Nonlinear H∞ control for semi-active suspension

This paper describes the development of a damping control system for semi-active suspension which is based on nonlinear H_∞ control theory instead of conventional linear control theory. A two degrees of freedom system is used as the structure for the vehicle suspension model. Since the structure is bilinear, it's not easy to design the controller. We designed the controller based on the Hamilton-Jacobi inequality by solving a linear Riccati equation. We were able to verify by simulation that nonlinear H_∞ control theory made it possible to control vehicle vibration optimally and smoothly.     

Nonlinear robust control of integrated vehicle dynamics

A new methodology to design the vehicle GCC (global chassis control) nonlinear controller is developed in this paper. Firstly, to handle the nonlinear coupling between sprung and unsprung masses, the vehicle is treated as a mechanical system of two-rigid-bodies which has 6 DOF (degree of freedom), including longitudinal, lateral, yaw, vertical, roll and pitch dynamics. The system equation is built in the yaw frame based on Lagrange's method, and it has been proved that the derived system remains the important physical properties of the general mechanical system. Then the GCC design problem is formulated as the trajectory tracking problem for a cascade system, with a Lagrange's system interconnecting with a linear system. The nonlinear robust control design problem of this cascade interconnected system is divided into two H _∞ control problems with respect to the two sub-systems. The parameter uncertainties in the system are tackled by adaptive theory, while the external uncertainties and disturbances are dealt with the H _∞ control theory. And the passivity of the mechanical system is applied to construct the solution of nonlinear H _∞ control problem. Finally, the effectiveness of the proposed controller is validated by simulation results even during the emergency manoeuvre.     

Non-fragile multi-objective static output feedback control of vehicle active suspension with time-delay

This paper presents an approach to design a delay-dependent non-fragile H_∞/L₂–L_∞ static output feedback (SOF) controller for active suspension with input time-delay. The control problem of quarter-car active suspension with actuator time-delay is formulated to a H_∞/L₂–L_∞ control problem. By employing a delay-dependent Lyapunov function, new existence conditions of delay-dependent non-fragile SOF H_∞ controller and L₂–L_∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities (BMIs). Then, a procedure based on linear matrix inequality optimisation and a hybrid algorithm of the particle swarm optimisation and differential evolution is used to solve an optimisation problem with BMI constraints. Design and simulation results of non-fragile H_∞/L₂–L_∞ controller for active suspension show that the designed controller not only can achieve the optimal performance and stability of the closed-loop system in spite of the existence of the actuator time-delay, but also has significantly improved the non-fragility characteristics over controller perturbations.     

New energy recovery H∞ robust controller for electric bicycles

The electric controller is one of the most crucial components in an electric bicycle. The overall performance of the whole system heavily depends on the properties of the controller. The authors use the robust control theory to design a new H_∞ robust controller for the closed speed-current dual-loop driving and braking system. The designed controller also incorporates the driving and energy recovery braking circuit. Therefore, it has energy recovery ability, which coverts the kinetic energy wasted in braking into electric energy to recharge the battery. This prolongs the driving distance per battery charge. The simulations and experiments show that the new H_∞ robust controller out-performs the traditional PID controller in many respects including stability, error, responding speed and driving distance per battery charge.     

Research on control strategy for differential steering system based on H mixed sensitivity

The differential steering system (DSS) of electric wheel vehicle gets rid of the restrictions of traditional steering system completely. As an ideal steering technology, it not only realizes the perfect combination of the road feel and the steering portability, but also realizes the harmony and unification between the steering maneuverability and safety. The structure and basic theory of the DSS of electric wheel vehicle are discussed in this paper. Based on these, the dynamic model of the steering system is built. Considering of the uncertainties and disturbances existing in the model, the H_∞ mixed sensitivity control theory is applied to achieve better tracking performance and road feel in the process of steering. Then, a H_∞ mixed sensitivity controller is designed to restrain the effect of the road disturbance and model uncertainties. The simulation results indicate that the DSS with the designed controller can effectively restrain the effect of noises and disturbances caused by random motivation from road, torque sensor measurement and model parameter uncertainty, and enable the driver to obtain satisfactory road feel.     

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.     

H 2 optimal control of disturbance-delayed systems with application to vehicle suspensions

Optimal control of systems with time delays among disturbances, such as vehicle suspensions, is a relatively simple but long-standing problem in time-delayed control. We consider the exact H ₂ optimal control of systems with time-delayed disturbances and develop a computationally efficient approach for controller synthesis. We extend the Lyapunov-based H ₂ norm computation to systems with time-delayed disturbances and then derive a concise formula to explicitly evaluate the sensitivity of the system H ₂ norm with respect to controller gains. Thence, a set of necessary conditions for H ₂ optimal control of such systems using static output feedback are obtained in the form of algebraic equations. Gradient-based methods are adapted to optimize the controller gains. The method is also extended to reduced-order and decentralized control. As an application, a passive suspension system for an eight-DOF four-wheel vehicle is designed via structured H ₂ optimization. The results are compared with those of a design based on a Pade expansion for the time delays and a design obtained by neglecting the disturbance delays.     

Lateral Collision Avoidance Robust Control of Electric Vehicles Combining a Lane-Changing Model Based on Vehicle Edge Turning Trajectory and a Vehicle Semi-Uncertainty Dynamic Model

This paper presents a new control scheme for lateral collision avoidance (CA) systems to improve the safety of four-in-wheel-motor-driven electric vehicles (FIWMD-EVs). There are two major contributions in the design of lateral CA systems. The first contribution is a new lane-changing model based on vehicle edge turning trajectory (VETT) to make vehicle adapt to different driving roads and conform to drivers’ characteristic, in addition to ensure vehicle steering safety. The second contribution is vehicle semi-uncertainty dynamic model (SUDM), which is SISO model. The problem of stability performance without the information on sideslip angle is solved by the proposed SUDM. Based on the proposed VETT and SUDM, the lateral CA system can be designed with H_∞ robust controller to restrain the effect of uncertainties resulting from parameter perturbation and lateral wind disturbance. Single and mixed driving cycles simulation experiments are carried out with CarSim to demonstrate the effectiveness in control scheme, simplicity in structure for lateral CA system based on the proposed VETT and SUDM.     

Output feedback H ∞/GH 2 preview control of active vehicle suspensions: a comparison study of LQG preview

This study concerns with multi-objective H _∞/GH ₂ preview control of active vehicle suspensions. This control scheme has two main aspects: first, it allows constrained outputs of the system to vary freely as long as they remain within their given bounds, in order that the best possible performance could be delivered. Secondly, the optimisation as well as constraint fulfilment is done for the worst-case road disturbances to cover all road types. To design a system to perform satisfactorily for a wide range of road irregularities, H _∞-norm is used wherever minimisation is required, and generalised H ₂-norm is used to care for the constraints on suspension working space. Moreover, to ensure desired stability margins for the system, pole location constraints are considered in the design. The proposed approach is evaluated on a quarter-car model and compared with the state-of-the-art preview control algorithm in the literature, namely, Linear quadratic Gaussian preview. Simulation results demonstrate the effectiveness of the proposed approach.     

Active lateral secondary suspension with H ∞ control to improve ride comfort: simulations on a full-scale model

In this study, a full-scale rail vehicle model is used to investigate how lateral ride comfort is influenced by implementing the H _∞ and sky-hook damping control strategies. Simulations show that significant ride comfort improvements can be achieved on straight track with both control strategies compared with a passive system. In curves, it is beneficial to add a carbody centring Hold-Off Device (HOD) to reduce large spring deflections and hence to minimise the risk of bumpstop contact. In curve transitions, the relative lateral displacement between carbody and bogie is reduced by the concept of H _∞ control in combination with the HOD. However, the corresponding concept with sky-hook damping degrades the effect of the carbody centring function. Moreover, it is shown that lateral and yaw mode separation is a way to further improve the performance of the studied control strategies.     

Robust control and actuator dynamics compensation for railway vehicles

A robust controller is designed for active steering of a high speed train bogie with solid axle wheel sets to reduce track irregularity effects on the vehicle’s dynamics and improve stability and curving performance. A half-car railway vehicle model with seven degrees of freedom equipped with practical accelerometers and angular velocity sensors is considered for the H_∞ control design. The controller is robust against the wheel/rail contact parameter variations. Field measurement data are used as the track irregularities in simulations. The control force is applied to the vehicle model via ball-screw electromechanical actuators. To compensate the actuator dynamics, the time delay is identified online and is used in a second-order polynomial extrapolation carried out to predict and modify the control command to the actuator. The performance of the proposed controller and actuator dynamics compensation technique are examined on a one-car railway vehicle model with realistic structural parameters and nonlinear wheel and rail profiles. The results showed that for the case of nonlinear wheel and rail profiles significant improvements in the active control performance can be achieved using the proposed compensation technique.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> preview control of an active suspension system with norm-bounded uncertainties

A robust H _∞ preview control is investigated for an active suspension system with look-ahead sensors. The uncertain system is described by a state-space model with linear nominal parts and additional nonlinear time-varying norm-bounded uncertainties. Proof of robust stability and a feedback-type robust H _∞ preview controller are derived by augmenting the dynamics of the original system and previewed road input. As, however, the augmented previewed road input gives the system a much larger dimension than the original system, much more computation time is required for solving of Riccati equations. To resolve this problem, a decomposed robust H _∞ preview controller is proposed. Robust stability and performance variations for system uncertainties are shown using a numerical example of a quarter-car model.     

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.     

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.     

Multi-objective control of a full-car model using linear-matrix-inequalities and fixed-order optimisation

This paper studies multi-objective control of a full-vehicle suspension excited by random road disturbances. The control problem is first formulated as a mixed ?₂/?_∞ synthesis problem and an output-feedback solution is obtained by using linear-matrix-inequalities. Next, the multi-objective control problem is re-formulated as a non-convex and non-smooth optimisation problem with controller order restricted to be less than the vehicle model order. For a range of orders, controllers are synthesised by using the HIFOO toolbox. The efficacy of the presented procedures are demonstrated by several design examples.     

Design of an Active Unilateral Brake Control System for Five-Axle Tractor-Semitrailer Based on Sensitivity Analysis

SUMMARY

This paper presents the results of a parametric sensitivity analysis of a five-axle tractor-semitrailer vehicle combination using 3-DOF linear yaw/plane model. The first order logarithmic sensitivity functions are derived with respect to several vehicle design parameters. For stabilization of the vehicle's directional behaviour a fairly new control concept called “Active Unilateral Braking Control (AUBC)” acting on the tractor rear wheel's in order to produce a stabilizing yaw torque is investigated. The AUBC system improves not only the directional stability, but also affects the roll dynamics of the vehicle. The sensitivity of the controlled vehicle system with linear quadratic controller (LQR) is also examined, a robust controller design procedure is proposed as a result of the sensitivity analysis. The robustness of this controller in the presence of both internal (including parametric uncertainties, non-linear dynamics) and external disturbances (such as road irregularities and side wind) allows its implementation with confidence with a non-linear vehicle model. The applicability of this control system to a non-linear vehicle model is tested using a 34 DOF, non-linear vehicle model of the tractor-semitrailer combination.     

A nonlinear virtual rider for motorcycles

This work presents a virtual rider for the guidance of a nonlinear motorcycle model. The target motion is defined in terms of roll angle and speed. The virtual rider inputs are the steering torque, the rear-wheel driving/braking torque and front-wheel braking torque. The virtual rider capability is assessed by guiding the nonlinear motorcycle model in demanding manoeuvres with roll angles of 50° and longitudinal accelerations up to 0.8 g. Considerations on the effective preview distance used by the virtual rider are included.     

Torque coordinating robust control of shifting process for dry dual clutch transmission equipped in a hybrid car

For a hybrid car equipped with dual clutch transmission (DCT), the coordination control problems of clutches and power sources are investigated while taking full advantage of the integrated starter generator motor's fast response speed and high accuracy (speed and torque). First, a dynamic model of the shifting process is established, the vehicle acceleration is quantified according to the intentions of the driver, and the torque transmitted by clutches is calculated based on the designed disengaging principle during the torque phase. Next, a robust H_∞ controller is designed to ensure speed synchronisation despite the existence of model uncertainties, measurement noise, and engine torque lag. The engine torque lag and measurement noise are used as external disturbances to initially modify the output torque of the power source. Additionally, during the torque switch phase, the torque of the power sources is smoothly transitioned to the driver's demanded torque. Finally, the torque of the power sources is further distributed based on the optimisation of system efficiency, and the throttle opening of the engine is constrained to avoid sharp torque variations. The simulation results verify that the proposed control strategies effectively address the problem of coordinating control of clutches and power sources, establishing a foundation for the application of DCT in hybrid cars.     

Dynamic analysis and control of an anti-lock brake system for a motorcycle with a camber angle

This paper analyses the dynamic response of a motorcycle with an anti-lock brake system (ABS) and camber or steering angle. Most studies have assumed that motorcycles brake in a straight line – that is, without a steering or camber angle. In this work, the performance of an ABS modulator is designed and analysed at first. Then, a controller is designed for motorcycle turning. The controller uses angular acceleration and the pressure value in brake calipers on the front and rear wheels, camber angle and lateral acceleration as commands to control brake pressure on each wheel to prevent wheel locking. The equation of motion for a motorcycle is based on Weir's equations. This motorcycle model combines a mathematical equation of the ABS modulator, tyre model and controller in simulations.     

基于三自由度的智能汽车模糊滑模横向运动控制研究

针对智能汽车运动过程中存在的车身姿态变化问题以及运动控制精度问题，设计了一种基于非线性3自由度动力学模型的模糊滑模横向运动控制器。建立了包括侧倾运动的3自由度动力学模型，进行了模型线性化；对基于线性化处理后的动力学模型进行了滑模控制器设计，通过控制前轮转角实现了路径跟踪横向控制，并引入了模糊控制提高控制效果，本控制系统能够在跟踪过程中对车身姿态变化进行观察。仿真结果表明，搭建的基于3自由度动力学模型的模糊滑模控制器能够在考虑侧倾运动的基础上，实现路径跟踪，且构建的模糊滑模控制系统相较于传统滑模控制其横向偏差与方向偏差分别降低了7.28%和1.50%，同时模糊控制也减弱了滑模控制固有的抖振影响。