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.     

Torque-based optimal vehicle speed control

This paper describes an optimal vehicle speed controller that uses torque-based control concepts. The controller design was divided into two steps: first, for a given vehicle speed trajectory, the engine torque demand was determined; in the second stage, a torque controller was implemented to track this torque demand. The torque demand was determined by a primary component and a correction component. The primary component was determined by solving an off-line optimization problem, and the correction component was added to compensate for the error caused by the off-line optimization. A modelbased proportional-integral (PI) feedback torque controller was employed to realize the engine torque tracking. Simulation results generated by a benchmark simulator were given to demonstrate performance of the optimal vehicle speed controller and a conventional PI speed controller that was included for comparison.     

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.     

Sliding mode observation and control for semiactive vehicle suspensions

This paper investigates the application of robust, nonlinear observation and control strategies, namely sliding mode observation and control (SMOC), to semiactive vehicle suspensions using a model reference approach. The vehicle suspension models include realistic nonlinearities in the spring and magnetorheological (MR) damper elements, and the nonlinear reference models incorporate skyhook damping. Since full state measurement is difficult to achieve in practice, a sliding mode observer (SMO) that requires only suspension deflection as a measured input is developed. The performance and robustness of sliding mode control (SMC), SMO, and SMOC are demonstrated through comprehensive computer simulations and compared to popular alternatives. The results of these simulations reveal the benefits of sliding mode observation and control for improved ride quality, and should be directly transferable to commercial semiactive vehicle suspension implementations.     

Sliding mode observation and control for semiactive vehicle suspensions

This paper investigates the application of robust, nonlinear observation and control strategies, namely sliding mode observation and control (SMOC), to semiactive vehicle suspensions using a model reference approach. The vehicle suspension models include realistic nonlinearities in the spring and magnetorheological (MR) damper elements, and the nonlinear reference models incorporate skyhook damping. Since full state measurement is difficult to achieve in practice, a sliding mode observer (SMO) that requires only suspension deflection as a measured input is developed. The performance and robustness of sliding mode control (SMC), SMO, and SMOC are demonstrated through comprehensive computer simulations and compared to popular alternatives. The results of these simulations reveal the benefits of sliding mode observation and control for improved ride quality, and should be directly transferable to commercial semiactive vehicle suspension implementations.     

Integrated fuzzy/optimal vehicle dynamic control

There are basically two methods to control yaw moment which is the most efficient way to improve vehicle stability and handling. The first method is indirect yaw moment control, which works based on control of the lateral tire force through steering angle control. It is mainly known as active steering control (ASC). Nowadays, the most practical approach to steering control is active front steering (AFS). The other method is direct yaw moment control (DYC), in which an unequal distribution of longitudinal tire forces (mainly braking forces) produces a compensating external yaw moment. It is well known that the AFS performance is limited in the non-linear vehicle handling region. On the other hand, in spite of a good performance of DYC in both the linear and non-linear vehicle handling regions, continued DYC activation could lead to uncomfortable driving conditions and an increase in the stopping distance in the case of emergency braking. It is recommended that DYC be used only in high-g critical maneuvers. In this paper, an integrated fuzzy/optimal AFS/DYC controller has been designed. The control system includes five individual optimal LQR control strategies; each one, has been designed for a specific driving condition. The strategies can cover low, medium, and high lateral acceleration maneuvers on high-μ or low-μ roads. A fuzzy blending logic also has been utilized to mange each LQR control strategy contribution level in the final control action. The simulation results show the advantages of the proposed control system over the individual AFS or DYC controllers.     

Adaptive neuron control using an integrated error approach with application to active suspensions

This paper proposes a new neuron control strategy for an active vehicle suspension system, with the emphasis on the study of multivariable and uncertain suspension characteristics. The novelty of this strategy is in the use of integrated error, which consists of multiple output errors in the regulated plant. By combining the integrated error approach with the traditional neuron control (TNC), integrated error neuron control (IENC) is presented. It provides a direct control to the multiple outputs of the control plant simultaneously. Taking a quarter-car model as an example, the proposed control strategy is applied and comparative simulations are carried out with various vehicle parameters and road input conditions. Simulation results prove the effectiveness and robustness of the proposed IENC method. In addition, the newly proposed neuron scheme provides a simple yet efficient new possibility for the control of a class of uncertain multivariable systems similar to an active vehicle suspension.     

Analytical solutions for optimal ride comfort and tyre grip for passive vehicle suspensions

The paper derives analytical solutions for the global optimum of the ride comfort and tyre grip performance measures for a quarter-car vehicle model optimised both individually and in combination. The solutions are derived for six simple suspension networks comprising one or two springs, one damper and possibly one inerter. The solutions are functions of four vehicle parameters: the sprung mass, the unsprung mass, the tyre stiffness and the static stiffness, of the suspension.     

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.     

Road disturbance estimation for the optimal preview control of an active suspension systems based on tracked vehicle model

This research investigates stochastic estimation of a look-ahead sensor scheme using the optimal preview control for an active suspension system of a full tracked vehicle (FTV). In this scheme, wheel disturbance input to the front wheels are estimated using the dynamic equations of the system. The estimated road disturbance input at the front wheels are utilized as preview information for the control of subsequently following wheels of FTV. The design of optimal preview control is used as a classical linear quadratic Gaussian problem by combining dynamics of the original system and estimation of previewed road inputs. The effectiveness of the preview controller is evaluated by comparing the estimated information with the measured information for different road profiles, where Kalman filter is used for the state-variables estimation of the FTV. This research also considers the reduced order estimation using commonly available sensors in order to decrease the number of sensors and measurements. The simulation results’ using an active suspension system with different preview information shows that the proposed system can be beneficial for the improvement of ride comfort of tracked vehicles without using any specialized sensors for preview information calculation.     

Pro-active optimal control for semi-active vehicle suspension based on sensitivity updates

This article suggests a strategy to control semi-active suspensions of vehicles in a pro-active way to adapt to future road profiles. The control strategy aims to maximise comfort while maintaining good handling properties. It employs suitably defined optimal control problems in combination with a parametric sensitivity analysis. The optimal control techniques are used to optimise the time-dependent damper coefficients in an electro-rheological damper for given nominal road profiles. The parametric sensitivity analysis is used to adapt the computed nominal optimal controls to perturbed road profiles in real time. The method is particularly useful for events with a low excitation frequency such as ramps, bumps, or potholes. For high-frequency excitations standard controllers are preferable; so we propose a switched open–closed-loop controller design. Various examples demonstrate the performance of the approach.     

联合仿真技市在车辆动力学稳定几天控制上的应用

首先介绍了目前车辆动力学稳定性控制的研究现状．提出了基于联合仿真平台进行控制仿真研究的新思路；其次详细分析了车辆动力学稳定性控制的原理。应用直接横摆力矩状态反馈控制策略，基于ADAMS／Car和Matlab／simulink的联合仿真技术．采用阶跃转向和单移线仿真工况有效验证了该控制策略的正确性，提高车辆在危险工况下的稳定性和可控性，为实际设计车辆动力学稳定性控制系统提供了理论基础。     

Identification of dynamic parameters in low-mobility mechanical systems: application to short long arm vehicle suspension

The identification of dynamic parameters in low-mobility mechanical systems is addressed and applied to short long arm (SLA) front car suspension. The main goal of the identification technique is to obtain, from experimental measurements, the values of those dynamic parameters (masses, location of the centre of masses, terms of the inertial matrix of the links, constant friction terms and elastic and viscous damping constant terms) that affect the dynamic behaviour of the system. Moreover, additional but important information that could be obtained from the procedure is related to the weight of those terms inside the dynamics of the system, so that simplified dynamic models based on relevant and well-identified parameters can be established. First, a systematic procedure will be presented for obtaining the equations of motion in a linear form with regard to the dynamic parameters to be identified. The main drawbacks related to the identification of parameters in low-mobility mechanisms will be pointed out, mainly the difficulty of determining a natural cutoff point into the singular values of the observation matrix which allows us to determine the true dimension of the set of base parameters and of obtaining an observation matrix well conditioned from the numerical point of view that allows an identification in the presence of measurement error. The procedure proposed for overcoming these problems will be based on the development of symbolic relationships among the physical parameters in order to determine the true rank of the observation matrix and on the consideration of a reduced subset of the base parameters set. These relevant parameters will be selected according to their influence on the dynamic behaviour of the mechanical system. A virtual benchmark will be used for testing purposes. The dynamic models based on relevant parameters show a better adjustment than the complete ones, mainly when the level of noise in the measurements used in the identification process increases.     

Nonlinear optimal integrated vehicle control using individual braking torque and steering angle with on-line control allocation by using state-dependent Riccati equation technique

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.     

Design of passive vehicle suspensions for maximal least damping ratio

This paper studies the use of the least damping ratio among system poles as a performance metric in passive vehicle suspensions. Methods are developed which allow optimal solutions to be computed in terms of non-dimensional quantities in a quarter-car vehicle model. Solutions are provided in graphical form for convenient use across vehicle types. Three suspension arrangements are studied: the standard suspension involving a parallel spring and damper and two further suspension arrangements involving an inerter. The key parameters for the optimal solutions are the ratios of unsprung mass to sprung mass and suspension static stiffness to tyre vertical stiffness. A discussion is provided of performance trends in terms of the key parameters. A comparison is made with the optimisation of ride comfort and tyre grip metrics for various vehicle types.     

基于ADAMS整车操纵稳定性分析

利用ADAMS软件,建立整车模型。对整车进行操纵稳定性分析,包括稳态回转、角跃阶输入、低速与高速转向回正以及单移线试验。从而实现了虚拟样机技术的应用,仿真分析整车的操纵稳定性,也验证了模型建立的准确性。     

Non-linear modelling and control of semi-active suspensions with variable damping

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f–v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief–desire–intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.     

New level of vehicle comfort and vehicle stability via utilisation of the suspensions anti-dive and anti-squat geometry

In this article a novel vehicle dynamics control concept is designed for a vehicle equipped with wheel individual electric traction machines, electronically controlled brakes and semi-active suspensions. The suspension's cross-couplings between traction forces and vertical forces via anti-dive and anti-squat geometry is utilised in the control concept to improve driving comfort and driving stability. The control concept is divided into one main and two cascaded branches. The main controller consists of a multivariable vehicle dynamics controller and a control allocation scheme to improve the vehicle's driving comfort. The cascaded feedback loops maintain the vehicle's stability according to wheel slip and vehicle sideslip. The performance of the combined vehicle dynamics controller is compared to a standard approach in simulation. It can be stated that the controller piloting semi-active suspensions together with brake and traction devices enables a superior performance regarding comfort and stability.     

驾驶员方向控制模型及在汽车智能驾驶研究中的应用

分析了驾驶员开车行为特性，利用模糊决策理论介绍了汽车预期行驶轨迹驾驶员模糊决策模型，并结合驾驶员预瞄最优曲率模型建立了一个新的驾驶员方向控制模型，同时也论述了该驾驶员方向控制模型在汽车智能驾驶研究中的应用。仿真结果表明所提出的模型可以描述驾驶员对汽车行驶方向的控制行为，并为汽车智能驾驶的研究提供了一条可行途径。