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Nonlinear Model Reduction for Automotive System Descriptions 汽车系统描述的非线性模型简化
Zeyu Liu, J. Wagner
The mathematical modeling of dynamic systems is an important task in the design, analysis, and implementation of advanced automotive control systems. Although most vehicle control algorithms tend to use model-free calibration architectures, a need exists to migrate to model-based control algorithms which offer greater operating performance. However, in many instances, the analytical descriptions are too complex for real-time powertrain and chassis model-based control algorithms. Therefore, model reduction strategies may be applied to transform the original model into a simplified lower-order form while preserving the dynamic characteristics of the original high-order system. In this paper, an empirical gramian balanced nonlinear model reduction strategy is examined for the simplification process of dynamic system descriptions. The empirical gramians may be computed using either experimental or simulation data. These gramians are then balanced and unimportant system dynamics truncated. For comparison purposes, a Taylor Series linearization will also be introduced to linearize the original nonlinear system about an equilibrium operating point and then a balanced realization linear reduction strategy will be applied. To demonstrate the functionality of each model reduction strategy, two nonlinear dynamic system models are investigated and respective transient performances compared.
动态系统的数学建模是先进汽车控制系统设计、分析和实现中的一项重要任务。尽管大多数车辆控制算法倾向于使用无模型校准架构,但仍需要迁移到基于模型的控制算法,以提供更好的操作性能。然而,在许多情况下,分析描述对于基于实时动力系统和底盘模型的控制算法来说过于复杂。因此,可以采用模型约简策略将原模型转化为简化的低阶形式,同时保留原高阶系统的动态特性。本文研究了一种经验格兰曼平衡非线性模型约简策略,用于动态系统描述的简化过程。经验公式可以用实验数据或模拟数据来计算。然后平衡这些语法,截断不重要的系统动力学。为了比较,我们还将引入泰勒级数线性化来对原始非线性系统进行线性化,然后采用平衡实现线性化策略。为了证明每种模型约简策略的功能,研究了两种非线性动态系统模型,并比较了各自的瞬态性能。
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引用次数: 0
An Experimental Hand/Arm Model for Human Interaction With a Telemanipulation System 人与遥控系统交互的实验手/臂模型
J. Speich, L. Shao, M. Goldfarb
This paper describes the development of a linear single degree-of-freedom lumped-parameter hand/arm model for the operator of a telemanipulaton system. The model form and parameters were determined from experimental data taken from a single degree-of-freedom telemanipulation system. Typically, the human is modeled as a second order mass-spring-damper system [1, 2]. The model developed in this paper, however, includes an additional spring and damper to better approximate the dynamics of the human while interacting with the manipulator. This model can be used in the design and simulation of control architectures for telemanipulation systems and haptic interfaces.
本文描述了一种用于远程操纵系统操作者的线性单自由度集总参数手/臂模型的建立。模型的形式和参数是根据单自由度遥控系统的实验数据确定的。通常,人被建模为一个二阶质量-弹簧-阻尼系统[1,2]。然而,本文开发的模型包括一个额外的弹簧和阻尼器,以便在与机械手交互时更好地近似人的动力学。该模型可用于遥控操作系统和触觉界面控制体系结构的设计和仿真。
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引用次数: 4
A Hardware-in-the-Loop Transient Diesel Engine Test System for Control and Diagnostic Development 一种用于控制与诊断的柴油机暂态测试系统的研制
C. Tartt, J. Moskwa
This paper describes the design and capabilities of a state-of-the-art diesel engine transient test system, which has been developed and built in the Powertrain Control Research Laboratory (PCRL) at the University of Wisconsin - Madison. The system includes a hydrostatic transient dynamometer capable of approximately 300 Hz actuation bandwidth, which is integrated with a dynamic vehicle drivetrain model that runs in real time. This hardware-in-the-loop (HIL) system simulates dynamic torque loading on the engine while performing an FTP, NEDC, J10.15, or any other drive cycles. The dynamometer system is complemented with transient emissions instrumentation to evaluate the state and composition of engine feed gases, and pre and post catalytic converter gases. Included in this paper are details of the design philosophy, why a hydrostatic design was used, specifics on the hardware of the system, as well as experimental data from the system.
本文介绍了美国威斯康辛大学麦迪逊分校动力总成控制研究实验室(PCRL)开发的一种最先进的柴油机瞬态测试系统的设计和性能。该系统包括一个流体静压瞬态测力计,其驱动带宽约为300 Hz,并与实时运行的动态车辆传动系统模型集成。该硬件在环(HIL)系统在执行FTP、NEDC、J10.15或任何其他驱动循环时模拟发动机的动态扭矩负载。功率计系统与瞬态排放仪器相辅相成,以评估发动机进料气体的状态和成分,以及催化转化器前后的气体。本文详细介绍了该系统的设计理念、采用流体静力设计的原因、系统硬件的具体情况以及系统的实验数据。
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引用次数: 11
On the Nonlinear Modeling and Identification of Piezoelectric Inertial Actuators 压电惯性作动器的非线性建模与辨识
David W. Knowles, N. Jalili, T. Khan
Active counter-force vibration control has significant advantages over the more traditional motion-based active vibration suppression schemes. A piezoelectric ceramic (PZT) inertial actuator is an efficient and inexpensive solution for this type of structural vibration control. In order to properly tune the control parameters of the absorber subsection, an accurate mathematical model is necessary. For this, a nonlinear model for the PZT inertial actuators is presented. In particular, a polynomial form of non-linearity in the dynamical model of the actuator is assumed. An inverse problem is then formed to identify the model parameters of the actuator (absorber). The model parameters consist of the effective mass, damping and stiffness of the actuator as well as the polynomial form of the non-linearity. Using Lyapunov’s second method, the stability conditions for the proposed nonlinear model are established. An experimental setup is developed to validate the proposed nonlinear model. The results of the model identification using the actual experimental data demonstrate that the nonlinear model would better fit the experimental data, when compared to the linear model.
与传统的基于运动的主动振动抑制方案相比,主动反力振动控制具有显著的优势。压电陶瓷(PZT)惯性致动器是一种高效、廉价的结构振动控制解决方案。为了合理地调整减振器分段的控制参数,需要一个精确的数学模型。为此,建立了压电陶瓷惯性作动器的非线性模型。特别地,在作动器的动力学模型中假定非线性为多项式形式。然后形成一个反问题来确定执行器(吸收器)的模型参数。模型参数包括执行器的有效质量、阻尼和刚度以及非线性的多项式形式。利用Lyapunov第二方法,建立了非线性模型的稳定性条件。建立了一个实验装置来验证所提出的非线性模型。利用实际实验数据进行模型辨识的结果表明,与线性模型相比,非线性模型能更好地拟合实验数据。
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引用次数: 0
Piezoelectric Structural Vibration Control Using Active Resonator Absorber 利用有源谐振吸收器控制压电结构振动
David W. Knowles, N. Jalili, Sriram Ramadurai
A novel dynamic vibration absorber is presented while exploring its practical implementation using piezoelectric ceramic (PZT) inertial actuators. It is referred to as active resonator absorber (ARA). The ARA is a passive absorber with an additional dynamic feedback compensator within the PZT actuator. Without any controller, the PZT inertial actuator becomes a passive vibration absorber due to the internal damping and stiffness properties of piezoelectric materials. Hence, it is inherently fail-safe. For active operation, the compensator parameters are designed such that a resonance condition is intentionally created within the absorber to mimic the vibratory energy from the system of concern to which it is attached. The resonance condition can be created through the appropriate design of the compensator and implemented through adjusting the external electrical voltage applied to the absorber. Because the parameters of the PZT actuators (i.e. stiffness, damping, and effective mass) are estimates, compensator designs based on these parameters would result in partial vibration suppression, when utilized in real applications. An auto-tuning method is, therefore, introduced to effectively tune the compensator parameters to improve vibration suppression quality. The effectiveness and stability of the proposed absorber is demonstrated through simulations when appended on a SDOF primary system.
提出了一种新型的动态吸振器,并探讨了利用压电陶瓷惯性作动器实现动态吸振器的方法。它被称为有源谐振吸收器(ARA)。ARA是一个被动吸收器,在PZT执行器内附加了一个动态反馈补偿器。在没有任何控制器的情况下,由于压电材料的内部阻尼和刚度特性,PZT惯性致动器成为被动吸振器。因此,它本质上是故障安全的。对于主动操作,补偿器参数的设计使得在吸收器内有意创建共振条件,以模拟它所连接的有关系统的振动能量。谐振条件可以通过补偿器的适当设计产生,并通过调节施加到吸收器上的外部电压来实现。由于PZT作动器的参数(即刚度、阻尼和有效质量)是估计的,因此在实际应用中,基于这些参数的补偿器设计将导致部分振动抑制。为此,提出了一种自整定方法来有效地整定补偿器的参数,以提高振动抑制质量。通过仿真验证了该吸波器的有效性和稳定性。
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引用次数: 2
A Method for the Frequency Domain Design of PWM-Controlled Pneumatic Systems pwm控制气动系统的频域设计方法
E. Barth, Jianlong Zhang, M. Goldfarb
This paper presents a rigorous analysis and design method for PWM-based control of pneumatic systems. An equivalent analytical model incorporating the effects of a finite PWM switching period is formulated. This equivalent model was motivated by a lack of control design and analysis techniques needed to treat the inherently non-analytical switching models associated with PWM-based systems. The equivalent model enables the design of a loop compensator that rigorously addresses control design issues of stability robustness, disturbance rejection, insensitivity to sensor noise, performance bandwidth and actuator saturation. Simulation of this compensator with both the equivalent design model and a full nonlinear switching model for a particular pneumatic robot application is presented which demonstrates and validates the proposed method.
本文提出了一种基于pwm的气动系统控制的严密分析和设计方法。建立了一个等效的分析模型,该模型考虑了有限PWM开关周期的影响。这种等效模型的动机是缺乏控制设计和分析技术,需要处理与基于pwm的系统相关的固有非分析开关模型。等效模型使环路补偿器的设计能够严格解决控制设计问题,如稳定性,鲁棒性,抗干扰性,对传感器噪声的不敏感性,性能带宽和执行器饱和。最后对该补偿器进行了等效设计模型和全非线性开关模型的仿真,验证了所提方法的有效性。
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引用次数: 3
Modeling and Analysis for Thermal Control of Spindles for Reconfigurable Machines 可重构机床主轴热控制建模与分析
J. Stein, J. Harder
Control of thermally induced bearing loads remains an important but unsolved problem for precision, high-speed, metal cutting, machining spindles. Spindle dynamic performance, as well as spindle life, depends on bearing loads. Because these loads can change drastically with a change in process conditions, poor spindle dynamic performance, and dramatically reduced bearing life can result. The purpose of this paper is to evaluate the feasibility of controlling bearing loads by controlling the heat generated by a thermal actuator placed around the housing of the spindle. A mathematical model of the open loop response of a laboratory prototype spindle is developed and validated. The model is then used to evaluate the closed loop performance. The results show that closed loop control of the bearing load is achievable in steady state and under bandwidth limited transient conditions. The proposed system has reasonable command authority when additional heat is required, however, it is possible for the system to lose control when the heater is required to “provide” negative heat. This situation can be mitigated by proper choice of initial preload. As expected, measurement noise limits the control gain but is not a limiting factor. More open loop tests are suggested to validate the model under a broader set of conditions. In addition, closed loop validation is suggested. However, based on results obtained it appears bearing load control is achievable by controlling the thermal field around the spindle.
对于精密、高速、金属切削加工主轴来说,热致轴承载荷的控制一直是一个重要但尚未解决的问题。主轴动态性能,以及主轴寿命,取决于轴承载荷。由于这些载荷会随着工艺条件的变化而急剧变化,因此会导致主轴动态性能差,轴承寿命急剧降低。本文的目的是评估通过控制放置在主轴外壳周围的热致动器产生的热量来控制轴承负荷的可行性。建立并验证了实验室样机主轴开环响应的数学模型。然后利用该模型对闭环性能进行评价。结果表明,在稳态和带宽有限的瞬态条件下,轴承载荷的闭环控制是可以实现的。当需要额外的热量时,拟议的系统具有合理的指挥权限,然而,当加热器被要求“提供”负热量时,系统有可能失去控制。这种情况可以通过适当选择初始预紧力来缓解。正如预期的那样,测量噪声限制了控制增益,但不是一个限制因素。建议进行更多的开环试验,以便在更广泛的条件下验证该模型。此外,建议进行闭环验证。然而,根据所获得的结果,似乎可以通过控制主轴周围的热场来实现轴承负荷控制。
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引用次数: 0
Control Design for Ultimate Boundedness of Linear Switched Systems With Controlled and Uncontrolled Subsystems 具有受控和非受控子系统的线性切换系统的极限有界性控制设计
R. Yedavalli, A. Sparks
Motivated by the Satellite Formation Keeping Control Problem, this paper presents a theoretical framework for designing controllers for the ultimate boundedness of linear switched systems consisting of both controlled (and thus stable) and uncontrolled (unstable) subsystems. It is shown that if the dwell time in the controlled mode (i.e ‘on time’) and that of the uncontrolled mode (’off time’) are chosen judiciously, ultimate boundedness of the switched system is guaranteed. Towards this direction explicit formulae for the switching times between controlled and uncontrolled modes are provided as a function of the parameters of the ultimate boundedness region. Using Lyapunov theory, a control design procedure is presented that achieves a good trade off between the ratio of ‘off’ and ‘on’ times and the size of the ellipsoidal boundedness regions which are representative of the system performance. The proposed control design technique has useful applications in mechanical and aerospace systems. The importance of this theory and possible extensions of these concepts are discussed.
在卫星编队保持控制问题的启发下,本文提出了线性切换系统的最终有界控制器设计的理论框架,该系统由受控(因此是稳定)子系统和非受控(不稳定)子系统组成。结果表明,如果合理地选择受控模式(即“开启时间”)和非受控模式(即“关闭时间”)的停留时间,则可以保证切换系统的最终有界性。针对这一方向,给出了受控模式和非受控模式切换时间作为最终有界区域参数的函数的显式公式。利用李雅普诺夫理论,提出了一种控制设计方法,在“关闭”和“打开”时间的比率与代表系统性能的椭球有界区域的大小之间实现了良好的权衡。所提出的控制设计技术在机械和航空航天系统中具有广泛的应用前景。讨论了这一理论的重要性以及这些概念的可能扩展。
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引用次数: 0
Singular Value Decomposition of Road Events Into Characteristic Shapes 道路事件特征形状的奇异值分解
J. Ferris
Road profiles are typically characterized by their spectral content. It has been noted by several researches, however, that road profiles are generally nonstationary signals that contain significant irregularities such as potholes. Such signals are not well described in the spectral domain. The objective of this work is to describe road profiles in the spatial domain by developing a set of characteristic shapes onto which individual events can be cast. A set of analytical functions describing these shapes is also developed. In order to develop a set a characteristic shapes, more than a million events are investigated from a mixture of road types (from highways to gravel roads) and a variety of locations throughout the United States. A set of characteristic shapes is developed for each road type and location. Although the events were drawn from diverse samples, the resulting sets of characteristic shapes are nearly indistinguishable. This similarity allows a single set of characteristic shapes to describe events for a wide class of roads. Variations in these sets are discussed and used in deriving a set of orthogonal analytical functions that describe the characteristic shapes. Individual road events are then mapped onto this set of characteristic shapes. The implications of decomposing road events into these characteristic shapes are discussed.
道路轮廓的典型特征是其光谱含量。然而,一些研究已经注意到,道路轮廓通常是非平稳信号,其中包含显著的不规则性,如坑洼。这种信号在谱域中不能很好地描述。这项工作的目的是通过开发一组特征形状来描述空间域的道路轮廓,这些特征形状可以投射到单个事件上。本文还提出了一组描述这些形状的解析函数。为了开发一套独特的形状,研究人员从美国各地的各种道路类型(从高速公路到砾石路)和各种地点调查了100多万个事件。为每种道路类型和位置开发了一套特征形状。尽管这些事件是从不同的样本中提取的,但所得到的特征形状集几乎是无法区分的。这种相似性使得单一的一组特征形状可以描述各种道路的事件。讨论了这些集合的变化,并将其用于推导描述特征形状的一组正交解析函数。然后将单个道路事件映射到这组特征形状上。讨论了将道路事件分解成这些特征形状的含义。
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引用次数: 2
Time Delay Modeling and Sample Time Selection for Networked Control Systems 网络控制系统的时延建模与采样时间选择
Feng‐Li Lian, J. Moyne, D. Tilbury
This paper discusses the impact of network architecture on control performance in a class of distributed control systems called Networked Control Systems (NCS), and provides design considerations related to control quality of performance (QoP) as well as network quality of service (QoS). The integrated network-control system changes the characteristics of time delays between application devices. This study first identifies several key components of the time delay through an analysis of network protocols and control dynamics. The analysis of network and control parameters is used to determine an acceptable working range of sampling periods in an NCS. A network-control simulator and an experimental networked machine tool have been developed to help validate and demonstrate the performance analysis results, and identify the special performance characteristics in an NCS. These performance characteristics are useful guidelines for choosing the network and control parameters when designing an NCS.
本文讨论了网络体系结构对一类称为网络控制系统(NCS)的分布式控制系统的控制性能的影响,并提供了与控制性能质量(QoP)和网络服务质量(QoS)相关的设计考虑。综合网络控制系统改变了应用设备间的时延特性。本研究首先通过对网络协议和控制动力学的分析,确定了时间延迟的几个关键组成部分。通过对网络和控制参数的分析,确定了网络控制系统可接受的采样周期工作范围。开发了一个网络控制模拟器和一个实验性网络机床,以帮助验证和演示性能分析结果,并确定NCS中的特殊性能特征。这些性能特征是设计NCS时选择网络和控制参数的有用指南。
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引用次数: 41
期刊
Proceedings of the ASME Dynamic Systems and Control Conference. ASME Dynamic Systems and Control Conference
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