基于能量整形方案实现具有通讯时滞欠驱动Euler-Lagrange网络的一致性

本文主要基于能量整形方案研究具有通讯时滞网络化欠驱动Euler-Lagrange (EL)系统的一致性问题,通过利用阻尼注入和互连分配的无源控制(PBC)技术,在有向连通网络拓扑下提出了一个简单的分布式协议,来实现在无引导者和有引导者-跟随者两种情形下欠驱动EL网络的一致性. 本文提出的一致性能量整形方案的主要特点是有机地整合了系统欠驱动和驱动部分以及控制器三部分能量作为整个系统的总能量,这个总能量被利用作为一个合适的Lyapunov函数,它能够充分确保网络化欠驱动EL系统达到所期望的分布式一致性. 最后,通过由欠驱动EL网络所描述柔性关节机械臂系统的数值模拟,来分析通讯时滞对一致性的效应和验证所提出控制算法的正确性.     

Further constructive results on interconnection and damping assignment control of mechanical systems: the Acrobot example

Interconnection and damping assignment passivity‐based control is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed‐loop system with a Hamiltonian structure with a desired energy function—that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. A class of underactuation degree one systems for which the partial differential equations can be explicitly solved—making the procedure truly constructive—was recently reported by the authors. In this brief note, largely motivated by the interesting Acrobot example, we pursue this investigation for two degrees‐of‐freedom systems where a constant inertia matrix can be assigned. We concentrate then our attention on potential energy shaping and give conditions under which an explicit solution of the associated partial differential equation can be obtained. Using these results we show that it is possible to swing‐up the Acrobot from some configuration positions in the lower half plane, provided some conditions on the robot parameters are satisfied. Copyright © 2006 John Wiley & Sons, Ltd.     

On feedback equivalence to port controlled Hamiltonian systems

In the last few years port controlled Hamiltonian (PCH) systems have emerged as an interesting class of nonlinear models suitable for a large number of physical applications. In this paper we study the question of feedback equivalence of nonlinear systems to PCH systems. More precisely, we give conditions under which a general nonlinear system can be transformed into a PCH system via static state feedback. We consider the two extreme cases where the target PCH system is completely a priori fixed or completely free, as well as the case where it is only partially predetermined. When the energy function is free a set of partial differential equations needs to be solved, on the other hand, if it is fixed we have to deal with a set of algebraic equations. In the former case, we give some verifiable necessary and sufficient conditions for solvability. As a by-product of our analysis we obtain some stabilization results for nonlinear systems.     

Stabilization of distributed control systems with delay

In this paper the asymptotic stabilization of linear distributed parameter control systems with delay is considered. Specifically, we are concerned with the class of control systems described by the equation x^′(t)=Ax(t)+L(x_t)+Bu(t), where A is the infinitesimal generator of a strongly continuous semigroup on a Banach space X. Assuming appropriate conditions, we will show that the usual spectral controllability assumption implies the feedback stabilization of the system. Applications to systems described by partial differential equations with delay are given.     

On passivity-based output feedback global stabilization of euler-lagrange systems

It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the latter objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propggation condition. This allows us to determine a class of Euler-Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties.     

Generic properties and control of linear structured systems: a survey

In this survey paper, we consider linear structured systems in state space form, where a linear system is structured when each entry of its matrices, like A,B,C and D, is either a fixed zero or a free parameter. The location of the fixed zeros in these matrices constitutes the structure of the system. Indeed a lot of man-made physical systems which admit a linear model are structured. A structured system is representative of a class of linear systems in the usual sense. It is of interest to investigate properties of structured systems which are true for almost any value of the free parameters, therefore also called generic properties. Interestingly, a lot of classical properties of linear systems can be studied in terms of genericity. Moreover, these generic properties can, in general, be checked by means of directed graphs that can be associated to a structured system in a natural way. We review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms. By properties we mean here system-specific properties like controllability, the finite and infinite zero structure, and so on, as well as, solvability issues of certain classical control problems like disturbance rejection, input-output decoupling, and so on. In this paper, we do not try to be exhaustive but instead, by a selection of results, we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool. We emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only. Moreover, the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well-known polynomially bounded combinatorial techniques for larger systems.     

Output control design and separation principle for a class of port‐Hamiltonian systems

Using a structure preserving observer, a dynamic output controller is proposed for a class of port‐Hamiltonian systems. The core of this method is based on the notion of contractive port‐Hamiltonian systems. The proposed method utilizes an extended form of IDA‐PBC (interconnection and damping assignment passivity‐based control), a well‐known controller design method for port‐Hamiltonian systems and paves the way for using IDA‐PBC in output control design of challenging control objectives, such as output tracking for underactuated mechanical systems. In the line of output control design, a useful separation principle for a class of port‐Hamiltonian systems is achieved, which is valuable in the field of nonlinear systems. Some simulations on magnetic levitation and ball on wheel testbeds show the potency and applicability of the proposed method.     

Switched seesaw control for the stabilization of underactuated vehicles

This paper addresses the stabilization of a class of nonlinear systems in the presence of disturbances, using switching controllers. To this effect we introduce two new classes of switched systems and provide conditions under which they are input-to-state practically stable (ISpS). By exploiting these results, a methodology for control systems design—called switched seesaw control—is obtained that allows for the development of nonlinear control laws yielding input-to-state stability. The range of applicability and the efficacy of the methodology proposed are illustrated via two nontrivial design examples. Namely, stabilization of the extended nonholonomic double integrator (ENDI) and stabilization of an underactuated autonomous underwater vehicle (AUV) in the presence of input disturbances and measurement noise.     

Survey on Passivity Based Control of Induction Machine

Induction machines (IM) constitute a theoretically interesting and practically important class of nonlinear systems. They are frequently used as wind generators for their power/cost ratio. They are described by a fifth‐order nonlinear differential equation with two inputs and only three state variables available for measurement. The control task is further complicated by the fact that IM are subject to unknown (load) disturbances and the parameters can be of great uncertainty. One is then faced with the challenging problem of controlling a highly nonlinear system, with unknown time‐varying parameters, where the regulated output, besides being unmeasurable, is perturbed by an unknown additive signal. Passivity‐based control (PBC) is a well‐established structure‐preserving design methodology which has shown to be very powerful to design robust controllers for physical systems described by Euler‐Lagrange equations of motion. PBCs provide a natural procedure to "shape" the potential energy yielding controllers with a clear physical interpretation in terms of interconnection of the system with its environment and are robust vis á vis to unmodeled dissipative effects. One recent approach of PBC is the Interconnection and Damping Assignment Passivity‐Based Control (IDA‐PBC) which is a very useful technique to control nonlinear systems assigning a desired (Port‐Controlled Hamiltonian) structure to the closed‐loop. The aim of this paper is to give a survey on different PBC of IM. The originality of this work is that the author proves that the well known field oriented control of IM is a particular case of the IDA‐PBC with disturbance.     

Power-based control of physical systems

It is well known that energy-balancing control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, the alternative paradigm of power shaping was introduced in Ortega, Jeltsema, and Scherpen (2003) —where, as suggested by its name, stabilization is achieved shaping a function akin to the power instead of the energy function. In this paper we extend this technique to general nonlinear systems. The method relies on the solution of a PDE, which identifies the open-loop storage function. We show through some physical examples, that the power-shaping methodology yields storage functions which have units of power. To motivate the application of this control technique we illustrate the procedure with two case studies: a tunnel diode circuit and a two-tanks system.     

Stabilization and Control of Delayed Recycling High Order Systems with one Unstable Pole at the Direct Path

In this work the stabilization and control of delayed recycling systems is addressed. Recycling systems are characterized by possessing two main paths, named the direct (feedforward) and the recycling (feedback) paths. Such class of systems reuse the energy and/or the partially processed matter increasing the efficiency of the overall process. A control methodology is proposed for the stabilization and control of this kind of system. The particular class of systems addressed here contains one unstable pole, m stable poles, a delay term and possible p left half plane (LHP) zeros in the direct path and a delayed stable subsystem in the recycling path. The strategy is based on an asymptotic observer‐predictor to estimate the required internal signals. Necessary and sufficient conditions are stated in order to guarantee the stabilization of the proposed scheme, achieving step tracking and rejection.     

An adaptive overlay network inspired by social behaviour

Nature is a great source of inspiration for scientists, because natural systems seem to be able to find the best way to solve a given problem by using simple and robust mechanisms. Studying complex natural systems, scientists usually find that simple local dynamics lead to sophisticated macroscopic structures and behaviour. It seems that some kind of local interaction rules naturally allow the system to auto-organize itself as an efficient and robust structure, which can easily solve different tasks. Examples of such complex systems are social networks, where a small set of basic interaction rules leads to a relatively robust and efficient communication structure. In this paper, we present PROSA, a semantic peer-to-peer (P2P) overlay network inspired by social dynamics. The way queries are forwarded and links among peers are established in PROSA resemble the way people ask other people for collaboration, help or information. Behaving as a social network of peers, PROSA naturally evolves to a small world, where all peers can be reached in a fast and efficient way. The underlying algorithm used for query forwarding, based only on local choices, is both reliable and effective: peers sharing similar resources are eventually connected with each other, allowing queries to be successfully answered in a really small amount of time. The resulting emergent structure can guarantee fast responses and good query recall.     

A constructive solution for stabilization via immersion and invariance: The cart and pendulum system

Immersion and Invariance (I&I) is the method to design asymptotically stabilizing control laws for nonlinear systems that was proposed in [Astolfi, A., & Ortega, R. (2003). Immersion and invariance: A new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic Control, 48, 590-606]. The key steps of I&I are (i) the definition of a target dynamics, whose order is strictly smaller than the order of the system to be controlled; (ii) the construction of an invariant manifold such that the restriction of the system dynamics to this manifold coincides with the target dynamics; (iii) the design of a control law that renders the manifold attractive and ensures that all signals are bounded. The second step requires the solution of a partial differential equation (PDE) that may be difficult to obtain. In this short note we use the classical cart and pendulum system to show that by interlacing the first and second steps, and invoking physical considerations, it is possible to obviate the solution of the PDE. To underscore the generality of the proposed variation of I&I, we show that it is also applicable to a class of n-dimensional systems that contain, as a particular case, the cart and pendulum system.     

Adaptive robust control of uncertain nonlinear systems with nonlinear delayed state perturbations

The problem of robust stabilization of uncertain nonlinear dynamical systems with multiple time delays is considered. In the paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown. Here, we do not require that the nonlinear terms including delayed states are linear norm-bounded in the states. An improved adaptation law with σ-modification is employed to estimate the unknown parameters, and a class of memoryless adaptive robust state feedback controllers is proposed. It is also shown that the proposed adaptive robust controllers can guarantee the uniform asymptotic stability of uncertain nonlinear time-delay systems. Finally, as a numerical example, an uncertain time-delay ecosystem with two competing species is given to demonstrate the validity of the results.     

An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems

Stabilization of nonlinear feedback passive systems is achieved assigning a storage function with a minimum at the desired equilibrium. For physical systems a natural candidate storage function is the difference between the stored and the supplied energies—leading to the so-called energy-balancing control, whose underlying stabilization mechanism is particularly appealing. Unfortunately, energy-balancing stabilization is stymied by the existence of pervasive dissipation, that appears in many engineering applications. To overcome the dissipation obstacle the method of Interconnection and Damping Assignment, that endows the closed-loop system with a special—port-controlled Hamiltonian—structure, has been proposed. If, as in most practical examples, the open-loop system already has this structure, and the damping is not pervasive, both methods are equivalent. In this brief note we show that the methods are also equivalent, with an alternative definition of the supplied energy, when the damping is pervasive. Instrumental for our developments is the observation that, swapping the damping terms in the classical dissipation inequality, we can establish passivity of port-controlled Hamiltonian systems with respect to some new external variables—but with the same storage function.     

Stabilization of nonlinear sandwich systems via state feedback—Discrete‐time systems

A recent paper (IEEE Trans. Aut. Contr. 2010; 55 (9):2156–2160) considered stabilization of a class of continuous‐time nonlinear sandwich systems via state feedback. This paper is a discrete‐time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched between linear systems. We focus first on single‐layer sandwich systems, which consist of a single saturation sandwiched between two linear systems. For such systems, we present necessary and sufficient conditions for semi‐global and global stabilization problems by state feedback, and develop design methodologies to achieve the prescribed stabilization. We extend the results to single‐layer sandwich systems subject to additional actuator saturation. Finally, we discuss further extension to general multi‐layer sandwich systems with an arbitrary number of saturations sandwiched between linear systems, both with and without actuator saturation. The design methodologies can be viewed as extensions of classical low‐gain design methodologies developed during the 1990s in the context of stabilizing linear systems subject to actuator saturation. Copyright © 2010 John Wiley & Sons, Ltd.     

Conditions for stabilization of the tokamak plasma vertical instability using only a massless plasma analysis

This paper describes the problem of feedback control for stabilization of the plasma vertical instability in a tokamak. Such controllers are typically designed based on a model that assumes the plasma mass m is identically zero while in reality the mass is small but positive. The assumption that m is zero can lead to a controller that appears to be stabilizing according to the massless analysis but in fact can increase the instability of the physical system.In this work, we consider a general class of controllers, which contains as a special case the type of controller most commonly used in operating tokamaks to stabilize the vertical instability, a proportional-derivative controller. Suppose C is a controller in this class which stabilizes the vertical instability with plasma mass assumed to be zero. We give easy-to-check necessary and sufficient conditions for C to also stabilize the physical system, in which the plasma actually has a small mass. We allow for the possibility that the tokamak could have both superconducting and resistive conductors.The practical implications of the results presented provide substantial insight into some long-standing issues regarding feedback stabilization of the vertical instability with PD controllers and also provide a rigorous foundation for the common practice of designing controllers assuming m=0. For controllers that operate only on the plasma vertical position, we settle the question: when are m=0 models predictive of actual plasma behavior?     

Bond graph modelling and simulation of multidisciplinary systems – An introduction

This paper introduces a graphical, computer aided modelling methodology that is particularly suited for the concurrent design of multidisciplinary systems, viz. of engineering systems with mechanical, electrical, hydraulic or pneumatic components, including interactions of physical effects from various energy domains.Following the introduction, bond graph modelling of multibody systems, as an example of an advanced topic, is briefly addressed in order to demonstrate the potential of this powerful approach to modelling multidisciplinary systems. It is shown how models of multibody systems including flexible bodies can be built in a systematic manner.     

Asymptotic stabilization of passive systems without damping injection: A sampled integral technique

Passivity in physical systems is a restatement of energy balancing, and therefore is a ubiquitous property in engineering applications. Under some weak conditions, the unique equilibrium state of passive systems is stable. However, to ensure asymptotic stability, strict output passivity and a detectability property are required. Although strict output passivity may be enforced via a damping injection that feeds back the passive output, this signal may be noisy or unmeasurable — the paradigmatic example being velocity in mechanical systems. In this paper a sampled integral stabilization (SIS) technique for the asymptotic regulation of passive systems, that requires only the knowledge of the time integral of the passive output — i.e. position in mechanical systems — is proposed. As a generalization of the previous result, it is shown that SIS is applicable to cascade connections of passive systems measuring only the storage function of the second one. Several examples, including a planar elbow manipulator and the rigid body dynamics are shown to satisfy the assumptions for the application of SIS.     

A new separation result for a class of quadratic-like systems with application to Euler-Lagrange models

A separation result for some kind of global stabilization via output feedback of a class of nonlinear systems, under the form of some stabilizability by state feedback on the one hand, and some unboundedness observability on the other hand is presented. They allow to design, for any domain of output initial condition, some dynamic output feedback controller achieving global stability. It is also highlighted how disturbance attenuation can further be achieved on the same basis. As an example, the proposed conditions are shown to be satisfied by the class of so-called Euler-Lagrange systems, for which a tracking output feedback control law is thus proposed.