Control For Port-controlled Hamiltonian Systems Research Articles

Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation.

The finite-time stabilization and finite-time H∞ control problems of Port-controlled Hamiltonian (PCH) systems with disturbances and input saturation (IS) are studied in this paper. First, by designing an appropriate output feedback, a strictly dissipative PCH system is obtained and finite-time stabilization result for nominal system is given. Second, with the help of the Hamilton function method and truncation inequality technique, a novel output feedback controller is developed to make the PCH system finite-time stable when IS occurs. Further, a finite-time H∞ controller is designed to attenuate disturbances for PCH systems with IS, and sufficient conditions are presented. Finally, a numerical example and a circuit example are given to reveal the feasibility of the obtained theoretical results.

Disturbance tolerance and H ∞ control of port-controlled hamiltonian systems in the presence of actuator saturation

This paper investigates the disturbance tolerance and H ∞ control of multi-input Port-Controlled Hamiltonian (PCH) systems in the presence of actuator saturation which may be not openloop stable. A simple condition is derived under which trajectories starting from the origin will remain inside an ellipsoid. The disturbance tolerance ability of the closed-loop system under a given feedback control law is measured by the size of this ellipsoid. Based on the above mentioned condition, the problem of disturbance tolerance can be expressed in the form of the linear matrix inequalities (LMIs) optimization problem with constraints. In addition, an H ∞ control approach is presented to attenuate the disturbances, and disturbance rejection ability in terms of L 2 gain is also determined by the solution of an LMI optimization problem. Study of an illustrative example with simulations shows the effectiveness of the methods proposed.

Bounded Control of Port-Controlled Hamiltonian Systems and Application in Synchronous Generator

Bounded Control of Port-Controlled Hamiltonian Systems and Application in Synchronous Generator

Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations

This paper addresses trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations and passivity-based control. The main strategy adopted in this paper is to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. After obtaining the error system, tracking control of the original system can be achieved by stabilizing the error system via passivity-based approach. First, a fundamental framework is provided for constructing the error system via generalized canonical transformations. Then a concrete design procedure is derived for a class of electro-mechanical systems. Furthermore, the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness.

Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems

Passivity-based control (PBC) is a well-established technique that has shown to be very powerful to design robust controllers for physical systems described by Euler–Lagrange (EL) equations of motion. For regulation problems of mechanical systems, which can be stabilized “shaping” only the potential energy, PBC preserves the EL structure and furthermore assigns a closed-loop energy function equal to the difference between the energy of the system and the energy supplied by the controller. Thus, we say that stabilization is achieved via energy balancing. Unfortunately, these nice properties of EL–PBC are lost when used in other applications which require shaping of the total energy, for instance, in electrical or electromechanical systems, or even some underactuated mechanical devices. Our main objective in this paper is to develop a new PBC theory which extends to a broader class of systems the aforementioned energy-balancing stabilization mechanism and the structure invariance. Towards this end, we depart from the EL description of the systems and consider instead port-controlled Hamiltonian models, which result from the network modelling of energy-conserving lumped-parameter physical systems with independent storage elements, and strictly contain the class of EL models.

General Framework of Trajectory Tracking Control of Hamiltonian Systems via Generalized Canonical Transformations

This paper is devoted to trajectory tracking control of port-controlled Hamiltonian systems based on generalized canonical transformations. A general framework of tracking control utilizing the passivity property is proposed. Firstly, it is shown how to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. Secondly, a practical procedure to construct tracking controllers of port-controlled Hamiltonian systems including nonholonomic systems is derived. Finally, a simple example of tracking control of a nonholonomic system demonstrates the effectiveness of the proposed method. This method is a natural extension of the conventional passivity based control and is expected to derive robustly stable control systems.

一般化正準変換を用いたハミルトニアンシステムの軌道追従制御

This paper addresses trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations and passivity-based control. The main strategy adopted in this paper is to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. After obtaining the error system, tracking control of the original system can be achieved by stabilizing the error system via passivity-based approach. First, a fundamental framework is provided for constructing the error system via generalized canonical transformations. Then a concrete design procedure is derived for a class of electro-mechanical systems. Furthermore, the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness.