Control Algorithms for Active Cab Suspensions on Agricultural Tractors

This paper describes active agricultural tractor cab suspensions based on optimal control theory. Control algorithms based on time invariant state feedback and on adaptive control are developed and studied. The influence of different observers and measurement noise levels on the vibration damping capacity are studied as well as the power consumption for the suspensions.

The principle for the adaptive algorithm is based on the parameters in the penalty matrices being varied so that the resulting controller always strives to make optimum use of available travel space. The feedback and observer gains are also changed depending on the characteristics of the vehicle's frame movements.

The results show that it is possible to design an effective active suspension, but that the choice of feedback gains must be dependent on the surface characteristics to reach satisfactory vibration damping performance.     

Optimal Linear Active Suspensions with Multivariable Integral Control

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.     

An Optimal Continuous Time Control Strategy for Active Suspensions with Preview

A continuous time control strategy for an active suspension with preview, based on optimal control theory, is presented. No approximation is needed to model the time delay between the excitation of the front and the rear wheels. The suspension is applied to a two DOF model of the rear side of the tractor of a tractor-semitrailer. The purpose of the suspension is to reduce either the required suspension working space or the maximum absolute acceleration of the sprung mass, without an increase of the dynamic tire force variation. For a step function as road input, reductions of 65% and 55%, respectively, are possible compared with a passive suspension.     

Optimal Linear Active Suspensions with Derivative Constraints and Output Feedback Control

In optimally controlled active suspensions with either full or incomplete state feedback there is tradeoff between system performance and overall stiffness. It is sought to remove this limitation by incorporating integral action which results in a system with infinite stiffness towards static loading, but which is soft with respect to road inputs. The system is also able to eliminate the steady state deflections due to step and (potentially) ramp type inputs at the wheel. Optimality is retained at the cost only of a derivative constraint and the system can be physically realised using output feedback control.     

Optimal Linear Active Suspensions with Integral Constraint

This paper considers the application of linear optimal control to the design of an active automobile suspension system. By inclusion of an integral constraint in the performance index it is possible to achieve zero steady state axle to body response to both static body forces and ramp road inputs. Full state feedback is achieved by reconstructing the state variables from easily measured quantities.     

Optimal Linear Active Suspensions with Vibration Absorbers and Integral Output Feedback Control

The bandwidth of the body response to a road input in an active suspension may be considerably reduced if the axle motions are independently controlled and if, at the same time, the effects of static and dynamic loads are counteracted by integral action in the body force control system. The paper presents a further application of the Ferguson-Rekasius method, leading to optimal output control with incomplete state feedback. To achieve narrow bandwidth body response the support springs are replaced by hydraulic actuators, and vibration absorbers or active wheel dampers are employed for the control of the axle motions. Active wheel damping is the more effective and gives good results. Proportional-plus-integral control action is shown to reduce the transient body displacements due to external forces.     

Optimal Linear Active Suspensions with Vibration Absorbers and Integral Output Feedback Control

SUMMARY

The bandwidth of the body response to a road input in an active suspension may be considerably reduced if the axle motions are independently controlled and if, at the same time, the effects of static and dynamic loads are counteracted by integral action in the body force control system. The paper presents a further application of the Ferguson-Rekasius method, leading to optimal output control with incomplete state feedback. To achieve narrow bandwidth body response the support springs are replaced by hydraulic actuators, and vibration absorbers or active wheel dampers are employed for the control of the axle motions. Active wheel damping is the more effective and gives good results. Proportional-plus-integral control action is shown to reduce the transient body displacements due to external forces.     

主动汽车悬架的非线性控制

本文采用１／４车模型对天棚阻尼器和主动悬架的动力学性能进行分析，针对执行器的非线性特性，探讨了微分几何法和反馈法线必互法在主动悬架控制中的应用，在系统控制设计中采用了离散滑模法，仿真结果显示非线性控制律能有效地改善主动悬架的隔振特性。     

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

SUMMARY

Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.     

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.     

Active Control of Non-stationary Response of Vehicles with Nonlinear Suspensions

Active control of non-stationary response of a single degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteresis type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.     

Active Control of Non-stationary Response of Vehicles with Nonlinear Suspensions

SUMMARY

Active control of non-stationary response of a single degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteresis type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.     

Optimal Adaptive Active Suspensions for a Full Car Model

In order to present a useful method for designing active suspension of a vehicle, a linear full-car model is used in this investigation. In this model, the dampers of passive system are totally replaced by actuators. The actuators are controlled with optimal full state vector feedback. After determining feedback coefficients, the responses of active and passive systems were compared and it was found that performance of active system is much superior. It is desired that, changes in vehicle parameters would not affect the system's performance and hence should not violate its optimality. In other words, the system should behave adaptively using Model Reference Adaptive Control. The optimally controlled active suspension was used as a model for the active suspension of vehicle. In this way, the suspension of vehicle is controlled in such a way that its output approaches to that of the optimal active model. Thus the suspension should behave just like the optimal one.     

主动悬架的参数估计自校正控制

本文采用二自由度的单轮模型，运用衰减记忆递推最小二乘法参数估计算法和广义加权最小方差自校正控制算法，通过控制律隐式结构直接估计控制器参数，再综合得到控制律，从而实现了主动悬架的参数估计自校正控制。经实例计算和数值仿真，证明了该控制方法的有效性和可行性。     

基于SIMULINK的车辆主动悬架LQG控制仿真研究

通过建立1／4车辆模型,应用最优控制理论进行了车辆主动悬架的LQG(Linear Quadratic Gaussian)控制器的设计,并在Matlab／Simulink环境中建立系统模型并进行仿真,将仿真结果与被动悬架仿真结果进行对比分析。仿真结果表明,具有LQG控制器的主动悬架对车辆行驶平顺性和乘坐舒适性的改善有良好的效果。     

汽车主动悬架的自校正控制

主动悬系统能使车辆的乘坐舒适性和操纵稳定性同时得到改善，其中执行机构和控制算法的优劣决定了该系统的性能。     

Fuzzy Logic Active and Semi-Active Control of Off-Road Vehicle Suspensions

For off-road vehicles, minimizing the absorbed power is the main objective of suspension control. The primary cause of increase in the absorbed power in off-road vehicles driven at high speeds on harsh courses is the exhaustion of the suspension travel. Fuzzy-logic approach to active and semi-active off-road vehicle suspension control, with the goal of improving the speed of the vehicle over rough terrains are developed. The ride metric used for quantifying improvements is the absorbed power of the sprung mass. Particular attention is paid to the proper modeling of the suspension using both the full kinematic constraints and the more convenient two degree of freedom linear model of the quarter vehicle suspension. The nonlinearities due to the kinematic constraints on motion are accounted for by modifying the stiffness and damping coefficients of the suspension spring and dashpot in the linear model. The control laws are developed using the less complex model and demonstrated in the fully constrained environment. Nonlinearities of the suspension, including tire stiffness/damping and bumpstops are included at all stages of controller development.     

Fuzzy Logic Active and Semi-Active Control of Off-Road Vehicle Suspensions

For off-road vehicles, minimizing the absorbed power is the main objective of suspension control. The primary cause of increase in the absorbed power in off-road vehicles driven at high speeds on harsh courses is the exhaustion of the suspension travel. Fuzzy-logic approach to active and semi-active off-road vehicle suspension control, with the goal of improving the speed of the vehicle over rough terrains are developed. The ride metric used for quantifying improvements is the absorbed power of the sprung mass. Particular attention is paid to the proper modeling of the suspension using both the full kinematic constraints and the more convenient two degree of freedom linear model of the quarter vehicle suspension. The nonlinearities due to the kinematic constraints on motion are accounted for by modifying the stiffness and damping coefficients of the suspension spring and dashpot in the linear model. The control laws are developed using the less complex model and demonstrated in the fully constrained environment. Nonlinearities of the suspension, including tire stiffness/damping and bumpstops are included at all stages of controller development.     

Technical Note: Force Control in Electrohydraulic Active Suspensions Revisited

The inner loop control for the actuator force can be quite simply compensated by means of a correction term to the desired force signal at the input. The correction requires only a measurement of the actuator piston velocity and is employed to cancel the loop disturbance caused by the oil flow to the actuator. Although an additional time constant is introduced by the integration in the inner loop force control, the overall performance is nevertheless quite close to that of an ideal optimal system.     

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.