tire force variation. For a step function as road input, reductions of 65% and 55%, respectively, are possible compared with a passive suspension.     

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.     

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。     

汽车主动悬架的自校正控制

主动悬系统能使车辆的乘坐舒适性和操纵稳定性同时得到改善，其中执行机构和控制算法的优劣决定了该系统的性能。     

Application of Nonlinear Control Theory to Electronically Controlled Suspensions

SUMMARY

This paper illustrates the use of nonlinear control theory for designing electro-hydraulic active suspensions. A nonlinear, “sliding” control law is developed and compared with the linear control of a quarter-car active suspension system acting under the effects of coulomb friction. A comparison will also be made with a passive quarter-car suspension system. Simulation and experimental results show that nonlinear control performs better than PID control and improves the ride quality compared to a passive suspension.     

Application of Nonlinear Control Theory to Electronically Controlled Suspensions

This paper illustrates the use of nonlinear control theory for designing electro-hydraulic active suspensions. A nonlinear, “sliding” control law is developed and compared with the linear control of a quarter-car active suspension system acting under the effects of coulomb friction. A comparison will also be made with a passive quarter-car suspension system. Simulation and experimental results show that nonlinear control performs better than PID control and improves the ride quality compared to a passive suspension.     

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.     

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

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 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.