Passivity-based robust feedback control for non-linear systems with input dynamical uncertainty

This paper addresses the robust feedback control problem for a class of non-linear systems with uncertain input dynamics. The main objective is to develop a passivity-based systematic design approach for this kind of uncertain system. First, a passivity condition is presented for a non-linear system in feedback interconnection form, and then it is shown that with the help of this condition, a state feedback control law can be designed to render the uncertain system passive. Moreover, the extensions of the passivation controller are investigated in two cases where the uncertainty allows unknown control direction and there exists the external disturbance, respectively. It will be shown that an adaptive controller with a Nussbaum-type function can be incorporated into the passivation controller to deal with the unknown control direction and the L ₂-gain performance can be achieved by gain re-assignment of the passivation controller. Finally, a numerical example is given to demonstrate the proposed approach.     

On output feedback stabilization of Euler-Lagrange systems with nondissipative forces

This paper provides a solution to the problem of output feedback stabilization of systems described by Euler-Lagrange equations perturbed by nondissipative forces. This class of forces appears in some applications where we must take into account the interaction of the system with its environment. The nonlinear dependence on the unmeasurable part of the state and the loss of the fundamental passivity property render most of the existing results on stabilization of nonlinear systems unapplicable to this problem. The technique we use consists of finding a dynamic output feedback controller and a nonlinear change of coordinates such that the closed loop can be decomposed as a cascade of an asymptotically stable system and an input-to-state stable system. This should be contrasted with the well-known passivity-based technique that aims at a feedback interconnection of passive systems. We believe this design methodology to be of potential applicability to other stabilization problems where passivity arguments are unapplicable.     

无刷双馈调速电机无源性分析及自适应控制

应用无源性控制理论从能量角度研究了无刷双馈电机控制系统.建立了无刷双馈电机的欧拉方程,并将其分解为电气和机械两个无源子系统的反馈并联,以此说明在设计控制器时只需考虑电气子系统,简化了控制算法.设计了电机的转矩和转速控制器.在此基础上,考虑电机功率及控制绕组电阻在运行中可能发生变化.设计自适应控制器以提高系统的鲁棒性.仿真结果表明此控制策略能快速地跟踪速度给定.动静态响应能力较好,且具有全局稳定、系统鲁棒性好的特点.     

Passivity‐based control of a magnetically levitated flexible beam

This paper solves the asymptotic stabilization problem for a magnetically levitated flexible beam using a nested‐loop passivity‐based controller design. Passivity analyses reveal that the system can be decomposed into two passive subsystems: a mechanical subsystem that consists of a flexible beam with both ends free and that defines a passive map from external forces to the velocity of the points on the flexible beam at which the external forces act; and an electrical subsystem that consists of a pair of electromagnets and that defines a strictly output‐passive map from voltages applied across the electromagnets to magnetic fluxes. The standard method for designing passivity‐based controllers leads to a nonlinear feed‐forward controller for the electrical subsystem, which enables the electrical subsystem to generate given desired magnetic forces, and an output feedback compensator for the mechanical subsystem, which computes the desired forces required to regulate the position and vibration of the beam. The asymptotic stability of each controller may be proven using Lyapunov's stability theory and LaSalle's invariant set theorem. Numerical simulations confirm the asymptotic stability of the equilibrium configuration of the closed‐loop system formed by the magnetically levitated flexible beam together with the proposed controllers. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust passivity and feedback passification of a class of uncertain fractional-order linear systems

Theoretical results on robust passivity and feedback passification of a class of uncertain fractional-order (FO) linear systems are presented in the paper. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output matrices. Firstly, some suitable notions of passivity and dissipativity for FO systems are proposed, and the relationship between passivity and stability is obtained. Then, a sufficient condition in the form of linear matrix inequality (LMI) for such system to be robustly passive is given. Based on this condition, the design method of state feedback controller is proposed when the states are available. Moreover, by using matrix singular value decomposition and LMI techniques, the existing condition and method of designing a robust observer-based passive controller for such systems are derived. Numerical simulations demonstrate the effectiveness of the theoretical formulation.     

Feedback passivity‐based control of discrete nonlinear systems with time‐delay for variable geometry truss manipulator

In this paper, the feedback passivity‐based control of nonlinear discrete time‐delay systems for variable geometry truss manipulators is investigated. To determine an appropriate communication channel in the sense of feedback passivation, we first model the dynamics of the variable geometry truss manipulator as a generalized discrete nonlinear system with time‐delay. Then we further prove that when the infinite norm of estimated error is bounded, as long as there is a controller enables the closed‐loop system to be input‐strictly passive, there must be a deterministic equivalent controller to ensure that the system is stochastically quasi passive. After that, on the basis of the conclusion obtained, a more conclusive corollary is addressed for linear plants. Though passivity is a stricter condition than stability, feedback passivation does not impose more restrictions on estimate errors, and therefore does not require more communication channel information than mean square stability. Finally, we simplify the variable geometry truss dynamics to a linear plant to simulate to verify the validity of our method, and also compared the experimental results with the methods in the existing literature.     

Incremental passivity and output regulation

In this paper we investigate the use of incremental passivity concepts for the design of nonlinear global regulators. For a specific class of systems and exosystems we show how the problem of designing an internal model-based regulator reduces to the design of an output feedback controller rendering the controlled plant incrementally passive. In this framework we present a result for the design of an output feedback controller achieving incremental passivity for a particular class of nonlinear systems.     

基于生物启发模型的欠驱动水平TORA系统的有界输入镇定控制

针对欠驱动水平TORA(translational oscillators with rotating actuator)系统,提出一种基于生物启发模型的有界输入控制方法,实现系统在执行器存在饱和约束情况下的镇定控制.首先,根据水平TORA系统的动力学模型分析系统的无源特性,进而给出系统的控制目标;接着,基于无源特性构造一种新颖的Lyapunov函数,在此基础上设计一种结构简单的非线性状态反馈控制器;然后,考虑执行器的饱和约束条件,引入受生物启发建立的神经动力学模型,利用该模型的有界平滑输出特性,设计一种改进的状态反馈控制器;最后,根据LaSalle不变性原理对系统的稳定性进行严格的数学分析和证明.与其他方法相比,所提方法不仅考虑了执行器的饱和约束问题,而且设计的控制算法简单高效,易于工程实现.仿真与对比结果表明,所提方法具有更好的控制性能.     

交直流混合输电系统的新型无源性调制

交直流混合输电系统的动态响应性能直接影响电力系统的稳定性.为提高系统的动态响应速度和控制器的鲁棒性,本文基于无源性理论从具体结构出发,设计了直流输电系统的无源性调制控制器.以交直流并联的两机系统为研究对象,对系统的输入输出进行重构,并对系统的无源性进行验证.根据稳定性和无源性之间的关系,设计出反馈控制规律.对两种不同情况的仿真,显示出该控制律在保证系统的稳定性的同时.提高了系统的动态响应速度.     

Passivity-based adaptive inventory control

A new adaptive inventory control strategy is developed by applying online adaptation in the framework of passivity-based control. By using the system model and definition of the inventory, a feedback-feedforward control structure is derived from the passivity theorem. The stability analysis and the extension of the controller to a non-passive system are also given in this paper. This control strategy is demonstrated in a transfer function example and an application to a pressure tank unit in a chemical plant.     

有源箝位正激变换器无源控制方法的研究

以有源箝位正激变换器为研究对象,根据状态空间平均模型,建立系统误差模型,通过配置系统能量耗散特性方程中的无功力,保证系统的无源性,设计了一种无源化控制器。论文给出了变换器无源控制方法的推导过程和有源箝位正激变换器的无源控制策略;仿真和实验结果表明,该方案运行稳定,具有较强的鲁棒性、快速性和跟踪性,且纹波较小,控制算法简单等优点。     

TORQUE AND FLUX TRACKING OF INDUCTION MOTORS

The problem of torque tracking and rotor flux norm regulation of induction motors perturbed by an unknown constant load torque was recently solved with an observer-based controller in Reference 5. In this paper we extend this result to treat the practically important case when the rotor flux norm is required to follow a time-varying reference. The controller design follows the passivity-based approach and proceeds in two steps: first, we define a target closed-loop dynamics compatible with the physical model of the motor that delivers the desired rotor flux and torque. Second, we propose a nonlinear dynamic output feedback controller that ensures this behaviour is asymptotically achieved. A proof of global tracking is given under the assumption of known motor parameters. Some key features of our physically based design are that the control law does not require measurement of rotor variables, is always well defined and does not rely on (intrinsically nonrobust) nonlinear dynamics cancellation. A corollary of our main result is the proof that a slight modification of the classical indirect field-oriented controller ensures global tracking for current-fed machines. © 1997 by John Wiley & Sons, Ltd.     

On the globally defined sensorless control of induction motors

The sensorless control problem of induction motors imposes a current challenge since the nonlinear model of this kind of machines does not exhibit global observability properties, i.e. there are some operation regimes for which speed observability is lost. One way for dealing with this unavoidable limitation, and at the same time provide globally defined controllers, is to consider that the rotor variables are estimated via an open‐loop observer. In this paper a globally defined passivity‐based speed controller that belongs to the aforementioned class is presented. It is shown that the structure of previously reported passivity‐based controllers, developed under the assumption that the mechanical variables are available for measurement, can be extended to operate under sensorless conditions if a speed observer is included in the control scheme. Since the controller design methodology leads to inherent drawbacks regarding robustness issues, to evaluate the usefulness of the proposed scheme a numerically based study is included that cover topics such as parameters and disturbance (load torque) uncertainty. The advantages and limitations of the proposed scheme are established with respect to other globally defined sensorless controllers. Copyright © 2008 John Wiley & Sons, Ltd.     

PWM整流器的无源滑模非线性控制

为提高三相电压型PWM (pulse width modulation)整流器的稳态与动态控制性能,提出了无源滑模非线性控制方案.基于PWM整流器欧拉-拉格朗口系统动力学模型,分析了系统内在无源特性.从全局能量角度出发,利用系统无源性,通过能量成形与阻尼注入方法,给出了PWM整流器的辅助设计系统.设计了滑模变结构电流内环控制器与PI(proportional-integral)电压外环控制器,同时采用基于饱和函数的准滑模控制方法解决了控制力的抖动问题.仿真实验结果表明,所提控制方法可实现三相电压型PWM整流器的单位功率因数控制与直流电压快速调节,同时具有很强的抗电网电压和负载扰动能力以及对于参数摄动的鲁棒性.     

Passivity-based consensus for linear multi-agent systems under switching topologies

This paper studies the passivity-based consensus analysis and synthesis problems for a class of stochastic multi-agent systems with switching topologies. Based on Lyapunov methods, stochastic theory, and graph theory, new different storage Lyapunov functions are proposed to derive sufficient conditions on mean-square exponential consensus and stochastic passivity for multi-agent systems under two different switching cases, respectively. By designing passive time-varying consensus protocols, the solvability conditions for the passivity-based consensus protocol synthesis problem, i.e., passification, are derived based on linearization techniques. Numerical simulations are provided to illustrate the effectiveness of the proposed methods.     

A unified approach for stability analysis of a class oftime-varying nonlinear systems

It is shown that an integral with negative feedback from its output terminal through a strictly passive system is still strictly passive. By using successive negative feedback around integrals, the conditions of strict passivity and a unified approach for constructing strictly passive systems are obtained for time-varying nonlinear systems of different orders. A new concept of “dissipation factor” is defined in this paper. The stability of a class of time-varying nonlinear systems is examined by using this passivity analysis     

感应电机转矩跟踪无源控制及自适应观测器设计

针对感应电机高性能转矩跟踪控制和磁链难以直接测量问题,提出了基于无源性的转矩跟踪和自适应磁链观测器控制方案.首先基于感应电机的无源性特性设计了渐近稳定转矩跟踪控制器,重新配置了系统的平衡点,通过注入阻尼提高系统的收敛速度.然后通过将定子电流和转子磁链作为状态变量构建了自适应磁链观测器,简化了观测器结构,根据Lyapunov稳定性理论设计了自适应控制律,实现转子磁链、转速和定子电阻的在线估计.为减小转速估计误差对观测器的影响,给出了观测器增益矩阵的选择方法.仿真结果表明本文所提出的基于自适应观测器的无源控制方案能够有效提高感应电机的动静态性能.     

Robust control of the electrostatic torsional micromirrors

In order to simplify the sensors subsystems of the electrostatic torsional micromirrors (ETMs), the output feedback control for the ETM systems is investigated in this paper. The dynamics of the systems is established by combining the dynamics of both the mechanical and electronic subsystems, and it is proved that the dynamics of the overall system with uncertainties in electrical parameters can be exactly transformed into the third order linear system. Then an output feedback finite-time stabilizing (FTS) controller is presented by composing of a full state FTS observer and a state feedback FTS controller for the third order linear systems, such that the ETM systems can be stabilized in its full travel range by merely measuring the tilt angle. Some numerical simulations demonstrate the stability of the proposed output feedback FTS controller.     

Feedback passivity of nonlinear discrete-time systems with direct input-output link

This paper is devoted to the study of the feedback passivity property in nonlinear discrete-time systems. The relative degree and zero dynamics of the non-passive system are related to the feedback passivity of the system. Two main results are presented. First, some relative degree-related properties of passive systems in general form are stated. Second, sufficient conditions in order to render a multiple-input multiple-output (MIMO) system passive by means of a static state feedback control law are obtained.     

Transient stabilization of multimachine power systems with nontrivial transfer conductances

We provide a solution to the long-standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances. More specifically, we consider the full 3n-dimensional model of the n-generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. To design the control law we apply the recently introduced interconnection and damping assignment passivity-based control methodology that endows the closed-loop system with a port-controlled Hamiltonian structure with desired total energy function. The latter consists of terms akin to kinetic and potential energies, thus has a clear physical interpretation. Our derivations underscore the deleterious effects of resistive elements which, as is well known, hamper the assignment of simple "gradient" energy functions and compel us to include nonstandard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system which is obtained via the introduction of state-modulated interconnections that play the role of multipliers in classical passivity theory.