Port-Based Modeling and Simulation of Mechanical Systems With Rigid and Flexible Links

In this paper, a systematic procedure for the definition of the dynamical model in port-Hamiltonian form of mechanical systems is presented as the result of the power-conserving interconnection of a set of basic components (rigid bodies, flexible links, and kinematic pairs). Since rigid bodies and flexible links are described within the port-Hamiltonian formalism, their interconnection is possible once a proper relation between the power-conjugated port variables is deduced. These relations are the analogous of the Kirchhoff laws of circuit theory. From the analysis of a set of oriented graphs that describe the topology of the mechanism, an automatic procedure for deriving the dynamical model of a mechanical system is illustrated. The final model is a mixed port-Hamiltonian system, because of the presence of a finite-dimensional subsystem (modeling the rigid bodies) and an infinite-dimensional one (describing the flexible links). Besides facilitating the deduction of the dynamical equations, it is shown how the intrinsic modularity of this approach also simplifies the simulation phase.     

A port-Hamiltonian formulation of physical switching systems with varying constraints

This paper extends a generic method to design a port-Hamiltonian formulation modeling all geometric interconnection structures of a physical switching system with varying constraints. A non-minimal kernel representation of this family of structures (named Dirac structures) is presented. It is derived from the parameterized incidence matrices which are a mathematical representation of the primal and dual dynamic network graphs associated with the system. This representation has the advantage of making it possible to model complex physical switching systems with varying constraints and to fall within the framework of passivity-based control.     

On the control of non-linear processes: An IDA–PBC approach

A high performance non-linear controller that exploits the properties of port-Hamiltonian systems to precisely define the interconnections and energy dissipations of non-linear processes is presented for a large class of chemical processes. The controller is derived from classical interconnection and damping assignment–passivity based control theory but an additional degree of freedom is introduced in the controller design by the use of “non-exact matching” closed-loop storage functions. By a proper closed-loop interconnection assignment the proposed controller achieves total decoupling between outputs and since no inversion of the process dynamics is made in the design it is equally applicable to minimum phase and nonminimum phase system. The controller design methodology is presented and stability conditions are stated. As illustrative example the proposed method is used to design controllers for a multiple-input/multiple-output non-isothermal continued stirred tank reactor that exhibits nonminimum phase behavior.     

Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints

In this paper, the dynamic response of a planar rigid multi-body system with stick?Cslip friction in revolute clearance joints is studied. LuGre friction law is proposed to model the stick?Cslip friction at the revolute clearance joints. This is because using this law, one can capture the variation of the friction force with slip velocity, thus making it suitable for studies involving stick?Cslip motions. The effective coefficient of friction is represented as a function of the relative tangential velocity of the contacting bodies, that is, the journal and the bearing, and an internal state. In LuGre friction model, the internal state is considered to be the average bristle deflection of the contacting bodies. By applying the LuGre friction law on a typical slider?Ccrank mechanism, the friction force in the revolute joint having clearance is seen not to have a discontinuity at zero slip velocity throughout the simulation unlike in static friction models. In addition, LuGre model was observed to capture the Stribeck effect which is a phenomenon associated directly with stick?Cslip friction. The friction forces are seen to increase with increase in input speed. The effect of stick?Cslip friction on the overall dynamic behavior of a mechanical system at different speeds was seen to vary from one clearance joint to another.     

Perspectives in modeling for control of power networks

Increasing integration of renewable energy sources in the power grid leads to a complete re-thinking of its operation. This necessitates the consideration of new modeling and analysis approaches, which can serve as natural starting points for robust and scalable control and design strategies.In this ‘vision’ paper we will highlight two topics within the broad area of power networks: the modeling and analysis of the synchronous generator, and the modeling and analysis of power networks using the swing equation as an approximate model for the generator. In both cases we will discuss a port-Hamiltonian formulation, which reflects the underlying physics of power flow and energy storage. Although the port-Hamiltonian model of the synchronous generator reveals a clear structure it still poses fundamental challenges for its non-zero steady state stability analysis. It is shown how the swing equation can be directly deduced from the power balance of the port-Hamiltonian model of the synchronous generator. Under the phasor assumption, this leads to a port-Hamiltonian model of power networks of generators, which enables a straightforward stability analysis and provides a starting point for control.     

Adaptive robust control of linear motors with dynamic friction compensation using modified LuGre model

LuGre model has been widely used in dynamic friction modeling and compensation. However, there are some practical difficulties when applying it to systems experiencing large range of motion speeds such as, the linear motor drive system studied in the article. This article first details the digital implementation problems of the LuGre model based dynamic friction compensation. A modified model is then presented to overcome those shortcomings. The proposed model is equivalent to LuGre model at low speed, and the static friction model at high speed, with a continuous transition between them. A discontinuous projection based adaptive robust controller (ARC) is then constructed, which explicitly incorporates the proposed modified dynamic friction model for a better friction compensation. Nonlinear observers are built to estimate the unmeasurable internal state of the dynamic friction model. On-line parameter adaptation is utilized to reduce the effect of various parametric uncertainties, while certain robust control laws are synthesized to effectively handle various modeling uncertainties for a guaranteed robust performance. The proposed controller is also implemented on a linear motor driven industrial gantry system, along with controllers with the traditional static friction compensation and LuGre model compensation. Extensive comparative experimental results have been obtained, revealing the instability when using the traditional LuGre model for dynamic friction compensation at high speed experiments and the improved tracking accuracy when using the proposed modified dynamic friction model. The results validate the effectiveness of the proposed approach in practical applications.     

含有LuGre摩擦并联机械臂的自适应控制

本文研究了含有LuGre摩擦的并联机械臂自适应控制问题.首先,在并联机械臂动力学模型中引入LuGre摩擦模型来描述伺服关节内部的摩擦行为;其次,构造含有动态摩擦补偿的自适应控制算法,并使用Lyapunov方法证明控制算法的有效性;最后,通过平面3 RRR并联机械臂数值算例,验证所提出控制算法的效果以及LuGre摩擦补偿的必要性.     

控制力矩陀螺框架伺服系统期望补偿自适应鲁棒控制

本文针对控制力矩陀螺框架伺服系统中存在的参数不确定性、摩擦非线性及外部干扰问题,提出了一种考虑LuGre摩擦的自适应鲁棒控制方法.针对陀螺框架伺服系统未知惯量和阻尼系数、LuGre摩擦参数不确定性及未知外部干扰上界,设计参数更新律对其进行估计.在此基础上,为提高系统对不确定参数及未知干扰的鲁棒性,设计带有期望补偿的自适应鲁棒控制器,可实现对LuGre摩擦非线性的精确补偿,同时减小测量信号噪声及外部干扰对系统的不利影响.应用Lyapunov稳定性理论分析了闭环系统的稳定性.对挠性航天器姿态机动控制的仿真结果,验证了所提方法的有效性.     

Stability analysis of a controlled mechanical system with parametric uncertainties in LuGre friction model

Parameters of friction model identified for a specific control system development are not constants. They vary over time and have a significant effect on the control system stability. Although much research has been devoted to the stability analysis under parametric uncertainty, less attention has been paid to incorporating a realistic friction model into their analysis. After reviewing the common friction models for controller design, a modified LuGre friction model is selected to carry out the stability analysis in this study. Two parameters of the LuGre model, namely σ₀ and σ₁, are critical to the demonstration of dynamic friction features, yet the identification of which is difficult to carry out, resulting in a high level of uncertainties in their values. Aiming at uncovering the effect of the σ₀ and σ₁ variations on the control system stability, a servomechanism with modified LuGre friction model is investigated. Two set-point position controllers are synthesised based on the servomechanism model to form two case studies. Through Lyapunov exponents, it is clear that the variation of σ₀ and σ₁ has an obvious effect on the stabiltiy of the studied systems and should not be overlooked in the design phase.     

Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity

Model reduction of port-Hamiltonian systems by means of the Krylov methods is considered, aiming at port-Hamiltonian structure preservation. It is shown how to employ the Arnoldi method for model reduction in a particular coordinate system in order to preserve not only a specific number of the Markov parameters but also the port-Hamiltonian structure for the reduced order model. Furthermore it is shown how the Lanczos method can be applied in a structure preserving manner to a subclass of port-Hamiltonian systems which is characterized by an algebraic condition. In fact, for the same subclass of port-Hamiltonian systems the Arnoldi method and the Lanczos method turn out to be equivalent in the sense of producing reduced order port-Hamiltonian models with the same transfer function.     

LuGre摩擦模型对伺服系统的影响与补偿

摩擦是影响伺服系统性能的一个主要因素. 为了研究摩擦的影响与补偿, 本文首先建立了基于动态LuGre摩擦的机电伺服系统模型. 根据LuGre模型, 构造了一个非线性观测器来估计摩擦力矩. 然后, 积分反步自适应控制算法被设计从而实现了摩擦补偿和负载扰动估计, 并使用Lyapunov函数证明了闭环系统的稳定性. 仿真结果表明:LuGre摩擦会对伺服系统产生极限环振荡以及低速爬行的影响, 并且提出的补偿方法能够降低摩擦对伺服系统性能的影响以及提高了系统的跟踪精度和鲁棒性.     

Adaptive integral backstepping sliding mode control for opto-electronic tracking system based on modified LuGre friction model

In order to improve the control accuracy and stability of opto-electronic tracking system fixed on reef or airport under friction and external disturbance conditions, adaptive integral backstepping sliding mode control approach with friction compensation is developed to achieve accurate and stable tracking for fast moving target. The nonlinear observer and slide mode controller based on modified LuGre model with friction compensation can effectively reduce the influence of nonlinear friction and disturbance of this servo system. The stability of the closed-loop system is guaranteed by Lyapunov theory. The steady-state error of the system is eliminated by integral action. The adaptive integral backstepping sliding mode controller and its performance are validated by a nonlinear modified LuGre dynamic model of the opto-electronic tracking system in simulation and practical experiments. The experiment results demonstrate that the proposed controller can effectively realise the accuracy and stability control of opto-electronic tracking system.     

Desired Compensation Adaptive Robust Control of Electrical-optical Gyro-stabilized Platform with Continuous Friction Compensation Using Modified LuGre Model

Continuous friction compensation along with other modeling uncertainties is concerned in this paper, to result in a continuous control input, which is more suitable for controller implementation. To accomplish this control task, a novel continuously differentiable nonlinear friction model is synthesized by modifying the traditional piecewise continuous LuGre model, then a desired compensation version of the adaptive robust controller is proposed for precise tracking control of electrical-optical gyro-stabilized platform systems. As a result, the adaptive compensation and the regressor in the proposed controller will depend on the desired trajectory and on-line parameter estimates only. Hence, the effect of measurement noise can be reduced and then high control performance can be expected. Furthermore, the proposed controller theoretically guarantees an asymptotic output tracking performance even in the presence of modeling uncertainties. Extensively comparative experimental results are obtained to verify the effectiveness of the proposed control strategy.

     

基于LuGre 摩擦模型的机械臂模糊神经网络控制

针对未知摩擦非线性会使机械臂控制精度难以提高的缺陷,建立基于动态LuGre摩擦的机械臂模型.在系统参数未知和机械臂负载变化的情况下,设计一种自适应模糊神经网络控制器,采用基函数中心和宽度均自适应变化的模糊神经网络补偿器,实现对系统中包括LuGre摩擦在内的非线性环节的逼近,并利用滑模控制项减小逼近误差.通过Lyapunov方法证明了闭环系统的稳定性,并通过仿真结果验证了所提出控制方法的有效性.     

高速AWID车辆车轮独立制动控制研究

全部车轮均独立驱动/制动(AWID)的车辆比非独立驱动/制动的车辆在高速工况下具有更优越的动力、机动和操纵性能,论文对车轮独立制动控制问题进行研究;首先建立车轮独立制动的数学模型,简单介绍轮胎LuGre动态模型;然后分析制动控制的目标,设计控制系统结构和自抗扰控制器;最后对动态期望滑移率下的车轮制动控制进行仿真;结果表明,所设计的自抗扰控制器可以实现强鲁棒和高精度的车轮独立制动控制。     

Velocity Reversal Systems: A Simple Friction Model for Telescopes

In this paper we experimentally characterize friction in an astronomical telescope and introduce a new model for capturing the observed behavior of friction in both the micro and macro displacement regimes of motion. The model is a modification of the LuGre model and is developed for velocity reversal systems like an astronomical telescope. The proposed model is represented with a pair of masses separated by a linear spring. This model is then employed to synthesize a feedback linearizable controller for the system. The simulation results for the proposed friction model in open loop are presented and validated with the experimental results. The stability aspects of the closed loop system with the modified friction model is then investigated. For estimating the unmeasurable states of the system used in feedback linearization, we discuss the observability of the system with the new model for friction.     

Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems

Simplicial Dirac structures as finite analogues of the canonical Stokes–Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input–output finite-dimensional port-Hamiltonian systems that emulate the behavior of distributed-parameter port-Hamiltonian systems. This paper elaborates on the matrix representations of simplicial Dirac structures and the resulting port-Hamiltonian systems on simplicial manifolds. Employing these representations, we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port-Hamiltonian systems on simplicial manifolds.     

Design and realization of hybrid ACO-based PID and LuGre friction compensation controller for three degree-of-freedom high precision flight simulator

Three degree-of-freedom (3-DOF) high precision flight simulator is a type of key hardware-in-loop equipment in the fields of aeronautics and astronautics. The conventional Proportional–Integral–Derivative (PID) is a widely used industrial controller that uses a combination of proportional, integral and derivative action on the control error to form the output of the controller. It is well known that the undesired phenomena caused by friction can lead to overall flight simulator performance degradation or instability. This paper presents a novel kind of hybrid Ant Colony Optimization (ACO)-based PID and LuGre friction compensation controller for 3-DOF high precision flight simulator. On the basis of introduction of the basic principles of ACO, the controlling scheme design for the 3-DOF high precision flight simulator is presented. Based on the popular LuGre friction model, a novel nonlinear friction compensation controller for 3-DOF high precision flight simulator is also developed. The proposed Lyapunov function proves the robust global convergence of the tracking error. The parameters tuning of PID can be summed up as the typical continual spatial optimization problem, grid-based searching strategy is adopted in the improved ACO algorithm, and self-adaptive control strategy for the pheromone decay parameter is also adopted. Modularization design is adopted in the 3-DOF high precision flight simulator. This software can process the position and status signals, and display them on the friendly interface. Double buffer mechanism is adopted in the communication protocol between lower Industrial Personal Computer (IPC) and upper IPC. The series experimental results have verified the feasibility and effectiveness of the proposed hybrid ACO-based PID and LuGre friction compensation controller.     

Adaptive Dynamic Surface control of An electrohydraulic Actuator with Friction Compensation

In this paper, an adaptive nonlinear control scheme with a friction observer for position control of an electrohydraulic actuator is proposed. The observer based on the LuGre friction model is employed to compensate for the friction. Adaptation laws are used to handle parameter uncertainties in the actuator and friction model. The control law including dynamics of the observer is developed through a backstepping‐like dynamic surface control (DSC) technique. Experimental results have illustrated the success of the control scheme. The results also show that the adaptive DSC controller has better tracking performance than an adaptive backstepping and conventional PI controllers.