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.     

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 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.     

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.     

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.     

An H2 Formulation for the Design of a Passive Vibration-Isolation System for Cars

SUMMARY

Optimal design of an active suspension system for road vehicles can be solved using LQR techniques. Such a problem is equivalent, in the frequency domain, to determine the state feedback gain matrix that minimizes the H₂ norm of a suitable transfer matrix.

A passive suspension system can be seen as the physical realization of a suitable state feedback law whose gains are function of the system parameters. This law, and thus the characteristic elements of the passive suspension, can be determined as an approximation of the H₂ optimal solution. This methodology allows one to choose the best controller from a constrained subset (i.e., all possible passive suspensions of a particular form) of all possible controllers.     

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.     

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.     

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.     

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.     

An Active Suspension with Optimal Linear State Feedback

SUMMARY

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.     

Performance of Low-bandwidth,Semi-active Damping Concepts for Suspension Control

Abstract

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.     

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.     

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.     

The Response of Active and Semi-active Suspensions to Realistic Feedback Signals

SUMMARY

A simple vehicle model is presented incorporating passive, active, and semi-active suspensions. When the desired feedback variables are ideally available, the system response is well understood and excellent sprung mass isolation results. More often than not, the measured variables must be signal processed in some manner prior to their use in some control algorithm. This paper presents the expected response of a simple vehicle with an active and/or semi-active suspension, subject to non-ideal feedback information.     

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.     

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.     

Magneto-rheological suspensions for improving ground vehicle’s ride comfort,stability, and handling

ABSTRACT

A state-of-the-art discussion on the applications of magneto-rheological (MR) suspensions for improving ride comfort, handling, and stability in ground vehicles is discussed for both road and rail applications. A historical perspective on the discovery and engineering development of MR fluids is presented, followed by some of the common methods for modelling their non-Newtonian behaviour. The common modes of the MR fluids are discussed, along with the application of the fluid in valve mode for ground vehicles’ dampers (or shock absorbers). The applications span across nearly all road vehicles, including automobiles, trains, semi-trucks, motorcycles, and even bicycles. For each type of vehicle, the results of some of the past studies is presented briefly, with reference to the originating study. It is discussed that Past experimental and modelling studies have indicated that MR suspensions provide clear advantages for ground vehicles that far surpasses the performance of passive suspension. For rail vehicles, the primary advantage is in terms of increasing the speed at which the onset of hunting occurs, whereas for road vehicles – mainly automobiles – the performance improvements are in terms of a better balance between vehicle ride, handling, and stability. To further elaborate on this point, a single-suspension model is used to develop an index-based approach for studying the compromise that is offered by vehicle suspensions, using the H₂ optimisation approach. Evaluating three indices based on the sprung-mass acceleration, suspension rattlespace, and tyre deflection, it is clearly demonstrated that MR suspensions significantly improve road vehicle’s ride comfort, stability, and handling in comparison with passive suspensions. For rail vehicles, the simulation results indicate that using MR suspensions with an on-off switching control can increase the speed at which the on-set of hunting occurs by as much as 50% to more than 300%.     

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.     

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.