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.     

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

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.     

Analysis of Influence of Design Parameters on Steered Wheels Shimmy of Heavy Vehicles

SUMMARY

In choosing the steering system parameters the tendency is towards the minimization of kinematic errors that appear during turning. For that developed procedures exist that take into account also the influence of kinematic of the suspension system on kinematic parameters of vehicle turning. Besides that, maintenance tests have shown, that increased deflections of the suspension system lead to increased wear of tires of steered wheels. In this paper, a method is developed for minimization of steered wheel shimmy and its wear also during the straight-line drive of heavy vehicles. The procedure can also be used in the phase of designing the heavy vehicles.     

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.     

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.     

Actuator optimal placement studies of high-speed power bogie for active hunting stability

ABSTRACT

We put forward three actuator placements of the high-speed train power bogie to improve the train hunting stability. The active control forces act on the frame, between the frame and the motor, and on the motor by the inertial or retractable actuator, respectively, based on the feedback states of vibration velocity of the front and rear end beams. The feedback gains and the motor suspension parameters in different cases are optimised with the two objectives of system stability margin and control effort. The required actuator outputs of the three cases are compared based on the theoretical analysis with a 8 DOF bogie model. The results show that the three control cases can effectively improve the hunting stability, especially at high speed. The active control of motor lateral movement is helpful to increase the dynamic vibration absorbing function of the motor flexible suspension, and the control output is obviously smaller than the other two control cases. In addition, the influence of system delay on stability was analysed and we could use or avoid the effects of delay on the stability.     

High Frequency Characteristics of a Front Wheel Suspension

SUMMARY

This paper presents a modeling method to analyze the frequency characteristics of a suspension system. The method employs the superelement and lumped methods for structural modeling of flexible bodies, and it is incorporated with a multibidy dynamics formulation in which joint nonlinearities can be considered effectively. To verify the accuracy of the results obtained by the modeling method, a quarter car test was made. Test results showed that the computational model provided fairly accurate frequency characteristics for the suspension system. Other useful conclusions were also drawn from this study.     

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.     

Coordinated control strategies for active steering,differential braking and active suspension for vehicle stability,handling and safety improvement

ABSTRACT

In this paper, a coordinated control strategy is proposed to provide an effective improvement in handling stability of the vehicle, safety, and comfortable ride for passengers. This control strategy is based on the coordination among active steering, differential braking, and active suspension systems. Two families of controllers are used for this purpose, which are the high order sliding mode and the backstepping controllers. The control strategy was tested on a full nonlinear vehicle model in the environment of MATLAB/Simulink. Rollover avoidance and yaw stability control constraints have been considered. The control system mainly focuses on yaw stability control. When rollover risk is detected, the proposed strategy controls the roll dynamics to decrease rollover propensity. Simulation results for two different critical driving scenarios, the first one is a double lane change and the other one is a J-turn manoeuvre, show the effectiveness of the coordination strategy in stabilising the vehicle, enhancing handling and reducing rollover propensity.     

Advanced Control Methods of Active Suspension

SUMMARY

This paper describes new control methods for the active suspension. For improving ride comfort further, preview control rule is proposed. For improving stability further, roll stiffness distribution control rule is examined by the test vehicle. Simulations and vehicle driving tests are conducted to confirm the effect of these new control methods. The results of simulations and vehicle driving tests show in our research phase that preview control can achieve a substantial improvement in ride comfort and application of roll stiffness distribution control provides a large improvement in stability     

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.     

Comparison of the properties of active and semiactive suspension

In this article, the properties of active and semi-active suspension for heavy goods vehicles are compared. The criteria for the comparison are the RMS sprung mass vertical acceleration, RMS dynamic tyre force, and suspension power consumption. The active system is based on an air-spring with controlled in-flow and out-flow of the air. In the semi-active system, a controlled hydraulic damper is employed. The results concerning the semi-active suspension system were taken from the article by Besinger et al. [Besinger, F.H., Cebon, D. and Cole, D.J., 1995, Force control of a semi-active damper. Vehicle System Dynamics, 24(9), 695–723.].     

A Dynamical Analysis of a Towed Two-Wheel Trailer1

SUMMARY

The towed trailer method for skid resistance measurements is a practical one for characterizing the friction characteristics of highway pavements, and has been standardized by the ASTM 11). Numerous papers have been published about the improvement of equipment and field-testing techniques but little has been done toward a theoretical explanation.

This paper presents a mathematical model of the trailer which includes roll, pitch, and vertical motion. The skid resistance calculated by using this model gives an excellent check on the standard ASTM skid number formula. The response time and damping effect after locking one test wheel can be clearly seen in this model. Possible effects of the dimensions of trailer, stiffness of suspension system, tire pressure, etc. to skid resistance can also be examined.     

Power Requirement of Active Vibration Control Systems

SUMMARY

The paper deals with the theoretical estimation of the minimal power requirement, necessary for the operation of the active vibration control system (AVCS), connected with a passive one. It is assumed this compound system is used for the vibration control purposes in the heavy vehicle driver's seats. The systems considered in the paper are of two kinds. In the first case the electro-hydraulic actuator of the AVCS is situated in series to the spring-damper combination of the seat suspension. The second system under consideration is formed by parallel connection of electro-pneumatic actuator and the spring-damper combination of the seat suspension, which is a mechanical model of a real air spring with controlled in-flow and out-flow of the air. The comparison of results for both compound systems shows markedly higher power consumption of the serial system. The theoretical results are in acceptable agreement with the experimental data.     

The lateral stability of train suspension systems employing inerters

This paper investigates the benefits of lateral stability of train suspension systems employing a newly developed mechanical network element known as an inerter. An inerter was proposed as an ideal mechanical two-port element to substitute for the mass element in the mechanical/electrical analogy. As of now, inerters have been successfully applied to car and motorcycle suspension systems, for which significant performance benefits were reported. This paper discusses the improvements on lateral stability of train suspension systems employing inerters. The study was carried out in three parts. First, an existing 12 degrees-of-freedom (DOF) train model was built and verified by a multi-body-builder, AutoSim^TM. Second, inerters were applied to the train suspension system to increase the critical speed. Finally, the discussion was extended to a 16-DOF model to demonstrate the performance improvement by inerters. From the results, inerters were deemed effective in improving the lateral stability of train suspension systems.     

Switched control of vehicle suspension based on motion-mode detection

This paper presents a study on switched control of vehicle suspension based on motion-mode detection. This control strategy can be potentially implemented via the interconnected suspension such as hydraulically interconnected suspension by actively switching its interconnection configuration in terms of the dominant vehicle body motion-mode. The design of the switched control law is developed focusing on three vehicle body motion-modes: bounce, pitch, and roll. At first, an H_∞ optimal controller will be designed for each motion-mode with the use of a common quadratic Lyapunov function, which guarantees the stability of the switched system under arbitrary switching functions. Then, a motion-mode detection method based on the calculation of the motion-mode energy is introduced. And then, the possible implementation of the control system in practice is discussed. Finally, numerical simulations are used to validate the proposed study.     

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.     

Achieving anti-roll bar effect through air management in commercial vehicle pneumatic suspensions

ABSTRACT

This paper introduces the concept of managing air in commercial vehicle suspensions for reducing body roll. A conventional pneumatic suspension is re-designed to include higher-flow air hoses and dual levelling valves for improving the dynamic response of the suspension to the body roll, which commonly happens at relatively low frequencies. The improved air management allows air to get from the air tank to the airsprings quicker, and also changes the side-to-side suspension air pressure such that the suspension forces can more readily level the vehicle body, much in the same manner as an anti-roll bar (ARB). The results of a multi-domain simulation study in AMESim and TruckSim indicate that the proposed suspension configuration is capable of providing balanced airflow to the truck’s drive-axle suspensions, resulting in balanced suspension forces in response to single lane change and steady-state cornering steering maneuvers. The simulation results further indicate that a truck equipped with the reconfigured suspension experiences a uniform dynamic load sharing, smoother body motion (less roll angle), and improved handling and stability during steering maneuvers commonly occurring in commercial trucks during their intended use.     

I. Minutes of the IAVSD Board Meetings

SUMMARY

A theoretical analysis is presented to model a hydromechanical, semi-active suspension system, first as a single wheel station and then as fitted to each wheel of an off-road vehicle. Predicted results show that two benefits are obtained by comparison with the equivalent passive system. First, vehicle attitude is controlled for changes in body forces arising from static loads or braking/cornering inputs. Second, a significant improvement in ride comfort is obtained because low suspension stiffnesses can be used.     

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.