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.     

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.     

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.     

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 design methodology for mechatronic vehicles: application of multidisciplinary optimization, multibody dynamics and genetic algorithms

A design methodology for mechatronic vehicles is presented. With multidisciplinary optimization (MDO) methods, strongly coupled mechanical, control and other subsystems are integrated as a synergistic vehicle system. With genetic algorithms (GAs) at the system level, the mechanical, control and other relevant parameters can be optimized simultaneously. To demonstrate the feasibility and efficacy of the proposed design methodology for mechatronic vehicles, it is used to resolve the conflicting requirements for ride comfort, suspension working spaces and unsprung mass dynamic loads in the optimization of half-vehicle models with active suspensions. Both deterministic and random road excitations, both rigid and flexible vehicle bodies and both perfect measurement of full state variables and estimated limited state variables are considered. Numerical results show that the optimized vehicle systems based on the methodology have better overall performance than those using the linear quadratic Gaussian (LQG) controller. It is shown that the methodology is suitable for complex design optimization problems where: (1) there is interaction between different disciplines or subsystems; (2) there are multiple design criteria; (3) there are multiple local optima; (4) there is no need for sensitivity analysis for the optimizer at the system level; and (5) there are multiple design variables.     

A design methodology for mechatronic vehicles: application of multidisciplinary optimization,multibody dynamics and genetic algorithms

A design methodology for mechatronic vehicles is presented. With multidisciplinary optimization (MDO) methods, strongly coupled mechanical, control and other subsystems are integrated as a synergistic vehicle system. With genetic algorithms (GAs) at the system level, the mechanical, control and other relevant parameters can be optimized simultaneously. To demonstrate the feasibility and efficacy of the proposed design methodology for mechatronic vehicles, it is used to resolve the conflicting requirements for ride comfort, suspension working spaces and unsprung mass dynamic loads in the optimization of half-vehicle models with active suspensions. Both deterministic and random road excitations, both rigid and flexible vehicle bodies and both perfect measurement of full state variables and estimated limited state variables are considered. Numerical results show that the optimized vehicle systems based on the methodology have better overall performance than those using the linear quadratic Gaussian (LQG) controller. It is shown that the methodology is suitable for complex design optimization problems where: (1) there is interaction between different disciplines or subsystems; (2) there are multiple design criteria; (3) there are multiple local optima; (4) there is no need for sensitivity analysis for the optimizer at the system level; and (5) there are multiple design variables.     

Optimal Performance of Variable Component Suspensions

SUMMARY

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

Constrained Optimal Control of Semi-Active Suspension Systems with Preview

Controllers for semi-active suspensions have to account for constraints on damper range, tire force and suspension travel. Two approaches to incorporate these constraints in the design of controllers to minimize peak values in the chassis acceleration are considered. It is assumed that information on the oncoming road elevations (preview) is available. In the soft constraint approach, the constraints on tire force and suspension travel are included in a quadratic performance index. Two clipped optimal control laws, which deal with preview in a different way, are presented. Simulation results with a 2-DOF vehicle model on some rounded pulses show that these laws do not work satisfactorily with respect to the constraints. Therefore, the control problem is reformulated as a constrained optimization problem with hard constraints on tire force and suspension travel. Simulations with the same model on the same rounded pulses show that the hard constraint approach handles the constraints more properly.     

结合卡尔曼滤波器的车辆主动悬架轴距预瞄控制研究

利用轴距预瞄信息，即前后轮路面输入之关系，同时结合卡尔曼滤波器作为状态估计器，本文提出了一种算法用于车辆悬架控制律的设计，根据模拟结果，研究了算法的可行性，分析了卡尔曼滤波器对状态变量的估计精度，以及轴距预瞄控制对进一步改进车辆性能的潜力。     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

Adaptive Suspension Concepts for Road Vehicles

Most vehicle suspensions are composed of passive spring and damper devices, although improved suspension performance is possible if an active system is used to control forces or relative velocities. The complexity, power requirements, and cost of fully active suspensions have restricted their use. Various partially active suspensions have been proposed and suspensions with slow load levelers and variable dampers are in widespread use. Here we analyze a class of basically passive suspensions the parameters of which can be varied actively in response to various measured signals on the vehicle. These suspensions can come close to optimal performance with simpler means than many of the active or semi-active schemes previously proposed.     

Optimal Performance of Variable Component Suspensions

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

Active Damping in Road Vehicle Suspension Systems

Low order, linearized dynamic models of road vehicle suspension systems are analyzed to provide insight into the benefits of suspensions incorporating generalized velocity feedback compared with conventional passive suspensions. Damping forces from passive dampers are supplemented by forces generated by an active element requiring a power supply. A simple criterion is developed which indicates whether or not the introduction of activedamping forces will result in significant benefit for pneumatic tired vehicles.

An extended active suspension concept involving a high-gain load leveler as well as active damping is analyzed. The realization of active or semi-active damping forces through electrical or hydraulic means is briefly discussed.     

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.     

Adaptive Suspension Concepts for Road Vehicles

SUMMARY

Most vehicle suspensions are composed of passive spring and damper devices, although improved suspension performance is possible if an active system is used to control forces or relative velocities. The complexity, power requirements, and cost of fully active suspensions have restricted their use. Various partially active suspensions have been proposed and suspensions with slow load levelers and variable dampers are in widespread use. Here we analyze a class of basically passive suspensions the parameters of which can be varied actively in response to various measured signals on the vehicle. These suspensions can come close to optimal performance with simpler means than many of the active or semi-active schemes previously proposed.     

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.     

基于统一模型的转向-悬架系统最优综合控制方法

通过对车辆底盘系统中的转向和悬架系统建立统一的数学模型,利用M atlab/S imu link仿真,结合最优控制理论,分别对被动悬架兼前轮转向系统与主动悬架兼四轮转向综合控制系统进行了对比研究。理论分析与仿真试验表明,综合控制系统下车辆的操纵稳定性和平顺性都得到了很大的提高。     

Adaptive Ride Control In Active Suspension Systems

The paper describes the development of an adaptive control algorithm for active suspension systems based on optimal regulation methods. The objective is to design an algorithm which will automatically tune at start-up to changed vehicle conditions and adaptively re-tune to changes in driving conditions (in particular road generated disturbances). The proposed algorithm is a self-tuning regulator based on generalised minimum variance (GMV) control. Simulation results obtained for a 3 degree-of-freedom (DOF) quarter car suspension demonstrate potential benefits of fully adaptive control in automotive suspensions.     

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.