Global stabilisation for a class of more general high-order time-delay nonlinear systems by output feedback

This paper addresses the problem of global stabilisation by output feedback for a class of high-order time-delay nonlinear systems with more general uncertainties, which cover both high-order and low-order nonlinearities. By introducing sign function and necessarily modifying the homogeneous domination approach, an output feedback controller is successfully constructed to guarantee the global asymptotic stability of the resulting closed-loop system. Due to the versatility of the homogeneous domination approach and homogeneous properties, the proposed method is also utilised to the control design of upper-triangular systems.     

Dual‐rate sampled‐data stabilization for active suspension system of electric vehicle

In this paper, we consider the dual‐rate sampled‐data state‐feedback control problem for an active suspension system of an electric vehicle. In the active suspension system, there exist 2 accelerometers to measure the heave acceleration of the sprung mass and the vertical acceleration of the unsprung mass, respectively. When the 2 accelerations are measured by sampled data under different sampling periods, the difficulty arising from the dual‐rate sampled data makes the active suspension stabilization problem challenging but interesting. In this paper, a linear hybrid stabilizer is proposed, which is implemented using dual‐rate sampled‐data state feedback. In order to deal with the more difficult stabilization problem under different triggering time instants, a coordinate transformation is proposed. A useful technical theorem is proposed in the stability analysis to show that the proposed hybrid controller can guarantee the states of the active suspension system being asymptotically stabilized or at least bounded to arbitrarily small domains. The experiment result is similar to the simulation result and indicates that the proposed active suspension controlling system is effective.     

Adaptive backstepping‐based control design for uncertain nonlinear active suspension system with input delay

This paper addresses the control problem of adaptive backstepping control for a class of nonlinear active suspension systems considering the model uncertainties and actuator input delays and presents a novel adaptive backstepping‐based controller design method. Based on the established nonlinear active suspension model, a projector operator–based adaptive control law is first developed to estimate the uncertain sprung‐mass online, and then the desirable controller design and stability analysis are conducted by combining backstepping technique and Lyapunov stability theory, which can not only deal with the actuator input delay but also achieve better dynamics performances and safety constraints requirements of the closed‐loop control system. Furthermore, the relationship between the input delay and the state variables of this vehicle suspension system is derived to present a simple and effective method of calculating the critical input delay. Finally, a numerical simulation investigation is provided to illustrate the effectiveness of the proposed controller.     

A new model-free adaptive sliding controller for active suspension system

Active suspension systems are designed to provide better ride comfort and handling capability in the automotive industry. Since the active suspension system has nonlinear and time-varying characteristics, it is difficult to establish an accurate dynamic model for designing a model-based controller. Here, a functional approximation (FA) based adaptive sliding controller with fuzzy compensation is proposed for an active suspension system. The FA technique is employed to represent the unknown functions, which releases the model-based requirement of the sliding mode control. In addition, a fuzzy control scheme with online learning ability is employed to compensate for the modeling error of the FA with finite number of terms for reducing the implementation difficulty. To guarantee the control system stability, the update laws of the coefficients in the approximation function and the fuzzy tuning parameters are derived from the Lyapunov theorem. The proposed controller is employed on a quarter-car active suspension system. The simulation results and experimental results show that the proposed controller can suppress the oscillation amplitude of the sprung mass effectively. To evaluate the performance improvement of inducing a fuzzy compensator in this FA adaptive controller, the dynamic responses of the proposed hybrid controller are compared with those of FA-based adaptive sliding controller only.     

Finite‐time stabilization for a class of stochastic low‐order nonlinear systems with unknown control coefficients

This paper addresses the problem of finite‐time stabilization for a class of low‐order stochastic upper‐triangular nonlinear systems corrupted by unknown control coefficients. Unlike the relevant schemes, the control strategy draws into a dominate gain to cope with the deteriorative effects of both uncertain nonlinearities and unknown control coefficients without using traditional adaptive compensation method. Then, a state feedback controller is constructed by the adding a power integrator method and modified homogeneous domination approach, to ensure the finite‐time stability of the closed‐loop system. Finally, the effectiveness of proposed control strategy has been demonstrated by a simulation example.     

Global decentralised stabilisation for a class of uncertain large-scale feedforward nonlinear systems

In this paper, the problem of global decentralised stabilisation for a class of uncertain large-scale feedforward nonlinear systems is investigated. The system under consideration is allowed to contain unknown non-Lipschitz continuous nonlinear terms. The design of the global decentralised controllers takes a two steps procedure. First of all, based on the adding a power integrator technique and the homogeneous domination approach a local homogeneous decentralised controller is proposed for each subsystem of the large-scale feedforward nonlinear system. Then, we integrate a series of nested saturation functions with the homogeneous decentralised controllers and adjust the saturation levels to ensure globally asymptotic stability of the closed-loop system. Simulation studies are conducted to illustrate the effectiveness of the proposed control method.     

主被动一体悬架构型的多目标粒子群最优控制

为了解决轮毂电机电动汽车中轮毂电机导致的振动负效应问题,提出了将动态减振与主动悬架结合的悬架新构型方案.针对新构型中结构及控制参数复杂的特点,建立了能够表征平顺性、操稳性以及悬架作动效率的11自由度整车动力学模型.设计基于新构型的多目标粒子群线性二次最优(MOPSO–LQR)控制器.对模型进行仿真分析,仿真结果表明,新构型方案能够实现车辆平顺性、操稳性以及悬架效率的全局最优,对比传统轮毂电机悬架构型方案,在解决轮毂电机振动负效应问题上有良好的效果.     

MODELING AND CONTROL OF THE ACTIVE SUSPENSION SYSTEM USING PROPORTIONAL INTEGRAL SLIDING MODE APPROACH

The purposes of this paper are to present a new method in modeling an active suspension system for half‐car model in state space form and to develop a robust strategy in controlling the active suspension system. Proportional integral sliding mode control strategy is proposed for the system. A simulation study is performed to prove the effectiveness and robustness of the control approach and performance of the controller is compared to the linear quadratic regulator and the existing passive suspension system.     

Fuzzy Sliding Mode Control for Active Suspension System with Proportional Differential Sliding Mode Observer

In this paper, a generalized augmented transformation is considered for the quarter active suspension system with uncertainties. Specifically, the model uncertainties are converted to the augmented states and a new proportion differential sliding mode observer is used to estimate state variables and model uncertainties. A differential geometric method is applied to linearize the nonlinear suspension model. In order to weaken the vibration effect of sliding mode control force and reduce energy consumption, a fuzzy sliding mode controller is designed for the active suspension system and the fuzzy controller is applied to adjust switching control gain according to the reaching condition of sliding mode surface. The simulations are conducted to illustrate the effectiveness and advantages of this proposed observer and control strategy.     

基于模糊控制策略的车辆主动悬架研究

建立了车辆整车7自由度模型的主动悬架控制的系统状态方程模型,设计了两种模糊控制策略,方法一针对整车模型,采用一种控制方法,方法二针对整车模型的运动方式,设计不同的模糊控制器,垂直振动模糊控制器,俯仰振动模糊控制器,侧倾振动模糊控制器和逻辑控制器,仿真结果表明,所设计的模糊控制器对提高车辆的舒适性与操纵稳定性有较好的效果.     

植保机钟摆式喷杆主动悬架自适应模糊控制

针对具有不确定性与参数时变性的钟摆式喷杆主动悬架系统的运动控制问题,设计出一种基于间接型自适应模糊控制方法的喷杆位姿主动控制器。为一种结构简单、成本低廉且应用广泛的钟摆式喷杆主动悬架系统建立了数学模型,并在此基础上,为了不失一般性,对系统模型进行了输入输出线性化变换。应用间接自适应模糊控制方法克服由于系统不确定性以及外部干扰带来的一些负面影响。此外,应用Lyapunov综合法设计控制器中调整参数的自适应律。仿真结果表明,所提出的控制方法具有快速响应性以及较强的自适应性和鲁棒性。所设计的控制器有利于提高植保机的喷雾均匀性及喷杆的稳定性。     

The Design of a Coprime‐Factorized Predictive Functional Controller for Unstable Fractional Order Systems

In this paper, a new approach, called coprime‐factorized predictive functional control method (CFPFC‐F) is proposed to control unstable fractional order linear time invariant systems. To design the controller, first, a prediction model should be synthesized. For this purpose, coprime‐factorized representation is extended for unstable fractional order systems via a reduced approximated model of unstable fractional order (FO) system. That is, an approximated integer model of fractional order system is derived via the well‐known Oustaloup method. Then, the high order approximated model is reduced to a lower one via a balanced truncation model order reduction method. Next, the equivalent coprime‐factorized model of the unstable fractional‐order plant is employed to predict the output of the system. Then, a predictive functional controller (PFC) is designed to control the unstable plant. Finally, the robust stability of the closed‐loop system is analyzed via small gain theorem. The performance of the proposed control is investigated via simulations for the control of an unstable non‐laminated electromagnetic suspension system as our simulation test system.     

A generalized exact tracking control methodology for disturbed nonlinear systems via homogeneous domination approach

A generalized homogeneous exact set‐point tracking control methodology for a class of disturbed higher‐order nonlinear systems is investigated in this paper. By virtue of utilizing the disturbance estimation and active elimination approach, a homogeneous domination feedback technique is then integrated such that a generalized composite active anti‐disturbance control framework is proposed with a delicate handling procedure of the non‐vanishing nonlinearities. The proposed methodology has several new features. First, a genuine nonlinear composite controller employing the system nonlinearities will bring an improvement of the control performances. Second, the flexility of the design methodology renders its suitability for random output tracking with mismatched disturbances in every channel. Moreover, the control function is constructed in a neat nested form and hence easier to be implemented. Numerical simulation results affirm the output tracking control performances. Copyright © 2016 John Wiley & Sons, Ltd.     

Lateral motion stability control of electric vehicle via sampled-data state feedback by almost disturbance decoupling

The paper presents a lateral motion stability control method for electric vehicle (EV) driven by four in-wheel motors, which considers time-variable vehicle speed and uncertain disturbance caused by external factors. First, an EV lateral motion dynamics tracking control model is presented. Then in order to deal with the uncertain disturbance in the lateral motion model, an almost disturbance decoupling method using sampled-data state feedback is proposed. Third, a sampled-data state feedback controller is constructed based on the state feedback domination approach. The proposed controller can attenuate the disturbances’ effect on the output to an arbitrary degree of accuracy. Simulation and test results under different vehicle speeds show the effectiveness of the control method.     

Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain

This paper proposes a novel sampled-data asynchronous fuzzy output feedback control approach for active suspension systems in restricted frequency domain.In order to better investigate uncertain suspension dynamics,the sampleddata Takagi-Sugeno(T-S)fuzzy half-car active suspension(HCAS)system is considered,which is further modelled as a continuous system with an input delay.Firstly,considering that the fuzzy system and the fuzzy controller cannot share the identical premises due to the existence of input delay,a reconstructed method is employed to synchronize the time scales of membership functions between the fuzzy controller and the fuzzy system.Secondly,since external disturbances often belong to a restricted frequency range,a finite frequency control criterion is presented for control synthesis to reduce conservatism.Thirdly,given a full information of state variables is hardly available in practical suspension systems,a two-stage method is proposed to calculate the static output feedback control gains.Moreover,an iterative algorithm is proposed to compute the optimum solution.Finally,numerical simulations verify the effectiveness of the proposed controllers.     

Adaptive control of a class of quantised nonlinearly parameterised systems with unknown control directions

The problem of adaptive control is studied for a class of nonlinearly parameterised systems with quantised input signal and unknown control directions. The homogeneous domination approach and the Nussbaum-type gain method are applied to design an adaptive state-feedback controller. A hysteretic type of quantiser is incorporated to reduce actuator chattering. The proposed controller can ensure that all signals of the nonlinear system are globally bounded, and that the system state asymptotically converges to zero. Two numerical examples are presented to demonstrate the effectiveness and potential of the proposed techniques.     

Robust passivity-based control design for active nonlinear suspension system

In this article, we propose a novel interconnection and damping assignment passivity-based control (IDA-PBC) design for a quarter car nonlinear active suspension system. As an energy shaping method, IDA-PBC is suitable for applying the main concept of skyhook (SH) control. In addition to the damping term, we utilize the characteristics of the energy shaping method to change the sprung and unsprung masses, thereby strengthening the vibration suppression effect. An IDA-PBC-based controller design for an active suspension system, which includes a nonlinear spring, a nonlinear damper, and mass uncertainty, is proposed. Different from most IDA-PBC applications, which tend to control the position or the velocity, our methods focus on transforming a nonlinear suspension system into a desired linear system with ideal aseismatic properties. Unlike a conventional controller using the SH control strategy, we design a virtual vehicle body and an unsprung mass in addition to the damper coefficients. By deriving the port-Hamiltonian form of the suspension system from its dynamics and rewriting it based on the relative coordinates, we obtain a feedback law that only uses the relative displacement and velocity of the suspension system. We derive the conditions for ensuring the global asymptotical stability of the suspension system and propose the guidelines for parameter selection that can guarantee robust stability against parameter uncertainties.     

矿用自卸车主动油气悬架非线性控制方法研究

为了对矿用自卸车主动油气悬架进行有效控制,分析了其油气弹簧的刚度力与阻尼力的非线性特性,进而建立了两自由度油气悬架的非线性力学模型。应用微分几何线性化理论,经过恰当的坐标变换和反馈控制,实现非线性系统的精确线性化,而后对其设计使用线性PID控制研究;根据选定的控制目标及输出变量,通过制定相应的模糊控制规则表,设计模糊PID控制器,对悬架系统使用模糊PID控制研究。仿真结果表明,与被动悬架相比,精确线性化后的PID控制悬架以及模糊PID控制悬架均能显著提高车辆的平顺性和操稳性,使悬架的动态性能趋于稳定;另外,与模糊PID控制相比,线性化PID控制对于改善车辆行驶平顺性优势更加明显。     

Predictor Feedback Stabilization of Stochastic Linear Delayed Systems with Both Additive and Multiplicative Noises

In this paper we investigate memory control of stochastic linear delayed systems with both additive and multiplicative noises. A new formula is first presented to obtain the prediction vector from the system dynamics and then it is used for feedback to reduce the input delay in the original delayed system. To ensure the stability of closed‐loop system, some matrix inequality conditions are given that in the case of feasibility provide the stabilizing gain of the predictor controller. The proposed method is applied to stochastic quarter‐car model of an active suspension system to show the effectiveness of the approach.     

汽车主动悬架系统H∞控制器的降阶

基于整车模型设计的主动悬架控制系统,控制器阶数往往较高.在保证主动悬架闭环系统性能的情况下如何尽可能地降低控制器的阶数,是有待解决的问题.本文首先建立汽车7自由度整车悬架模型.针对人体敏感的振动频率范围,设计汽车主动悬架H_∞控制器.在此基础上采用Hankel范数最优降阶法对所设计的高阶控制器进行降阶研究,与模态截取法、均衡截取法进行比较,结果显示Hankel范数最优降阶法能获得更好的降阶效果.对采用降阶和全阶控制器的主动悬架系统进行仿真的结果表明,Hankel范数最优降阶法在较大程度地降低控制器阶数的同时,闭环系统频域和时域特性没有明显降低且汽车乘坐舒适性良好.