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.     

Optimal Linear Preview Control of Active Vehicle Suspension

The problem of linear preview control of vehicle suspension is considered as a continuous time stochastic optimal control problem. In the proposed approach minimal a priori information about the road irregularities is assumed and measurement errors are taken into account. It is shown that estimation and control issues can be decoupled. The problem formulation and the analytical solution are given in a general form and hence they apply to other problems in which the system disturbances are unknown a priori, even in a stochastic sense, but some preview information is possible.

The solution is applied to a two-degree-of-freedom (2-DOF) vehicle model. The effects of preview information on ride comfort, road holding, working space of the suspension and power requirements are examined in time and frequency domains. The results show that the greatest potential is for improving road holding properties. This effect could not have been observed in previous studies based on a 1-DOF vehicle model. It is also demonstrated that the presence of preview drastically reduces power requirements, thus relieving the performance versus actuator power dilemma.     

Optimal Linear Preview Control of Active Vehicle Suspension

SUMMARY

The problem of linear preview control of vehicle suspension is considered as a continuous time stochastic optimal control problem. In the proposed approach minimal a priori information about the road irregularities is assumed and measurement errors are taken into account. It is shown that estimation and control issues can be decoupled. The problem formulation and the analytical solution are given in a general form and hence they apply to other problems in which the system disturbances are unknown a priori, even in a stochastic sense, but some preview information is possible.

The solution is applied to a two-degree-of-freedom (2-DOF) vehicle model. The effects of preview information on ride comfort, road holding, working space of the suspension and power requirements are examined in time and frequency domains. The results show that the greatest potential is for improving road holding properties. This effect could not have been observed in previous studies based on a 1-DOF vehicle model. It is also demonstrated that the presence of preview drastically reduces power requirements, thus relieving the performance versus actuator power dilemma.     

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.     

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.     

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.     

An Optimal Self-Tuning Controller for an Active Suspension

An optimal self-tuning control algorithm is presented for vehicle suspension design. The controller, incorporating a weighting controller, state observer and parameter estimator, is designed according to linear optimal control (LQG) theory. Based on the updated estimates of vehicle parameters and states, and the adapted weighting parameters, the LQG controller provides the optimal set of gains over different operating conditions. The feasibility and effectiveness of the proposed self-tuning system was investigated and proved by simulation studies.     

线性最优控制主动悬架系统的鲁棒稳定性研究

本文采用系统性能分析和Ｍｏｎｔｅ－Ｃａｒｌｏ方法，对线性最优控制主动悬架系统作了鲁棒稳定性研究。     

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.     

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.     

Optimal Linear Active Suspensions with Integral Constraint

This paper considers the application of linear optimal control to the design of an active automobile suspension system. By inclusion of an integral constraint in the performance index it is possible to achieve zero steady state axle to body response to both static body forces and ramp road inputs. Full state feedback is achieved by reconstructing the state variables from easily measured quantities.     

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.     

基于闭环力反馈原理的非线性液压主动阻尼悬架模型的研究及优化设计

本文在理论上建立了一套基于主动力反馈原理的新型主动阻尼悬架的设计和优化方法。首先提出了该主动阻尼悬架的实现模型，该模型是在传统的液力减振器的基础上，应用半主动控制的思想，结合力反馈的原理建立起来的内部液压反馈阻尼网络模型。理论优化分析和计算机仿真表明，通过该液阻网络模型，即可以实现电控的主动阻尼悬架的功能，它可以根据汽车行驶路况的好坏，自适应地调节悬架阻尼大小以实现主动阻尼悬架的最优控制。     

汽车主动悬架的最优预见控制

本文针对1/2车辆模型,应用最优预见控制理论对汽车主动悬架进行控制系统的设计和研究。计算机仿真结果表明,所提出的系统能有效改善汽车乘坐舒适性。     

联合线性和模糊逻辑控制的4自由度主动悬架

文中提出了联合线性和模糊逻辑控制的4自由度汽车主动悬架。该主动悬架以线性控制为主，模糊逻辑控制为辅，前者以车身加速度作为控制量，后者以车身的垂直速度与俯仰速度的线性组合和车身位移作为模糊控制规则的输入变量。最后用Simulink进行仿真，并把所得结果与被动的结果进行比较，说明该系统对提高汽车的平顺性是非常有效的。     

结合轮胎包容特性的主动悬架模型

采用一个结合轮胎包容特性的车辆模型对主动悬架系统进行了研究，并对采用轮胎包容模型对主动悬架的影响进行了分析。     

汽车半车主动悬架的最优控制研究

本文运用车辆动力学理论,建立了半车四自由度主动悬架系统的动力学模型。同时依据最优控制理论设计了主动悬架最优控制器并进行了Matlb+simulink仿真。研究结果表明采用最优控制的主动悬架比被动悬架具有更好的平顺性。     

An Investigation into Vehicle Active Suspension with Electromagnetic Actuator

应用电磁感应的基本原理,设计了一种响应快、出力大和动行程长的车辆主动悬架用作动器.建立了该作动器的集总元件的动力学模型并进行仿真;同时对制作的样机进行了斜坡电压输入和方波电压输入的电磁力测试,测试与仿真结果很好吻合,验证了模型的准确性.最后,结合最优控制理论和矢量控制方法,对包含作动器动力学模型的车辆主动悬架系统进行了正弦路面激励下的仿真分析,结果表明,与被动悬架系统相比,主动悬架系统能明显提高车辆的平顺性.     

基于MATLAB的主动悬架的最优控制分析

本文通过建立二自由度车辆悬架模型,应用了最优控制理论设计了主动悬架控制器,并在MATLAB/SIMULINK中建立了系统模型并进行了仿真。研究结果表明主动悬架比被动悬架的控制效果要好。     

基于SIMULINK的主动悬架的最优控制研究

本文建立了二自由度车辆悬架模型,基于最优控制理论设计了主动悬架控制器,并在SIMULINK中对所设计的控制器进行了仿真验证。研究结果表明主动悬架比被动悬架具有更好的平顺性。