Performance Limitations and Constraints for Active and Passive Suspensions: a Mechanical Multi-port Approach

This paper develops a framework using mechanical multi-port networks to study the performance capabilities and constraints in vehicle suspensions. We seek to understand the set of dynamic responses which are achievable for both passive and active systems. To this end, we view a suspension system as a mechanical multi-port network and draw on concepts from electrical circuits such as passivity and reciprocity. We identify necessary conditions on the external behaviour of a quarter-car model for the suspension to be capable of passive realisation, and thereby establish that several behaviours or force laws cannot be implemented without an internal power source. We study the number of available degrees of freedom (i.e., independently specifiable impedances) in the quarter-, half- and full-car cases.     

Theoretical Limitations in Active Vehicle Suspensions

SUMMARY

Vehicle suspensions in which forces are generated in response to feedback signals by active elements obviously offer increased design flexibility compared to conventional suspensions using passive elements such as springs and dampers. It is often assumed that if practical difficulties are neglected, active systems could in principle produce arbitrary ideal, behavior. It is shown, using a simple linear two degree-of-freedom suspension system, model that even using complete state feed back and in the case of in which the system is controllable in the control theory sense, there still are limitations to suspension performance in the fully active case. If the ideal suspension performance is defined based on low-pass filtering of roadway unevenness inputs, an active suspension may not offer much better performance than a partially active or adaptive passive suspension depending upon the values of certain vehicle parameters.     

Theoretical Limitations in Active Vehicle Suspensions

Vehicle suspensions in which forces are generated in response to feedback signals by active elements obviously offer increased design flexibility compared to conventional suspensions using passive elements such as springs and dampers. It is often assumed that if practical difficulties are neglected, active systems could in principle produce arbitrary ideal, behavior. It is shown, using a simple linear two degree-of-freedom suspension system, model that even using complete state feed back and in the case of in which the system is controllable in the control theory sense, there still are limitations to suspension performance in the fully active case. If the ideal suspension performance is defined based on low-pass filtering of roadway unevenness inputs, an active suspension may not offer much better performance than a partially active or adaptive passive suspension depending upon the values of certain vehicle parameters.     

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。     

Performance Benefits in Passive Vehicle Suspensions Employing Inerters

A new ideal mechanical one-port network element named the inerter was recently introduced, and shown to be realisable, with the property that the applied force is proportional to the relative acceleration across the element. This paper makes a comparative study of several simple passive suspension struts, each containing at most one damper and inerter as a preliminary investigation into the potential performance advantages of the element. Improved performance for several different measures in a quarter-car model is demonstrated here in comparison with a conventional passive suspension strut. A study of a full-car model is also undertaken where performance improvements are also shown in comparison to conventional passive suspension struts. A prototype inerter has been built and tested. Experimental results are presented which demonstrate a characteristic phase advance property which cannot be achieved with conventional passive struts consisting of springs and dampers only.     

Performance Benefits in Passive Vehicle Suspensions Employing Inerters

A new ideal mechanical one-port network element named the inerter was recently introduced, and shown to be realisable, with the property that the applied force is proportional to the relative acceleration across the element. This paper makes a comparative study of several simple passive suspension struts, each containing at most one damper and inerter as a preliminary investigation into the potential performance advantages of the element. Improved performance for several different measures in a quarter-car model is demonstrated here in comparison with a conventional passive suspension strut. A study of a full-car model is also undertaken where performance improvements are also shown in comparison to conventional passive suspension struts. A prototype inerter has been built and tested. Experimental results are presented which demonstrate a characteristic phase advance property which cannot be achieved with conventional passive struts consisting of springs and dampers only.     

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.     

Suboptimal Control Design of Active and Passive Suspensions Based on a Full Car Model

An optimal control design method is introduced and then applied to the optimum design of active and passive suspension systems. A basic three-dimensional 7-DOF car riding model subjected to four correlated random road inputs is considered. The design method is basically developed to allow arbitrary choice of sensors for various car state variables to be used for feedback control of each suspension unit. Previous studies show that full-state control laws and even some limited-state control laws often include feedback gains which are almost zero. Some other gains, although not zero, don't play an important role in improving the system performance measures. With the method proposed in this work, every suspension unit can have its own feedback measurements and the criterion function can be related to all state and control variables. Thus a large number of active and semi-active suspension systems with full- or limited-state control laws based on different measurement combination can be suggested, studied, and compared with each other. Instead of comparing these optimized active and semi-active suspension systems with a basic, passive suspension, the passive system itself is optimized with the same criterion. Simulations in the time domain and frequency analyses are performed, and comparisons are made among the systems in terms of r.m.s. car response measures and ISO riding comfort criterion.     

Optimal Adaptive Active Suspensions for a Full Car Model

In order to present a useful method for designing active suspension of a vehicle, a linear full-car model is used in this investigation. In this model, the dampers of passive system are totally replaced by actuators. The actuators are controlled with optimal full state vector feedback. After determining feedback coefficients, the responses of active and passive systems were compared and it was found that performance of active system is much superior. It is desired that, changes in vehicle parameters would not affect the system's performance and hence should not violate its optimality. In other words, the system should behave adaptively using Model Reference Adaptive Control. The optimally controlled active suspension was used as a model for the active suspension of vehicle. In this way, the suspension of vehicle is controlled in such a way that its output approaches to that of the optimal active model. Thus the suspension should behave just like the optimal one.     

Optimization and Performance Enhancement of Active Suspensions for Automobiles under Preview of the Road

The problem of deriving control laws which minimize specified performance indices for a vehicle moving on a rough surface with preview of the surface elevation is considered. The approach is based on linear optimal tracking theory and consequently the system elements are taken to be linear and the performance index is constrained to be of quadratic form.

The ideas of overtaking optimality are applied to the problem in order to achieve a closed form solution for the control. Then, using the control laws derived, computer simulations of performance are conducted and time histories are shown. In the absence of limitations on either processing or actuator speeds, and for cases in which the preview is sufficient to give good control laws, the value of the preview in enhancing vehicle suspension performance is assessed. Comparisons are made with results in the literature.     

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.     

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.     

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.     

Preview Estimation and Control for (Semi-) Active Suspensions

SUMMARY

An active suspension with preview is tested for rounded pulses and a stochastic road surface, and is compared to a passive suspension. The spectacular performance improvement obtained for a step function as road surface is not achieved but the improvement is still significant. The frequency response of the active suspension is determined for comparison with some suspension systems found in literature

An observer to reconstruct the preview information is presented. No model of the road surface is needed. From simulations, it appears that the observer reconstructs both deterministic and stochastic road surfaces satisfactory. However, the influence of measurement noise is not reduced sufficiently.     

Preview Estimation and Control for (Semi-) Active Suspensions

An active suspension with preview is tested for rounded pulses and a stochastic road surface, and is compared to a passive suspension. The spectacular performance improvement obtained for a step function as road surface is not achieved but the improvement is still significant. The frequency response of the active suspension is determined for comparison with some suspension systems found in literature

An observer to reconstruct the preview information is presented. No model of the road surface is needed. From simulations, it appears that the observer reconstructs both deterministic and stochastic road surfaces satisfactory. However, the influence of measurement noise is not reduced sufficiently.     

Control Algorithms for Active Cab Suspensions on Agricultural Tractors

This paper describes active agricultural tractor cab suspensions based on optimal control theory. Control algorithms based on time invariant state feedback and on adaptive control are developed and studied. The influence of different observers and measurement noise levels on the vibration damping capacity are studied as well as the power consumption for the suspensions.

The principle for the adaptive algorithm is based on the parameters in the penalty matrices being varied so that the resulting controller always strives to make optimum use of available travel space. The feedback and observer gains are also changed depending on the characteristics of the vehicle's frame movements.

The results show that it is possible to design an effective active suspension, but that the choice of feedback gains must be dependent on the surface characteristics to reach satisfactory vibration damping performance.     

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。