Design of Robust Controllers for Active Vehicle Suspension Using the Mixed µ Synthesis

Summary The mixed µ synthesis for active suspension problems is proposed. Applying this method the real parametric uncertainties can be taken into consideration, which is more realistic than the traditional approaches, and the design process yields a less conservative compensator than other robust control design methods. The concept of the active suspension design using full-car models to handle the uncertain components is presented. The result of the mixed µ method is compared with the complex µ synthesis, and the passive system.     

Design of robust-stable and quadratic finite-horizon optimal controllers with low trajectory sensitivity for uncertain active suspension systems

This paper presents a design method for designing the robust-stable and quadratic-finite-horizon-optimal controllers of uncertain active suspension systems. The method integrates a robust stabilisability condition, the orthogonal functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA). Using the integrative computational method, a robust-stable and quadratic-finite-horizon-optimal controller with low-trajectory sensitivity can be obtained such that (i) the active suspension system with elemental parametric uncertainties is stabilised and (ii) a quadratic-finite-horizon-integral performance index including a quadratic trajectory sensitivity term for the nominal active suspension system is minimised. The robust stabilisability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal active suspension feedback dynamic equations. By using the OFA and the LMI-based robust stabilisability condition, the dynamic optimisation problem for the robust-stable and quadratic-finite-horizon-optimal controller design of the linear uncertain active suspension system is transformed into a static-constrained-optimisation problem represented by the algebraic equations with constraint of LMI-based robust stabilisability condition; thus greatly simplifies the design problem. Then, for the static-constrained-optimisation problem, the HTGA is employed to find the robust-stable and quadratic-finite-horizon-optimal controllers of the linear uncertain active suspension systems. A design example is given to demonstrate the applicability of the proposed integrative computational approach.     

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.     

Kinematic design of double-wishbone suspension systems using a multiobjective optimisation approach

This paper is focused on the kinematic design of double-wishbone suspension systems in vehicles, which is tackled using a multiobjective dimensional synthesis technique. The synthesis goal is to optimise an RSSR–SS linkage, subject to some constraints involved in the dynamic behaviour of vehicles. The synthesis method is based on gradient determination using exact differentiation to obtain the elements in the Jacobian matrix. These characteristics make the method adapt well to the optimum design of vehicle suspension systems. The method is capable of handling equality and inequality constraints, thus, the usual ranges of values may be imposed on the functional parameters. The formulation presented is easy to implement and the solutions obtained demonstrate the accuracy and robustness of the method.     

Design of active suspension and electronic stability program for rollover prevention

This paper presents a method for the design of a controller for rollover prevention using active suspension and an electronic stability program (ESP). Active suspension is designed with linear quadratic static output feedback control methodology to attenuate the effect of lateral acceleration on the roll angle and suspension stroke via control of the suspension stroke and tire deflection of the vehicle. However, this approach has a drawback in the loss of maneuverability because the active suspension for rollover prevention produces in vehicles an extreme over-steer characteristic. To overcome this drawback of the active suspension based method, ESP is designed. Through simulations, the proposed method is shown to be effective in preventing rollover.     

Theoretical Limitations in Active Vehicle Suspensions

SUMMARY

Vehicle suspensions in which forces are generated in response to feedback signals by active elements obviously offer increased design flexibility compared to conventional suspensions using passive elements such as springs and dampers. It is often assumed that if practical difficulties are neglected, active systems could in principle produce arbitrary ideal, behavior. It is shown, using a simple linear two degree-of-freedom suspension system, model that even using complete state feed back and in the case of in which the system is controllable in the control theory sense, there still are limitations to suspension performance in the fully active case. If the ideal suspension performance is defined based on low-pass filtering of roadway unevenness inputs, an active suspension may not offer much better performance than a partially active or adaptive passive suspension depending upon the values of certain vehicle parameters.     

Suboptimal Control Design of Active and Passive Suspensions Based on a Full Car Model

An optimal control design method is introduced and then applied to the optimum design of active and passive suspension systems. A basic three-dimensional 7-DOF car riding model subjected to four correlated random road inputs is considered. The design method is basically developed to allow arbitrary choice of sensors for various car state variables to be used for feedback control of each suspension unit. Previous studies show that full-state control laws and even some limited-state control laws often include feedback gains which are almost zero. Some other gains, although not zero, don't play an important role in improving the system performance measures. With the method proposed in this work, every suspension unit can have its own feedback measurements and the criterion function can be related to all state and control variables. Thus a large number of active and semi-active suspension systems with full- or limited-state control laws based on different measurement combination can be suggested, studied, and compared with each other. Instead of comparing these optimized active and semi-active suspension systems with a basic, passive suspension, the passive system itself is optimized with the same criterion. Simulations in the time domain and frequency analyses are performed, and comparisons are made among the systems in terms of r.m.s. car response measures and ISO riding comfort criterion.     

轿车悬架空间五连杆机构尺度综合

对轿车悬架五连杆机构进行自由度计算；论述应用位置反解方程进行该机构刚体导引尺度综合的一般方法；指出轮轴构件作圆弧轨迹平动时能使车轮轨迹角不变；阐述进行该机构尺度综合的设计计算方法；由算例得到一组与实际相符的位置与结构参数值，供悬架设计时参考。     

Nonlinear Backstepping Active Suspension Design Applied to a Half-Car Model

A fresh nonlinear backstepping design scheme, which is developed for the control of half-car active suspension systems to improve the inherent tradeoff between ride quality and suspension travel, is proposed in this paper. Since ride quality is dependent on a combination of vertical and angular displacements of a vehicle body, the design of active suspensions must have the potential to minimize heave and pitch movements in order to guarantee the ride comfort of passengers. The other important factor to be emphasized in the design of active suspensions is the suspension travel which means the space variation between the car body and the tires. In order to avoid damaging vehicle components and generating more passenger discomfort, the active suspension controllers must be capable of preventing the suspension from hitting its travel limits. Our design strategy, with two intentionally additional nonlinear filters, shows the potential to achieve these conflicting control objectives. The novelty of our active suspension design is in the use of two particular nonlinear filters at both the front and rear wheels. The effective bandwidths of these two nonlinear filters depend on the magnitudes of the front and rear suspension travels, individually. When suspension travel is small, the proposed controllers soften the suspension for enhancing passenger comfort. However, our control design shifts its attention to rattlespace utilization by stiffening the suspension when suspension travel approaches its limits. As a result, the improvement of tradeoff between ride quality and suspension travel can be guaranteed and is then demonstrated through comparative simulations.     

Theoretical Limitations in Active Vehicle Suspensions

Vehicle suspensions in which forces are generated in response to feedback signals by active elements obviously offer increased design flexibility compared to conventional suspensions using passive elements such as springs and dampers. It is often assumed that if practical difficulties are neglected, active systems could in principle produce arbitrary ideal, behavior. It is shown, using a simple linear two degree-of-freedom suspension system, model that even using complete state feed back and in the case of in which the system is controllable in the control theory sense, there still are limitations to suspension performance in the fully active case. If the ideal suspension performance is defined based on low-pass filtering of roadway unevenness inputs, an active suspension may not offer much better performance than a partially active or adaptive passive suspension depending upon the values of certain vehicle parameters.     

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。     

汽车主动悬架系统状态反馈控制技术研究

车辆的悬架系统对于其舒适性和操纵稳定性都起着关键作用。随着计算机技术和液压伺服元件的发展，出现了主动和半主动悬架系统，在其控制策略具有二次型性能指标的最优控制方法比较成熟。通过建立系统的数学模型和仿真计算，对全状态反馈和被动悬架进行比分析，表明主动悬架采用和有限状态的反馈较全状态反馈有明显优势，是一种比较实用的状态反馈控制方法。     

Structured H2 Optimization of Vehicle Suspensions Based on Multi-Wheel Models

Summary Various control techniques, especially LQG optimal control, have been applied to the design of active and semi-active vehicle suspensions over the past several decades. However passive suspensions remain dominant in the automotive marketplace because they are simple, reliable, and inexpensive. The force generated by a passive suspension at a given wheel can depend only on the relative displacement and velocity at that wheel, and the suspension parameters for the left and right wheels are usually required to be equal. Therefore, a passive vehicle suspension can be viewed as a decentralized feedback controller with constraints to guarantee suspension symmetry. In this paper, we cast the optimization of passive vehicle suspensions as structure-constrained LQG/H2 optimal control problems. Correlated road random excitations are taken as the disturbance inputs; ride comfort, road handling, suspension travel, and vehicle-body attitude are included in the cost outputs. We derive a set of necessary conditions for optimality and then develop a gradient-based method to efficiently solve the structure-constrained H2 optimization problem. An eight-DOF four-wheel-vehicle model is studied as an example to illustrate application of the procedure, which is useful for design of both passive suspensions and active suspensions with controller-structure constraints.     

Control system synthesis of seat suspensions used for protection of working machine operators

This paper deals with a novel approach to the control system synthesis of semi-active and active seat suspensions. An original control strategy is discussed in order to increase the effectiveness of vibration isolators used for protection of working machines operators. As an example of the proposed control system design, the suspension systems with a magneto-rheological damper and a pneumatic spring are investigated using a laboratory experimental set-up with seated humans.     

汽车主动悬架的最优预见控制

本文针对1/2车辆模型,应用最优预见控制理论对汽车主动悬架进行控制系统的设计和研究。计算机仿真结果表明,所提出的系统能有效改善汽车乘坐舒适性。     

An Original Feedback Control with a Reversible Electromechanical Actuator Used as an Active Isolation System for a Seat Suspension. Part I: Theoretical Study

This paper provides an overview of a theoretical study of an active seat suspension. The principal objective of this study is to improve ride passenger comfort by reducing transmitted seat acceleration. The seat is represented by a non-linear two degree of freedom model. The system is linearized for small perturbations around the equilibrium. To control the dynamic of the seat suspension, an original feedback control command with a reversible electromechanical actuator is achieved. The synthesis of the regulator is realized on the linearized model of the seat suspension and the root locus method is employed. Stability and robustness characteristics have been studied. Numerical simulations in time and frequency domain show the interests of the regulator and its capability to isolate seat passenger.     

Actively controlled vehicle suspension with energy regeneration capabilities

The paper presents an innovative dual purpose automotive suspension topology, combining for the first time the active damping qualities with mechanical vibrations power regeneration capabilities. The new configuration consists of a linear generator as an actuator, a power processing stage based on a gyrator operating under sliding mode control and dynamics controllers. The researched design is simple and energetically efficient, enables an accurate force–velocity suspension characteristic control as well as energy regeneration control, with no practical implementation constraints imposed over the theoretical design. Active damping is based on Skyhook suspension control scheme, which enables overcoming the passive damping tradeoff between high- and low-frequency performance, improving both body isolation and the tire's road grip. The system-level design includes configuration of three system operation modes: passive, semi–active or fully active damping, all using the same electro-mechanical infrastructure, and each focusing on different objective: dynamics improvement or power regeneration. Conclusively, the innovative hybrid suspension is theoretically researched, practically designed and analysed, and proven to be feasible as well as profitable in the aspects of power regeneration, vehicle dynamics improvement and human health risks reduction.     

An Original Feedback Control with a Reversible Electromechanical Actuator Used as an Active Isolation System for a Seat Suspension. Part I: Theoretical Study

This paper provides an overview of a theoretical study of an active seat suspension. The principal objective of this study is to improve ride passenger comfort by reducing transmitted seat acceleration. The seat is represented by a non-linear two degree of freedom model. The system is linearized for small perturbations around the equilibrium. To control the dynamic of the seat suspension, an original feedback control command with a reversible electromechanical actuator is achieved. The synthesis of the regulator is realized on the linearized model of the seat suspension and the root locus method is employed. Stability and robustness characteristics have been studied. Numerical simulations in time and frequency domain show the interests of the regulator and its capability to isolate seat passenger.     

Linear matrix inequality based control of vehicle active suspension system

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.     

Self-powered active control applied to a truck cab suspension

A method of active vibration control using regenerated vibration energy, i.e. self-powered active control, applied to the cab suspension of a heavy duty truck. In the proposed system, an electric generator that is installed in the suspension of the chassis regenerates vibration energy and stores it in the condenser. An actuator in the cab suspension achieves active vibration control using the energy stored in the condenser. Numerical simulations and basic experiments demonstrate better isolation performance of the self-powered active vibration control system than that of a passive and a semi-active control.