Decoupling control in velocity-varying four-wheel steering vehicles with H∞ performance by longitudinal velocity and yaw rate feedback

In this paper, decoupling control with H_∞ performance for four-wheel steering (4WS) vehicles under varying longitudinal velocity is studied. A novel control scheme for a nonlinear model of three states, respectively, the longitudinal and lateral velocities, and yaw rate, is proposed to address this issue. The scheme is composed of two varying-parameter controllers designing problems for both longitudinal and lateral systems with coupling performance. Varying parameters of both these controllers depend only on longitudinal velocity. Controlled by these controllers, the longitudinal system is decoupled with lateral velocity and yaw rate, and the lateral system is input–output decoupling with H_∞ performance. In addition, feedback signals are the longitudinal velocity and yaw rate, hence observations or measurements of lateral velocity are not necessary. Simulations show that vehicles controlled by our scheme are input–output diagonal decoupling and execute very well while longitudinal velocity varies in a large range, coupling appears between longitudinal and lateral systems, and external disturbances do exist. In summary, this control scheme can improve handling characteristics, safety and comfort proved from theory to practice in this paper.     

Analyses of Vision-based Lateral Control for Automated Highway System

The stability and performance of a vision-based vehicle lateral control system are analyzed. Effects of look-ahead distance, vision delay, and vehicle speed on the performance of vision feedback control system are examined by using frequency domain and time domain methods. A measurement model of the vision system is derived from the point of view of multiple sensors. The quantization error of the vision system is analyzed and the way of extracting essential information for control is studied. Based on this analysis, some guidelines for the design of vision-based controllers are proposed. A design example is further illustrated for a vision system with a substantial time delay.     

Analyses of Vision-based Lateral Control for Automated Highway System

SUMMARY

The stability and performance of a vision-based vehicle lateral control system are analyzed. Effects of look-ahead distance, vision delay, and vehicle speed on the performance of vision feedback control system are examined by using frequency domain and time domain methods. A measurement model of the vision system is derived from the point of view of multiple sensors. The quantization error of the vision system is analyzed and the way of extracting essential information for control is studied. Based on this analysis, some guidelines for the design of vision-based controllers are proposed. A design example is further illustrated for a vision system with a substantial time delay.     

Towards comfort-optimal trajectory planning and control

ABSTRACT

This paper describes a method to analyse and evaluate different trajectory planning methods and controller types for usage in automated vehicles. Its application is shown by using a novel trajectory planning approach considering comfort aspects (based on Rapidly Exploring Random Tree (RRT)), two different controllers to follow the planned path (cascade controller and flatness based controller) and a simulation method to obtain resulting lateral vehicle accelerations. The method is used to plan and drive a trajectory through a roundabout. It can be seen that the lateral accelerations of the controller-driven vehicle are in the range of the values used for planning. However, the results of both controllers show differences in lateral deviation and in smoothness of lateral accelerations. The simulation results are then compared to real-world test drives in the same roundabout. The measured lateral accelerations are in the same range as well but show a smoother progression than the two controller models.     

Active front wheel steering model and controller for integrated dynamics control systems

We report a model and controller for an active front-wheel steering (AFS) system. Two integrated dynamics control (IDC) systems are designed to investigate the performance of the AFS system when integrated with braking and steering systems. An 8-degrees-of-freedom vehicle model was employed to test the controllers. The controllers were inspected and compared under different driving and road conditions, with and without braking input, and with and without steering input. The results show that the AFS system performs kinematic steering assistance function and kinematic stabilisation function very well. Three controllers allowed the yaw rate to accurately follow a reference yaw rate, improving the lateral stability. The two IDC systems improved the lateral stability and vehicle control and were effective in reducing the sideslip angle.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Model Development,Validation and Comparison

SUMMARY

Recent research on autonomous highway vehicles has begun to focus on lateral control strategies. The initial work has focused on vehicle control during low-g maneuvers at constant vehicle speed, typical of lane merging and normal highway driving. In this paper, and its companion paper, to follow, the lateral control of vehicles during high-g emergency maneuvers is addressed. Models of the vehicle dynamics are developed, showing the accuracy of the different models under low and high-g conditions. Specifically, body roll, tire and drive-train dynamics, tire force saturation, and tire side force lag are shown to be important effects to include in models for emergency maneuvers. Current controllers, designed for low-g maneuvers only, neglect these effects. The follow on paper demonstrates the performance of lateral controllers during high-g lateral emergency maneuvers using these vehicle models.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Model Development, Validation and Comparison

Recent research on autonomous highway vehicles has begun to focus on lateral control strategies. The initial work has focused on vehicle control during low-g maneuvers at constant vehicle speed, typical of lane merging and normal highway driving. In this paper, and its companion paper, to follow, the lateral control of vehicles during high-g emergency maneuvers is addressed. Models of the vehicle dynamics are developed, showing the accuracy of the different models under low and high-g conditions. Specifically, body roll, tire and drive-train dynamics, tire force saturation, and tire side force lag are shown to be important effects to include in models for emergency maneuvers. Current controllers, designed for low-g maneuvers only, neglect these effects. The follow on paper demonstrates the performance of lateral controllers during high-g lateral emergency maneuvers using these vehicle models.     

Full drive-by-wire dynamic control for four-wheel-steer all-wheel-drive vehicles

Most of the controllers introduced for four-wheel-steer (4WS) vehicles are derived with the assumption that the longitudinal speed of the vehicle is constant. However, in real applications, the longitudinal speed varies, and the longitudinal, lateral, and yaw dynamics are coupled. In this paper, the longitudinal dynamics of the vehicle as well as its lateral and yaw motions are controlled simultaneously. This way, the effect of driving/braking forces of the tires on the lateral and yaw motions of the vehicle are automatically included in the control laws. To address the dynamic parameter uncertainty of the vehicle, a chatter-free variable structure controller is introduced. Elimination of chatter is achieved by introducing a dynamically adaptive boundary layer thickness. It is shown via simulations that the proposed control approach performs more robustly than the controllers developed based on dynamic models, in which longitudinal speed is assumed to be constant, and only lateral speed and yaw rate are used as system states. Furthermore, this approach supports all-wheel-drive vehicles. Front-wheel-drive or rear-wheel-drive vehicles are also supported as special cases of an all-wheel-drive vehicle.     

Handling stability improvement through robust active front steering and active differential control

The design of the integrated active front steering and active differential control for handling improvement of road vehicles is undertaken. The controller design algorithm is based on the solution of a set of linear matrix inequalities that guarantee robustness against a number of vehicle parameters such as speed, cornering and braking stiffnesses. Vehicle plane dynamics are first expressed in the generic linear parameter-varying form, where the above-stated parameters are treated as interval uncertainties. Then, static-state feedback controllers ensuring robust performance against changing road conditions are designed. In a first series of simulations, the performance of the integrated controller is evaluated for a fishhook manoeuvre for different values of road adhesion coefficient. Then, the controller is tested for an emergency braking manoeuvre executed on a split-μ road. In all cases, it is shown that static-state feedback controllers designed by the proposed method can achieve remarkable road handling performance compared with uncontrolled vehicles.     

Designing H∞/GH 2 static-output feedback controller for vehicle suspensions using linear matrix inequalities and genetic algorithms

This paper presents an approach to design the H_∞/GH ₂ static-output feedback controller for vehicle suspensions by using linear matrix inequalities (LMIs) and genetic algorithms (GAs). Three main performance requirements for an advanced vehicle suspension are considered in this paper. Among these requirements, the ride-comfort performance is optimized by minimizing the H_∞ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road-holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H₂ (GH ₂) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH ₂ norm as well. A four-degree-of-freedom half-car model with active suspension system is applied in this paper. Several kinds of H_∞/GH ₂ static-output feedback controllers, which use the available sprung mass velocities or the suspension deflections as feedback signals, are obtained by using the GAs to search for the possible control gain matrices and then resolving the LMIs together with the minimization optimization problem. These designed H_∞/GH ₂ static-output feedback controllers are validated by numerical simulations on both the bump and the random road responses which show that the designed H_∞/GH ₂ static-output feedback controllers can achieve similar or even better active suspension performances compared with the state-feedback control case in spite of their simplicities.     

Design of Nonlinear Controllers for Active Vehicle Suspensions Using Parameter-Varying Control Synthesis

Nonlinear suspension controllers have the potential to achieve superior performance compared to their linear counterparts. A nonlinear controller can focus on maximizing passenger comfort when the suspension deflection is small compared to its structural limit. As the deflection limit is approached, the controller can shift focus to prevent the suspension deflection from exceeding this limit. This results in superior ride quality over the range of road surfaces, as well as reduced wear of suspension components. This paper presents a novel approach to the design of such nonlinear controllers, based on linear parameter-varying control techniques. Parameter-dependent weighting functions are used to design active suspensions that stiffen as the suspension limits are reached. The controllers use only suspension deflection as a feedback signal. The proposed framework easily extends to the more general case where all the three main performance metrics, i.e., passenger comfort, suspension travel and road holding are considered, and to the design of road adaptive suspensions.     

Design of Nonlinear Controllers for Active Vehicle Suspensions Using Parameter-Varying Control Synthesis

Nonlinear suspension controllers have the potential to achieve superior performance compared to their linear counterparts. A nonlinear controller can focus on maximizing passenger comfort when the suspension deflection is small compared to its structural limit. As the deflection limit is approached, the controller can shift focus to prevent the suspension deflection from exceeding this limit. This results in superior ride quality over the range of road surfaces, as well as reduced wear of suspension components. This paper presents a novel approach to the design of such nonlinear controllers, based on linear parameter-varying control techniques. Parameter-dependent weighting functions are used to design active suspensions that stiffen as the suspension limits are reached. The controllers use only suspension deflection as a feedback signal. The proposed framework easily extends to the more general case where all the three main performance metrics, i.e., passenger comfort, suspension travel and road holding are considered, and to the design of road adaptive suspensions.     

Modal Controllers for Active Steering of Railway Vehicles with Solid Axle Wheelsets

This paper presents the development of a modal control strategy for the active steering of solid axle railway vehicles and reveals benefits of actively stabilising the wheelsets of a railway vehicle. A modal decomposition is applied to a 2-axle railway vehicle to de-couple its body lateral and yaw motions and hence to allow more detailed analysis of the vehicle behaviour and more robust design of active controllers. Independent controllers for the two motions are developed based on the two de-coupled modes. Parameter variations such as creep coefficients and wheelset conicity are taken into account in the design process to guarantee a robust design. The study shows that, compared to a passive vehicle, the vehicles with actively steered wheelsets not only perform much better on a curved track, but also improve the ride quality on straight track. Computer simulations are used in the study to verify the development of the controllers and assess the system performance with the control scheme proposed.     

Modal Controllers for Active Steering of Railway Vehicles with Solid Axle Wheelsets

This paper presents the development of a modal control strategy for the active steering of solid axle railway vehicles and reveals benefits of actively stabilising the wheelsets of a railway vehicle. A modal decomposition is applied to a 2-axle railway vehicle to de-couple its body lateral and yaw motions and hence to allow more detailed analysis of the vehicle behaviour and more robust design of active controllers. Independent controllers for the two motions are developed based on the two de-coupled modes. Parameter variations such as creep coefficients and wheelset conicity are taken into account in the design process to guarantee a robust design. The study shows that, compared to a passive vehicle, the vehicles with actively steered wheelsets not only perform much better on a curved track, but also improve the ride quality on straight track. Computer simulations are used in the study to verify the development of the controllers and assess the system performance with the control scheme proposed.     

Designing H ∞/GH 2 static-output feedback controller for vehicle suspensions using linear matrix inequalities and genetic algorithms

This paper presents an approach to design the H _∞/GH ₂ static-output feedback controller for vehicle suspensions by using linear matrix inequalities (LMIs) and genetic algorithms (GAs). Three main performance requirements for an advanced vehicle suspension are considered in this paper. Among these requirements, the ride-comfort performance is optimized by minimizing the H _∞ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road-holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H ₂ (GH ₂) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH ₂ norm as well. A four-degree-of-freedom half-car model with active suspension system is applied in this paper. Several kinds of H _∞/GH ₂ static-output feedback controllers, which use the available sprung mass velocities or the suspension deflections as feedback signals, are obtained by using the GAs to search for the possible control gain matrices and then resolving the LMIs together with the minimization optimization problem. These designed H _∞/GH ₂ static-output feedback controllers are validated by numerical simulations on both the bump and the random road responses which show that the designed H _∞/GH ₂ static-output feedback controllers can achieve similar or even better active suspension performances compared with the state-feedback control case in spite of their simplicities.     

Pole location control design of an active suspension system with uncertain parameters

This paper addresses the problem of robust control design for an active suspension quarter-car model by means of state feedback gains. Specifically, the design of controllers that assure robust pole location of the closed-loop system inside a circular region on the left-hand side of complex plane is investigated. Three sufficient conditions for the existence of a robust stabilizing state feedback gain are presented as linear matrix inequalities: (i) the quadratic stability based gain; (ii) a recently published condition that uses an augmented space and has been here modified to cope with the pole location specification; (iii) a condition that uses an extended number of equations and yields a parameter-dependent state feedback gain. Unlike other parameter-dependent strategies, neither extensive gridding nor approximations are needed. In the suspension model, the sprung mass, the damper coefficient and the spring constant are considered as uncertain parameters belonging to a known interval (polytope type uncertainty). It is shown that the parameter-dependent gain proposed allows one to impose the closed-loop system pole locations that in some situations cannot be obtained with constant feedback gains.     

Pole location control design of an active suspension system with uncertain parameters

This paper addresses the problem of robust control design for an active suspension quarter-car model by means of state feedback gains. Specifically, the design of controllers that assure robust pole location of the closed-loop system inside a circular region on the left-hand side of complex plane is investigated. Three sufficient conditions for the existence of a robust stabilizing state feedback gain are presented as linear matrix inequalities: (i) the quadratic stability based gain; (ii) a recently published condition that uses an augmented space and has been here modified to cope with the pole location specification; (iii) a condition that uses an extended number of equations and yields a parameter-dependent state feedback gain. Unlike other parameter-dependent strategies, neither extensive gridding nor approximations are needed. In the suspension model, the sprung mass, the damper coefficient and the spring constant are considered as uncertain parameters belonging to a known interval (polytope type uncertainty). It is shown that the parameter-dependent gain proposed allows one to impose the closed-loop system pole locations that in some situations cannot be obtained with constant feedback gains.     

Multivariable speed synchronisation for a parallel hybrid electric vehicle drivetrain

In this article, a new drivetrain configuration of a parallel hybrid electric vehicle is considered and a novel model-based control design strategy is given. In particular, the control design covers the speed synchronisation task during a restart of the internal combustion engine. The proposed multivariable synchronisation strategy is based on feedforward and decoupled feedback controllers. The performance and the robustness properties of the closed-loop system are illustrated by nonlinear simulation results.     

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

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.     

A model of driver steering control incorporating the driver's sensing of steering torque

Steering feel, or steering torque feedback, is widely regarded as an important aspect of the handling quality of a vehicle. Despite this, there is little theoretical understanding of its role. This paper describes an initial attempt to model the role of steering torque feedback arising from lateral tyre forces. The path-following control of a nonlinear vehicle model is implemented using a time-varying model predictive controller. A series of Kalman filters are used to represent the driver's ability to generate estimates of the system states from noisy sensory measurements, including the steering torque. It is found that under constant road friction conditions, the steering torque feedback reduces path-following errors provided the friction is sufficiently high to prevent frequent saturation of the tyres. When the driver model is extended to allow identification of, and adaptation to, a varying friction condition, it is found that the steering torque assists in the accurate identification of the friction condition. The simulation results give insight into the role of steering torque feedback arising from lateral tyre forces. The paper concludes with recommendations for further work.