Non-Contact Suspension and Propulsion Technology

As a result of extensive research and development in several countries, the technologies of magnetic suspension and linear electric drives are becoming available for transportation applications. The successful demonstration and operation of prototype vehicles has established the technical viability of these systems. Several urban transit or shuttle services, with magnetic suspension and/or linear motor propulsion are likely to be operational within 3-4 years. After the final stages ofdevelopment and rigorous testing, high speed systems are likely to be an option for intercity implementation by the end of the decade. This paper presents a report on the worldwide status of R&D and test programs of non-contact suspension and propulsion technology for guided ground transport.     

Optimization for Vehicle Suspension I: Time Domain

SUMMARY

A numerical procedure for finding the optimum values of a number of parameters describing a model vehicle suspension has been studied. The vehicle has been modelled by dynamic systems of linear springs and dampers, and the goal is to obtain lower acceleration peaks at an elected design point in the vehicle.

The problem is stated as a mathematical programming problem which can be solved by means of the sequential linear programming technique. The procedure has been implemented for a four wheel independent suspension model capable of being subjected to road irregularities and to centrifugal and braking accelerations.     

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.     

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.     

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.     

Adaptive Control of Vehicle Suspension

SUMMARY

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.     

Investigation on Stability and Possible Chaotic Motions in the Controlled Wheel Suspension System

SUMMARY

The suspension system has to fulfil a large number of partly contradictory requirements which can be improved by the application of controllable elements in the wheel suspension system. A number of studies dealing with the improvement of suspension characteristics have been published. In the present paper the stability of the controlled suspension systems will be examined. In the paper the stability problems of the active suspension system is analysed and the stable parameter regions are determined.     

Observer Design for Electronic Suspension Applications*

SUMMARY

This paper proposes a new methodology for designing observers for automotive suspensions. Automotive suspensions are disturbance-affected dynamic systems. Semi-active suspensions are bilinear while active suspensions with hydraulic actuators are nonlinear. The proposed methodology guarantees exponentially convergent state estimation for both these systems. It uses easily accessible and inexpensive measurements. The fact that sprung mass absolute velocity of the suspension cannot be estimated in an exponentially stable manner with such measurements is also demonstrated.

Controllers using estimated states are implemented experimentally on the Berkeley Active Suspension Test Rig. Experimental results for two cases are presented : use of observer states to improve ride quality in an active suspension and use of observer states to reduce dynamic tire loading in a semi-active heavy vehicle suspension.     

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.     

Robust Stability Analysis of LQG-Controlled Active Suspension with Model Uncertainty Using Structured Singular Value, μ, Method

SUMMARY

This paper presents a systematic approach toward robust stability analysis of LQG-con trolled active suspension systems. To perform this task, the paper starts with a brief background information on LQG control, its relation to H ₂ method, and showing how H ₂ could be formulated to become the frequency domain equivalent of LQG. Then unstructured and structured uncertainties of active suspension are formulated. The paper continues with the definition of maximum singular values and structured singular values of a transfer function matrix. Using these definitions, the robust stability of an active suspension system in the presence of assumed parameter variations are analyzed. These steps are illustrated by means of a numerical example of an active suspension system.     

Dynamic Response of a Six-axle Locomotive to Random Track Inputs

SUMMARY

Spectral analysis techniques are employed to analyze the dynamic response of a six-axle locomotive on tangent track to vertical and lateral random track irregularities. The locomotive is represented by a thirty-nine (39) degrees of freedom model. A linear model is employed by considering small displacements, linear suspension elements and a linear theory for the wheel-rail interaction. Power spectral densities of displacements, velocities and accelerations and the statistical average frequencies of the system are obtained for each degree of freedom. Comparison of the calculated dominating frequencies with existing experimental values shows good agreement. The technique of spectral analysis is an effective tool for model validation, and for the determination of rail vehicle response to track irregularities. The probability functions for the response can be used as a measure for the ride quality of rail vehicles and for the study of fatigue damage of components.

     

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.     

Road Vehicle Suspension System Design - a review

SUMMARY

Based mainly on English language literature, information relating to the design of automobile suspension systems for ride comfort and control of wheel load variations for frequencies below body structure resonances is reviewed. The information is interpreted in the context of vehicles which travel through a wide speed range on roads of markedly differing quality, which do so carrying different loads and which are required to possess good handling qualities.

Sections are devoted to describing road surfaces, modelling vehicles and setting up performance criteria, and to passive, active, semi-active and slow-active system types. Methods for deriving active system control laws are outlined. Strengths and weaknesses of the various systems are identified and their relative performance capabilities and equipment requirements are discussed. Attention is given to adaptation of the suspension or control system parameters to changing conditions. Remaining research needs are considered.     

Dynamics of Pneumatic Tire Vehicles with Connected Suspension Systems

SUMMARY

A vehicle model, with 10 degrees of freedom is used to investigate the skidding conditions of any wheel of the vehicle in motion. Equations for the load transfer and equations for the pneumatic tire spring and shock absorber are derived. Parameters such as gradual cornering, U-curve cornering, the wavy road surface of different wave lengths and cases of independent and connected suspension systems are inputs to the system. The tire calculated forces and their corresponding maximum resistance forces are the outputs of the systems. A connected suspension system is found to resist skidding better than the independent suspension system. The system is non-linear, and numerical solutions are obtained.     

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.     

The Development and Implementation of Adaptive Semi-Active Suspension Control*

SUMMARY

Using adjustable shock absorbers within vehicle suspension systems, it is possible to improve ride comfort significantly when a control strategy is applied based on the so-called skyhook principle. However, the drawback is a poorly damped wheel-hop mode which makes the road holding ability worse. Using adaptive semi-active suspension control based on the tire load variations as introduced in this paper, the trade-off between road holding and ride comfort can be relaxed. Implementation of adaptive skyhook control requires the determination of a number of important and difficult to measure states of the vehicle. This can either be accomplished by several sensors and filters or by a state estimator in combination with less sensors and an internal model of the vehicle. Both methods are discussed. Finally some preliminary test results are discussed.     

Force Generation in Semi-Active Suspensions Using Modulated Dissipative Elements

ABSTRACT

Large control forces in vehicle suspension systems or other vibration control systems may often be generated effectively by modulating the dissipation characteristics of an element using only modest control power. Most of the systems proposed in the past have involved hydraulic dampers, but a variety of other resistive elements can also be used. What is required is an efficient transducer from mechanical power to another form of power and a means to modulate a generalized resistor in the energy domain in question. Using bond graphs, it is shown that designs in the hydraulic domain can be transferred to other domains with possible benefits in certain cases.     

Comparison of Ride Comfort Criteria for Computer Optimization of Vehicles Travelling on Randomly Profiled Roads

SUMMARY

This paper discusses and compares some ride comfort criteria which may be suitable for randomly vibrating vehicles. The criteria consider single-figure measures based on response mean square spectral densities for plane linear combined vehicle-passenger models. Eight different measures divided into three groups are studied. The two vehicle suspension damper stiffnesses are numerically optimized with respect to the eight measures of ride comfort. The results are compared and discussed. Two optimizations with respect to five vehicle parameters are also reported.     

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.     

Advanced Ground Vehicle Suspension Systems - A Classified Bibliography

SUMMARY

This bibliographical list classifies the extensive literature related to the dynamic analysis and control design aspects of advanced ground vehicle suspension systems. It is restricted to the design of advanced suspensions for ride quality and safety. Brief generalized notices and definitions are presented.