Design of nonlinear controllers for active vehicle suspension with state constraints

Design of active vehicle suspension has tradeoffs between three main performance metrics (passenger comfort, suspension deflection and road holding ability). It has been known that each performance can be achieved by H _∞ controller and they can be gathered by LPV (Linear Parameter Varying) method. However, because the suspension deflection limit was not explicitly considered, this limit may be exceeded. In this paper, the authors propose a “reference shaping“ based method in order to improve the control performance. In this approach, a “virtual reference” signal is imposed to the system such that the suspension deflection is kept small. The effectiveness of the approach is examined by numerical simulations. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Multi-objective H ∞ control for vehicle active suspension systems with random actuator delay

This article is concerned with the problem of multi-objective H _∞ control for vehicle active suspension systems with random actuator delay, which can be represented by signal probability distribution. First, the dynamical equations of a quarter-car suspension model are established for the control design purpose. Secondly, when taking into account vehicle performance requirements, namely, ride comfort, suspension deflection and the probability distributed actuator delay, we present the corresponding dynamic system, which will be transformed to the stochastic system for the problem of multi-objective H _∞ controller design. Third, based on the stochastic stability theory, the state feedback controller is proposed to render that the closed-loop system is exponentially stable in mean-square while simultaneously satisfying H _∞ performance and the output constraint requirement. The presented condition is expressed in the form of convex optimisation problems so that it can be efficiently solved via standard numerical software. Finally, a practical design example is given to demonstrate the effectiveness of the proposed method.     

Novel Optimal Design Approach for Output‐Feedback H∞ Control of Vehicle Active Seat‐Suspension System

In this paper, the output‐feedback control problem of a vehicle active seat‐suspension system is investigated. A novel optimal design approach for an output‐feedback H_∞ controller is proposed. The main objective of the controller is to minimize the seat vertical acceleration to improve vehicle ride comfort. First, the human body and the seat are considered in the modeling of a vehicle active suspension system, which makes the model more precise. Other constraints, such as tire deflection, suspension deflection and actuator saturation, are also considered. Then the output‐feedback control strategy is adopted since some state variables, such as body acceleration and body deflection, are unavailable. A concise and effective approach for an output‐feedback H_∞ optimal control is presented. The desired controller is obtained by solving the corresponding linear matrix inequalities (LMIs) and by the calculation of equations proposed in this paper. Finally, a numerical example is presented to show the effectiveness and advantages of the proposed controller design approach.     

Robust non‐fragile H ∞ ∕ L2 − L ∞ control of uncertain linear system with time‐delay and application to vehicle active suspension

This paper presents an approach to design robust non‐fragile H _∞ ∕ L₂ ? L _∞ static output feedback controller, considering actuator time‐delay and the controller gain variations, and it is applied to design vehicle active suspension. According to suspension design requirements, the H _∞ and L₂ ? L _∞ norms are used, respectively, to reflect ride comfort and time‐domain hard constraints. By employing a delay‐dependent Lyapunov function, existence conditions of delay‐dependent robust non‐fragile static output feedback H _∞ controller and L₂ ? L _∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities. Then, a new procedure based on LMI optimization and a hybrid algorithm of the particle swarm optimization and differential evolution is used to solve an optimization problem with bilinear matrix inequality constraints. Simulation results show that the designed active suspension system still can guarantee their own performance in spite of the existence of the model uncertainties, the actuator time‐delay and the controller gain variations. Copyright © 2014 John Wiley & Sons, Ltd.     

Design of robust H ∞ controller for a half-vehicle active suspension system with input delay

This article is concerned with the problem of robust H _∞ control for a half-vehicle active suspension system with input delay. The delay is assumed to be interval time-varying delay with unknown derivative. The vehicle front sprung mass and the rear unsprung mass are assumed to be varying due to vehicle load variation and may result in parameter uncertainties being modelled by polytopic uncertainty. First of all, regarding the heave and pitch accelerations as the optimisation objectives, and suspension deflection and relative tire load constraints as the output constraints, we build the corresponding suspension systems. Then, by constructing a novel Lyapunov functional involved with the lower and upper bounds of the delay, sufficient condition for the existence of robust H _∞ controller is given to ensure robust asymptotical stability of the closed-loop system and also guarantee the constrained performance. The condition can be converted into convex optimisation problem and verified easily by means of standard software. Finally, a design example is exploited to demonstrate the effectiveness of the proposed design method.     

Finite Frequency Fuzzy H∞ Control for Uncertain Active Suspension Systems With Sensor Failure

This paper investigates the problem of finite frequency fuzzy H_∞ control for uncertain active vehicle suspension systems, in which sensor failure is taken into account. TakagiSugeno (T-S) fuzzy model is established for considered suspension systems. In order to describe the sensor fault effectively, a corresponding model is introduced. A vital performance index, H_∞ performance, is utilized to measure the drive comfort. In the framework of Kalman-Yakubovich-Popov theory, the H_∞ norm from external perturbation to controlled output is optimized effectively in the frequency domain of 4 Hz-8 Hz to enhance ride comfort level. Meanwhile, three suspension constrained requirements, i.e., ride comfort level, manipulation stability, suspension deflection are also guaranteed. Furthermore, sufficient conditions are developed to design a fuzzy controller to guarantee the desired performance of active suspension systems. Finally, the proposed control scheme is applied to a quarter-vehicle active suspension, and simulation results are given to illustrate the effectiveness of the proposed approach.      

Mixed GL2/H2/GH2 control with pole placement and its application to vehicle suspension systems

This paper presents a multi-channel multi-objective synthesis framework, in which generalized L ₂ (GL ₂), H ₂, and generalized H ₂ (GH ₂) criteria are specified for appropriate channels, and the poles of the closed-loop system are constrained within a subregion S(a, r,θ) of the left-half s-plane. The multi-objective framework is successfully applied to a seven degrees-of-freedom decoupled vehicle suspension system. The suspension control system has three channels: channel T ₁, relating to ride comfort, is from road disturbances to vehicle body accelerations, the suspension travel channel, T ₂, is from manoeuvre disturbances to suspension deflections, and channel T ₀ is used to address system uncertainty. The control objective is to minimize a mixture of ||T ₁|| _H2 and ||T ₂|| _GH2 while guaranteeing that the closed-loop system is robustly stable, with poles located within a specified subregion S(a, r,θ). The simulation results demonstrate that this multi-objective control can improve vehicle ride comfort and decrease suspension travel simultaneously. In addition, the multi-objective synthesis framework provides a simple but effective trade-off between vehicle ride comfort and suspension travel.     

Decentralized Dynamic Event-Triggered Communication and Active Suspension Control of In-Wheel Motor Driven Electric Vehicles with Dynamic Damping

This paper addresses the co-design problem of decentralized dynamic event-triggered communication and active suspension control for an in-wheel motor driven electric vehicle equipped with a dynamic damper. The main objective is to simultaneously improve the desired suspension performance caused by various road disturbances and alleviate the network resource utilization for the concerned in-vehicle networked suspension system. First, a T-S fuzzy active suspension model of an electric vehicle under dynamic damping is established. Second,a novel decentralized dynamic event-triggered communication mechanism is developed to regulate each sensor's data transmissions such that sampled data packets on each sensor are scheduled in an independent manner. In contrast to the traditional static triggering mechanisms, a key feature of the proposed mechanism is that the threshold parameter in the event trigger is adjusted adaptively over time to reduce the network resources occupancy. Third, co-design criteria for the desired event-triggered fuzzy controller and dynamic triggering mechanisms are derived. Finally, comprehensive comparative simulation studies of a 3-degrees-of-freedom quarter suspension model are provided under both bump road disturbance and ISO-2631 classified random road disturbance to validate the effectiveness of the proposed co-design approach. It is shown that ride comfort can be greatly improved in either road disturbance case and the suspension deflection, dynamic tyre load and actuator control input are all kept below the prescribed maximum allowable limits, while simultaneously maintaining desirable communication efficiency.     

Genetic-based fuzzy control for half-car active suspension systems

In this paper, a fuzzy controller is designed for automotive active suspension systems. A half-car model is used in order to consider the pitch angle of the body and the coupling dynamics of front and rear wheels. It is assumed that the three measurements of body acceleration, front suspension deflection and rear suspension deflection are available. The fuzzy control rules are separately designed for each measurement. After the fuzzy control rules are determined, a genetic algorithm is applied to tune the membership functions of these control rules. To measure the performance of the designed genetic-based fuzzy active suspension system, three road disturbance models are designed to simulate actual road conditions. The performance of the designed system is evaluated with respect to these disturbance models, and it is shown that the designed active suspension system provides good performance in improving ride quality and maintaining vehicle maneuvrability. It is also shown that the designed active suspension system shows robust performance with system model uncertainties.     

A Simultaneous Mixed LQR/H∞ Control Approach to the Design of Reliable Active Suspension Controllers

This paper is concerned with the synthesis of reliable controllers for quarter‐car active suspension systems. By a simultaneous mixed LQR/H_∞ control approach, a static output feedback controller is derived for guaranteeing good suspension performance under possible sensor fault or suspension component breakdown. The considered simultaneous mixed LQR/H_∞ control problem is a nonconvex optimization problem; therefore, the linear matrix inequality approach is not applicable. Based on the barrier method, we solve an auxiliary minimization problem to get an approximate solution for the simultaneous mixed LQR/H_∞ control problem. Necessary conditions for the local optimum of the auxiliary minimization problem are derived. Moreover, a three‐stage solution algorithm is developed for solving the auxiliary minimization problem. The simulation shows that the obtained static output feedback suspension controllers can improve suspension performance in nominal mode and all considered failure modes.     

Non-fragile output feedback H∞ vehicle suspension control using genetic algorithm

This paper presents an approach to design static output feedback and non-fragile static output feedback H_∞ controllers for active vehicle suspensions by using linear matrix inequalities and genetic algorithms. A quarter-car model with active suspension system is considered in this paper. By suitably formulating the minimization problem of the sprung mass acceleration, suspension deflection and tyre deflection, a static output feedback H_∞ controller and a non-fragile static output feedback H_∞ controller are obtained. The controller gain is naturally constrained in the design process. The approach is validated by numerical simulation which shows that the designed static output feedback H_∞ controller can achieve good active suspension performance in spite of its simplicity, and the non-fragile static output feedback H_∞ controller has significantly improved the non-fragility characteristics over controller gain variations.     

Studies on improving vehicle handling and lane keeping performance of closed-loop driver–vehicle system with integrated chassis control

This study proposes a new integrated robust model matching chassis controller to improve vehicle handling performance and lane keep ability. The design framework of the H_∞ controller is based on linear matrix inequalities (LMIs), which integrates active rear wheel steering control, longitudinal force compensation and active yaw moment control. To comprehensively evaluate the performance of the integrated chassis control system, a closed-loop driver–vehicle system is used. The effectiveness of the integrated controller on handling performance improvement is tested by a vehicle without driver model under a crosswind disturbance. At the same time, both the handling and lane keeping improving performance of the closed-loop driver–vehicle system is evaluated by tracking an S shape winding road. The simulation results reveal that the integrated chassis controller not only achieves preferable handling performance and stability, but also improves the vehicle lane keep ability significantly, and can alleviate the working load of the driver.     

Residual mode filters and H ∞ control for a class of infinite-dimensional discrete-time systems

An H _∞, control problem with measurement feedback.for infinite-dimensional discrete-time (IDDT) systems whose homogeneous parts are described by Riesz-spectra operators is considered. The aim is to construct a finite-dimensional stabilizing controller for the IDDT system that makes the H _∞ norm of the closed-loop transfer function less than a given positive number δ. For that purpose, we first formulate the IDDT system as an IDDT system in l² and derive a finite-dimensional reduced-order system for the IDDT system in l². A stabilizing controller that makes the H _∞ norm of the closed-loop transfer function less than another positive number is then constructed for the reduced-order model. The finite-dimensional controller together with a residual mode Jilter plays a role of a finite-dimensional stabilizing controller that makes the H _∞ norm of the closed-loop transfer function less than δ for the original IDDT system, if the order of the residual mode filter is chosen suficiently large.     

Vibration control of vehicle active suspension system using a new robust neural network control system

The main problem of vehicle vibration comes from road roughness. For that reason, it is necessary to control vibration of vehicle’s suspension by using a robust artificial neural network control system scheme. Neural network based robust control system is designed to control vibration of vehicle’s suspensions for full suspension system. Moreover, the full vehicle system has seven degrees of freedom on the vertical direction of vehicle’s chassis, on the angular variation around X-axis and on the angular variation around Y-axis. The proposed control system is consisted of a robust controller, a neural controller, a model neural network of vehicle’s suspension system. On the other hand, standard PID controller is also used to control whole vehicle’s suspension system for comparison.Consequently, random road roughnesses are used as disturbance of control system. The simulation results are indicated that the proposed control system has superior performance at adapting random road disturbance for vehicle’s suspension.     

Control of large model mismatch systems using multiple models

H _∞ control is an effective approach to handle model uncertainties. However, when modeling mismatch is large, it tends to be challenging to meet the desired requirements of both stability and performance by only using a single H _∞ controller. This study presents a switching method to enhance the robust stability and performance of H _∞ control by dividing the range of dynamics into multiple uncertain models. The candidate robust controllers are designed by solving a set of linear matrix inequalities for each uncertain model. A structural scheduling logic that selects the most proper controller into closed-loop is proposed. The selected controller can ensure bounded exponentially weighted H _∞ norm of the closed-loop switching systems. This work analyses their robust stability and disturbance attenuation performance via a linear fractional transformation by using the small gain theorem. The effectiveness of this method is validated with a fist-order inertial system with pure time delay.     

应用轴距预描的主动悬架最优控制器设计

设计主动悬架的关键任务之一是寻找一个好的控制律，随机线性最优控制理论能为车辆提供良好的性能，得到了广泛的应用。轴距预描控制利用前轮处的路面信息作为预描变量对后轮进行控制，能充分发挥主动悬架的潜力。该文以悬架理论为基础，应用最优控制理论进行了结合轴距预瞄信息的主动悬架最优控制器的设计，并用一个卡尔曼滤波器估计系统状态。最后在MATLAB环境中建模和仿真，将有、无预描主动悬架系统的车身加速度、悬架动行程及车轮动位移3项指标进行了对比。仿真结果表明，采用轴距预描控制在低速情况下能较大改善后悬架系统的性能．验证了轴距预描控制的可行性。     

Internal model based robust inversion feedforward and feedback 2DOF control for LPV system with disturbance

To reduce the adverse effects on the control performance and disturbance rejection caused by system uncertainty, a novel internal model based robust inversion feedforward and feedback 2DOF control approach was proposed for LPV system with disturbance. The proposed control approach combines the internal model control and robust inversion based 2DOF control, it utilizes internal model based control to reject external disturbance, utilizes robust inversion 2DOF control to enhance the control resolution and guarantee the system control performance. At first, a LMI synthesis approach for LPV system model identification and a disturbance compensator optimization design method which could minimize H_∞ norm of output error caused by disturbance are presented. Then, combined with internal loop for disturbance compensation, a robust inversion feedforward controller is designed by robust inversion approach and the feedback controller which could render the requirements of reference signal tracking performance and robustness satisfied is obtained by the H_∞ mixed sensitivity synthesis approach. Finally, atomic force microscopy (AFM) vertical positioning simulation experiments are conducted and the experiment results showed that the proposed control approach could achieve better output performance and disturbance rejection compared with conventional internal model based control and robust inversion based 2DOF control approach.     

H2 control of discrete-time periodic systems with Markovian jumps and multiplicative noise

This paper addresses the problem of optimal and robust H₂ control for discrete-time periodic systems with Markov jump parameters and multiplicative noise. To analyse the system performance in the presence of exogenous random disturbance, an H₂ norm is firstly established on the basis of Gramian matrices. Further, under the condition of exact observability, a necessary and sufficient condition is presented for the solvability of H₂ optimal control problem by means of a generalised Riccati equation. When the transition probabilities of jump parameter are incompletely measurable, an H₂-guaranteed cost norm is exploited and the robust H₂ controller is designed through a linear matrix inequality (LMI) optimisation approach. An example of a networked control system is supplied to illustrate the proposed results.     

基于模糊控制的汽车主动悬架系统仿真研究

汽车悬架直接影响汽车在行驶过程中抑制不平路面对车身的冲击力及车身倾斜度,传统被动悬架遇冲击自动调节能力较差,抗振能力不强,针对上述问题,通过对悬架受力特点分析,建立了1/4车体二自由度主动悬架数学模型,结合自动控制理论,设计车辆的主动悬架模糊控制器,利用MATLAB/Simulink模糊工具箱对其进行仿真,在相同输入的情况下,对主动悬架与被动悬架模型部分性能参数分析比较,仿真结果表明采用此模糊控制器的主动悬架在提高车辆乘坐的舒适性和操纵的稳定性方面明显优于被动悬架。实验证明,研究结果对汽车主动悬架系统的设计具有一定参考价值。     

Fixed-point DSP implementation of nonlinear controller for large gap electromagnetic suspension system

Electromagnetic suspension systems are inherently nonlinear and often face hardware limitation when digitally controlled. The main contributions of this paper are: the design of a nonlinear H_∞ controller, including dynamic weighting functions, applied to a large gap electromagnetic suspension system and the presentation of a procedure to implement this controller on a fixed-point DSP, through a methodology able to translate a floating-point algorithm into a fixed-point algorithm by using l_∞ norm minimization due to conversion error. Experimental results are also presented, in which the performance of the nonlinear controller is evaluated specifically in the initial suspension phase.