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.     

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.     

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.     

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.     

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.     

Power Requirements for Vehicle Suspension Systems

This paper attempts to analyze the power requirements of a vehicle due solely to its suspension system, neglecting the important powers associated with air and rolling resistance. Power requirements for active and passive suspensions are compared using the simplest possible mathematical model. A mass in a gravity field moves at constant velocity over a surface and is supported by a point contact on the surface by a massless but otherwise arbitrary suspension system. It is shown that the average propulsive power required is equal to the average power lost in the suspension. In the limit cases of very stiff or very soft suspensions this power vanishes. Passive suspensions require no other power, but active suspensions may require significant extra power from the prime mover to generate the suspension forces.     

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.     

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.     

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.     

Structured H2 Optimization of Vehicle Suspensions Based on Multi-Wheel Models

Summary Various control techniques, especially LQG optimal control, have been applied to the design of active and semi-active vehicle suspensions over the past several decades. However passive suspensions remain dominant in the automotive marketplace because they are simple, reliable, and inexpensive. The force generated by a passive suspension at a given wheel can depend only on the relative displacement and velocity at that wheel, and the suspension parameters for the left and right wheels are usually required to be equal. Therefore, a passive vehicle suspension can be viewed as a decentralized feedback controller with constraints to guarantee suspension symmetry. In this paper, we cast the optimization of passive vehicle suspensions as structure-constrained LQG/H2 optimal control problems. Correlated road random excitations are taken as the disturbance inputs; ride comfort, road handling, suspension travel, and vehicle-body attitude are included in the cost outputs. We derive a set of necessary conditions for optimality and then develop a gradient-based method to efficiently solve the structure-constrained H2 optimization problem. An eight-DOF four-wheel-vehicle model is studied as an example to illustrate application of the procedure, which is useful for design of both passive suspensions and active suspensions with controller-structure constraints.     

State of the art survey: active and semi-active suspension control

This survey paper aims to provide some insight into the design of suspension control system within the context of existing literature and share observations on current hardware implementation of active and semi-active suspension systems. It reviews the performance envelop of active, semi-active, and passive suspensions with a focus on linear quadratic-based optimisation including a specific example. The paper further discusses various design aspects including other design techniques, the decoupling of load and road disturbances, the decoupling of pitch and heave modes, the use of an inerter as an additional design element, and the application of preview. Various production and near production suspension systems were examined and described according to the features they offer, including self-levelling, variable damping, variable geometry, and anti-roll damping and stiffness. The lessons learned from these analytical insights and related hardware implementations are valuable and can be applied towards future active or semi-active suspension design.     

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.     

Semi-Active Control of Wheel Hop in Ground Vehicles

A two degree-of-freedom vehicle model is developed which incorporates passive, active, and semi-active secondary suspensions. The model is used to demonstrate the trade-offs which are inherent in attempting to provide desirable sprung weight isolation while at the same time controlling unsprung weight motions.

A linear model is used first in order to compare passive and active suspensions in an analytically understandable configuration. The semi-active suspension is inherently nonlinear and is compared to the others through computer simulation. The passive suspension is, of course, the most restrictive in providing simultaneous isolation of sprung and unsprung weight; however, the active suspension is also compromised in providing both functions. The semi-active suspension does an excellent job of tracking its active counterpart.     

Experimental Verification of Resistance Control, Semi-Active Damping

Electronically controlled vehicle suspensions offer substantial improvements in performance over conventional, passive suspensions but with the price of power, complexity, and actuating bandwidth. Low-bandwidth, semi-active damping addresses the problems of power and bandwidth by using low power modulation of controllable dampers at the frequency of the isolated mass. Resistance controlled, semi-active damping is experimentally verified to better sprung mass isolation while reducing suspension stroke, something that a passive system cannot do. It is also shown to compare reasonably well with computer simulation results. The experimental implementation is a 1/30 scale, two degree-of-freedom test bed that represents the standard quarter vehicle model.     

Actively controlled vehicle suspension with energy regeneration capabilities

The paper presents an innovative dual purpose automotive suspension topology, combining for the first time the active damping qualities with mechanical vibrations power regeneration capabilities. The new configuration consists of a linear generator as an actuator, a power processing stage based on a gyrator operating under sliding mode control and dynamics controllers. The researched design is simple and energetically efficient, enables an accurate force–velocity suspension characteristic control as well as energy regeneration control, with no practical implementation constraints imposed over the theoretical design. Active damping is based on Skyhook suspension control scheme, which enables overcoming the passive damping tradeoff between high- and low-frequency performance, improving both body isolation and the tire's road grip. The system-level design includes configuration of three system operation modes: passive, semi–active or fully active damping, all using the same electro-mechanical infrastructure, and each focusing on different objective: dynamics improvement or power regeneration. Conclusively, the innovative hybrid suspension is theoretically researched, practically designed and analysed, and proven to be feasible as well as profitable in the aspects of power regeneration, vehicle dynamics improvement and human health risks reduction.     

Energy Requirements of a Passive and an Electromechanical Active Suspension System

Passive suspensions are designed to dissipate the energy otherwise transferred to a vehicle's body through interactions with a roadway or terrain. A bond graph representation of an independent suspension design was developed to study the energy flow through a vehicle. The bond graph model was tuned and validated through experimental tests and was found to produce suitable results. Examining the bond graph reveals that the dissipated energy associated with vertical and transverse coordinates generally originates from the longitudinal motion of the vehicle and is transferred through the tire-ground contact patch. Additionally, since the longitudinal energy originates from the vehicle's engine, the energy dissipated via the suspension shock absorber as well as other components (e.g., mechanical joints, etc.) essentially dissipate some engine energy. The plots presented in the paper support this theory by showing that upon traveling a rough terrain, the vehicle's longitudinal velocity drops more when vertical vibrations increase. Results show that a vehicle equipped with a passive suspension experiences a larger velocity drop compared to one with an active suspension traversing the same rough terrain. The paper compares the results of simulation of an analytical bond graph model of an active suspension system with experimental results and finds good agreement between the two. Other simulations show that relative to passive suspensions, not only do active suspensions yield substantial improvement in ride quality, they can also result in substantial energy savings. This paper concludes that if electromechanical actuators are supplemented by passive springs to support the vehicle static weight, the amount of energy required for operation of actuators is significantly less than the amount dissipated by conventional shock absorbers.     

基于串联型模糊神经网络的汽车半主动悬架的研究

本文建立了五自由度汽车半主动悬架系统模型，提出一种用于汽车悬 半主动振动控制系统的模糊神经网络方法，对半主动悬架 计算机仿真和结果分析，并通过与被动悬架相比较，证明半主动悬架系统在减少振动，提高汽车平一方面要优于被动悬架。     

Semi-Active Control of Wheel Hop in Ground Vehicles

ABSTRACT

A two degree-of-freedom vehicle model is developed which incorporates passive, active, and semi-active secondary suspensions. The model is used to demonstrate the trade-offs which are inherent in attempting to provide desirable sprung weight isolation while at the same time controlling unsprung weight motions.

A linear model is used first in order to compare passive and active suspensions in an analytically understandable configuration. The semi-active suspension is inherently nonlinear and is compared to the others through computer simulation. The passive suspension is, of course, the most restrictive in providing simultaneous isolation of sprung and unsprung weight; however, the active suspension is also compromised in providing both functions. The semi-active suspension does an excellent job of tracking its active counterpart.     

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.