Optimal Linear Preview Control of Active Vehicle Suspension

SUMMARY

The problem of linear preview control of vehicle suspension is considered as a continuous time stochastic optimal control problem. In the proposed approach minimal a priori information about the road irregularities is assumed and measurement errors are taken into account. It is shown that estimation and control issues can be decoupled. The problem formulation and the analytical solution are given in a general form and hence they apply to other problems in which the system disturbances are unknown a priori, even in a stochastic sense, but some preview information is possible.

The solution is applied to a two-degree-of-freedom (2-DOF) vehicle model. The effects of preview information on ride comfort, road holding, working space of the suspension and power requirements are examined in time and frequency domains. The results show that the greatest potential is for improving road holding properties. This effect could not have been observed in previous studies based on a 1-DOF vehicle model. It is also demonstrated that the presence of preview drastically reduces power requirements, thus relieving the performance versus actuator power dilemma.     

Constrained Optimal Control of Semi-Active Suspension Systems with Preview

Controllers for semi-active suspensions have to account for constraints on damper range, tire force and suspension travel. Two approaches to incorporate these constraints in the design of controllers to minimize peak values in the chassis acceleration are considered. It is assumed that information on the oncoming road elevations (preview) is available. In the soft constraint approach, the constraints on tire force and suspension travel are included in a quadratic performance index. Two clipped optimal control laws, which deal with preview in a different way, are presented. Simulation results with a 2-DOF vehicle model on some rounded pulses show that these laws do not work satisfactorily with respect to the constraints. Therefore, the control problem is reformulated as a constrained optimization problem with hard constraints on tire force and suspension travel. Simulations with the same model on the same rounded pulses show that the hard constraint approach handles the constraints more properly.     

Using the lead vehicle as preview sensor in convoy vehicle active suspension control

Both ride quality and roadholding of actively suspended vehicles can be improved by sensing the road ahead of the vehicle and using this information in a preview controller. Previous applications have used look-ahead sensors mounted on the front bumper to measure terrain beneath. Such sensors are vulnerable, potentially confused by water, snow, or other soft obstacles and offer a fixed preview time. For convoy vehicle applications, this paper proposes using the overall response of the preceding vehicle(s) to generate preview controller information for follower vehicles. A robust observer is used to estimate the states of a quarter-car vehicle model, from which road profile is estimated and passed on to the follower vehicle(s) to generate a preview function. The preview-active suspension, implemented in discrete time using a shift register approach to improve simulation time, reduces sprung mass acceleration and dynamic tyre deflection peaks by more than 50% and 40%, respectively. Terrain can change from one vehicle to the next if a loose obstacle is dislodged, or if the vehicle paths are sufficiently different so that one vehicle misses a discrete road event. The resulting spurious preview information can give suspension performance worse than that of a passive or conventional active system. In this paper, each vehicle can effectively estimate the road profile based on its own state trajectory. By comparing its own road estimate with the preview information, preview errors can be detected and suspension control quickly switched from preview to conventional active control to preserve performance improvements compared to passive suspensions.     

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.     

Optimal Preview Control of a Two-dof Vehicle Model Using Stochastic Optimal Control Theory

An optimal preview control algorithm is applied to a two degree of freedom(dof) vehicle model travelling with constant velocity on a randomly profiled road. The road roughness is modelled as a homogeneous random process being the output of a linear first order filter to white noise. The input from the road irregularity is assumed to be measured at some distance in front of the vehicle and this measured infonnation is utilized by the active controller to prepare the system for the ensuing input. The preview control algorithm is obtained by minimizing a quadratic performance index and by describing the average behaviour of the system by the covariance matrix of the vehicle response state vector. Results are presented for full state feedback and significant improvements in sprung mass acceleration, suspension working space and road holding are observed.     

Hydro-pneumatic Slow-active Suspension with Preview Control

In this work, the preview control problem is considered for fully active and hydro-pneumatic slow-active systems. Based on the quarter car model, linear optimal control theory is used to derive the control laws. The Pade approximation technique is used to represent the preview time resulting from a preview sensor mounted at the front bumper to measure the road irregularities ahead of the front wheels. The results for the slow-active system with preview showed that there is 15% improvement in ride comfort compared to slow-active without preview and 28.5% improvement over passive system at similar root mean square (r.m.s) dynamic tyre load and suspension working space. The performance gains are, however, lower by about 15% than those obtainable with the theoretically ideal, fully active system with preview. The power results for slow active with and without preview showed that a 2kW fixed displacement hydraulic pump is enough for full vehicle requirements.     

Preview Estimation and Control for (Semi-) Active Suspensions

An active suspension with preview is tested for rounded pulses and a stochastic road surface, and is compared to a passive suspension. The spectacular performance improvement obtained for a step function as road surface is not achieved but the improvement is still significant. The frequency response of the active suspension is determined for comparison with some suspension systems found in literature

An observer to reconstruct the preview information is presented. No model of the road surface is needed. From simulations, it appears that the observer reconstructs both deterministic and stochastic road surfaces satisfactory. However, the influence of measurement noise is not reduced sufficiently.     

Preview Estimation and Control for (Semi-) Active Suspensions

SUMMARY

An active suspension with preview is tested for rounded pulses and a stochastic road surface, and is compared to a passive suspension. The spectacular performance improvement obtained for a step function as road surface is not achieved but the improvement is still significant. The frequency response of the active suspension is determined for comparison with some suspension systems found in literature

An observer to reconstruct the preview information is presented. No model of the road surface is needed. From simulations, it appears that the observer reconstructs both deterministic and stochastic road surfaces satisfactory. However, the influence of measurement noise is not reduced sufficiently.     

Preview suspension control for a full tracked vehicle

In this study, preview control algorithms for the active and semi-active suspension systems of a full tracked vehicle (FTV) are designed based on a 3-D.O.F model and evaluated. The main issue of this study is to make the ride comfort characteristics of a fast moving tracked vehicle better to keep an operator’s driving capability. Since road wheels almost trace the profiles of the road surface as long as the track doesn’t depart from the ground, the preview information can be obtained by measuring only the absolute position or velocity of the first road wheel. Simulation results show that the performance of the sky-hook suspension system almost follows that of full state feedback suspension system and the on-off semi-active system carries out remarkable performance with the combination of 12 on-off semi-active suspension units. The results simulated with 1^st and 2^nd weighting sets mean that the suspension system combined with the soft type of inner suspension and hard type of outer suspension can carry out better ride comfort characteristics than that with identical suspensions. The full tracked vehicle (FTV) system is uncontrollable and the system is split into controllable and uncontrollable subspace using singular value decomposition transformation. Frequency response curves to four types of inputs, such as heaving, pitching, rolling, and warping inputs, also demonstrate the merits of preview control in ride comfort. All the frequency characteristic responses confirm the continuous time results.     

结合卡尔曼滤波器的车辆主动悬架轴距预瞄控制研究

利用轴距预瞄信息，即前后轮路面输入之关系，同时结合卡尔曼滤波器作为状态估计器，本文提出了一种算法用于车辆悬架控制律的设计，根据模拟结果，研究了算法的可行性，分析了卡尔曼滤波器对状态变量的估计精度，以及轴距预瞄控制对进一步改进车辆性能的潜力。     

Performance Index for a Preview Active Suspension Applied to a Quarter-Car Model

A simple and convenient matrix expression is derived for the performance index in the case of a linear vehicle model with two degrees of freedom and a preview active suspension, subject to a unit step road input and employing optimal control. The usual quadratic integral-type performance index is assumed and the effect of an additional form of constraint is described briefly. The effects of preview time on the performance index and the optimal feed-forward control are illustrated graphically for a particular example.     

Performance Index for a Preview Active Suspension Applied to a Quarter-Car Model

A simple and convenient matrix expression is derived for the performance index in the case of a linear vehicle model with two degrees of freedom and a preview active suspension, subject to a unit step road input and employing optimal control. The usual quadratic integral-type performance index is assumed and the effect of an additional form of constraint is described briefly. The effects of preview time on the performance index and the optimal feed-forward control are illustrated graphically for a particular example.     

主动悬架最优控制整车模型的研究

以一个车辆的整车模型为研究对象，通过利用轴距预瞄信息，应用最优控制理论设计了一个车辆的悬架控制策略，通过模拟和仿真的结果，验证了该模型和算法的可行性，并分析了轴距预瞄控制对于改进车辆性能的能力，检验了所建立的整车模型。     

Optimization and Performance Enhancement of Active Suspensions for Automobiles under Preview of the Road

The problem of deriving control laws which minimize specified performance indices for a vehicle moving on a rough surface with preview of the surface elevation is considered. The approach is based on linear optimal tracking theory and consequently the system elements are taken to be linear and the performance index is constrained to be of quadratic form.

The ideas of overtaking optimality are applied to the problem in order to achieve a closed form solution for the control. Then, using the control laws derived, computer simulations of performance are conducted and time histories are shown. In the absence of limitations on either processing or actuator speeds, and for cases in which the preview is sufficient to give good control laws, the value of the preview in enhancing vehicle suspension performance is assessed. Comparisons are made with results in the literature.     

油气弹簧非线性特性对车辆平顺性的影响分析

推导并建立了某工程车辆油气弹簧的非线性刚度和阻尼特性的数学模型，并将其导入到车辆模型中。根据汽车悬架质量分配特点．将汽车简化为两自由度的舣质量振动系统，对此两自由度模型的车轮加速度、车身加速度和悬架动行程进行了仿真从仿真结果可以看出，非线性油气弹簧能很好地衰减由路面传递来的振动。分析了刚度和阻尼的变化对车辆平顺性的影响。     

RMS Values for Force, Stroke and Deflection in a Quarter-car Model Active Suspension with Preview

Summary In the case of a quarter-car vehicle model incorporating an active suspension, the addition of preview to the system necessitates finding new techniques for the direct computation of rms values for control force, suspension stroke and tyre deflection on a random road. Here we obtain these rms values from the performance index components as derived analytically by means of matrix operations requiring the solution of Lyapunov equations and the use of similarity transformations. Some numerical examples and MATLAB programs are included.     

An Experimental Investigation of Preview Control

There is mounting theoretical evidence to suggest that preview control can be of substantial benefit to a semi-active suspension for random road inputs. In this paper, the benefits of wheel-base preview control are measured experimentally, using a prototype semi-active damper in a half-car 'Hardware-in-the-loop' (HiL) rig with a planar two-axle heavy vehicle model. The benefits of preview control using the prototype semi-active damper are found to be less than theoretically possible, due to the phase lag between the demanded and achieved damping force. It is shown that the performance of the prototype damper can be improved significantly by having a theoretical simulation running ahead of the HiL vehicle. The theoretical simulation is used to predict the demanded damper force for the HiL vehicle, and thereby compensate for the phase lag in the prototype damper.     

An Experimental Investigation of Preview Control

There is mounting theoretical evidence to suggest that preview control can be of substantial benefit to a semi-active suspension for random road inputs. In this paper, the benefits of wheel-base preview control are measured experimentally, using a prototype semi-active damper in a half-car ‘Hardware-in-the-loop’ (HiL) rig with a planar two-axle heavy vehicle model. The benefits of preview control using the prototype semi-active damper are found to be less than theoretically possible, due to the phase lag between the demanded and achieved damping force. It is shown that the performance of the prototype damper can be improved significantly by having a theoretical simulation running ahead of the HiL vehicle. The theoretical simulation is used to predict the demanded damper force for the HiL vehicle, and thereby compensate for the phase lag in the prototype damper.     

Level and attitude control of the active suspension system with integral and derivative action

A 7-DOF full-car model with optimal active control suspension is utilized to evaluate the vehicle dynamic performances which are achieved through proposed controllers. The optimal controller, which includes the integral action for the suspension deflection, considerably improves the attitude control of a vehicle because the rolling and pitching motion in cornering and braking maneuvers are reduced, respectively. In the viewpoint of level control, the integral control acting on the suspension deflection results in the zero steady-state deflection in response to static body forces and ramp road input. The dynamic characteristics of the suspension control system are evaluated in terms of time domain and frequency domain. The simulations in the time domain demonstrate the advantages of the active suspension system obtained by penalizing the integral and derivative of suspension deflections and the derivative of roll and pitch angles in the performance index. The frequency characteristic curves obtained by simulations regarding integral action or derivative action show the increase of both ride comfort and road-holding performances by maximizing the use of suspension deflections. The potential of derivative control is shown by the performances of the car traveling over a bump and braking.     

Level and attitude control of the active suspension system with integral and derivative action

A 7-DOF full-car model with optimal active control suspension is utilized to evaluate the vehicle dynamic performances which are achieved through proposed controllers. The optimal controller, which includes the integral action for the suspension deflection, considerably improves the attitude control of a vehicle because the rolling and pitching motion in cornering and braking maneuvers are reduced, respectively. In the viewpoint of level control, the integral control acting on the suspension deflection results in the zero steady-state deflection in response to static body forces and ramp road input. The dynamic characteristics of the suspension control system are evaluated in terms of time domain and frequency domain. The simulations in the time domain demonstrate the advantages of the active suspension system obtained by penalizing the integral and derivative of suspension deflections and the derivative of roll and pitch angles in the performance index. The frequency characteristic curves obtained by simulations regarding integral action or derivative action show the increase of both ride comfort and road-holding performances by maximizing the use of suspension deflections. The potential of derivative control is shown by the performances of the car traveling over a bump and braking.