This article studies a class of control systems in a Hilbert space H given $\dot x(t) = Ax(t) + bu(t)$, where A generates a holomorphic semigroup on H, $u(t)$ is a scalar control, and the control input b is possibly u...
详细信息
This article studies a class of control systems in a Hilbert space H given $\dot x(t) = Ax(t) + bu(t)$, where A generates a holomorphic semigroup on H, $u(t)$ is a scalar control, and the control input b is possibly unbounded. Many systems with boundary or point control can be represented in this form. The author considers the question of what eigenvalues $\{ \alpha _k \} _{k \in I} $, the closed-loop system can have when $u(t)$ is a feedback control. Shun-Hua Sun’s condition on $\{ \alpha _k \} _{k \in I} $ [SIAM J. Control Optim., 19 (1981), pp. 730–743] is generalized to the case where b is unbounded but satisfies an admissibility criterion; this condition is generalized further when unbounded feedback elements are allowed. These results are applied to a structurally damped elastic beam with a single point actuator. Similar techniques also prove a spectral assignability result for a damped elastic beam with a moment control force at one end, even though the associated input element is not admissible in the appropriate sense.
In this paper, a certain class of distributed parameter systems is considered. We propose a three-step design method for finding finite dimensional observer-based boundary feedback controllers. The first step is calle...
详细信息
In this paper, a certain class of distributed parameter systems is considered. We propose a three-step design method for finding finite dimensional observer-based boundary feedback controllers. The first step is called the boundary-equation normalization, which transforms the boundary and system equations into a normal form. The second step is called the boundary input transformation, which integrates the boundary input equation into the system equation, and forms a type of distributedparameter system called the general boundary input system. The final step is to design the desired finite dimensional controller, based on the general boundary input system model. The design procedure utilizes the finite dimensional linear quadratic optimal control theory, so well-developed computation tools can be applied. Though the acquired controllers are only sub-optimal for the distributed parameter systems, an estimation of the performance degradation from that of the ideal case is derived for comparison purpose.
In this paper, we present a technical overview of the design and analysis of active boundary controllers for distributedparameter (vibration and noise) systems. This presentation is done in the context of Lyapunov co...
详细信息
In this paper, we present a technical overview of the design and analysis of active boundary controllers for distributedparameter (vibration and noise) systems. This presentation is done in the context of Lyapunov control design and stability analysis tools, which are commonly applied to non-linear finite dimensional systems. The main purpose of this presentation is to shed more light on this powerful control design philosophy for distributed parameter systems. The Lyapunov-based boundary control framework will be illustrated through three example systems-the transverse vibrating string, the acoustic noise duct, and the flexible rotor-each with an increasing level of complexity. To complement the theoretical content of the paper, the experimental implementation of the flexible rotor controller is also presented. (C) 2002 Elsevier Science Ltd.
Observer design for second-order distributed parameter systems in R-2 is addressed. Particularly, second order distributed parameter systems without distributed damping are studied. Based on finite number of measureme...
详细信息
Observer design for second-order distributed parameter systems in R-2 is addressed. Particularly, second order distributed parameter systems without distributed damping are studied. Based on finite number of measurements, exponentially stable observer is designed. The existence, uniqueness and stability of solutions of the observer are based on semigroup theory.
A model reference adaptive control law is defined for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand tri...
详细信息
A model reference adaptive control law is defined for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand triple of reflexive Banach and Hilbert spaces. The resulting nonlinear closed-loop system is shown to be well posed. The tracking error is shown to converge to zero, and regularity results for the control input and the output are established. With an additional richness, or persistence of excitation assumption, the parameter error is shown to converge to zero as well. A finite-dimensional approximation theory is developed. Examples involving both first- and second-order, parabolic and hyperbolic, and linear and nonlinear systems are discussed, and numerical simulation results are presented.
This study addresses the problems of finite-time (FT) stability and stabilisation for distributed parameter systems. First, the authors extend the concepts of FT stability and FT stabilisation to the distributed param...
详细信息
This study addresses the problems of finite-time (FT) stability and stabilisation for distributed parameter systems. First, the authors extend the concepts of FT stability and FT stabilisation to the distributed parameter systems. Then, sufficient conditions of the L-2-FT stability and W-1,W-2-FT stability for the distributed parameter systems are established in terms of linear matrix inequalities. Based on these sufficient conditions, the authors design the state feedback controllers which guarantee the closed-loop distributed parameter systems to be L-2-FT stable and W-1,W-2-FT stable, respectively. Finally, numerical examples are given to illustrate the proposed results.
A class of time-varying delay distributed parameter systems with input saturation is investigated in this paper. The periodic intermittent control method is adopted to make the system stable in finite time, improve th...
详细信息
A class of time-varying delay distributed parameter systems with input saturation is investigated in this paper. The periodic intermittent control method is adopted to make the system stable in finite time, improve the control performance of the system, and save on control cost. A periodic intermittent controller combined saturated input is designed to ensure the stability of the proposed system in finite time. Lyapunov-Krasoviskii stability theory and matrix inequality techniques are used to analyze the finite-time stability of the system, and sufficient conditions for the system to be stable in finite time are obtained. Finally, the correctness of the theorems is verified by simulation experiments.
In this tutorial article the rich variety of transfer functions for systems described by partial-differential equations is illustrated by means of several examples under various boundary conditions. An important featu...
详细信息
In this tutorial article the rich variety of transfer functions for systems described by partial-differential equations is illustrated by means of several examples under various boundary conditions. An important feature is the strong influence of the choice of boundary conditions on the dynamics and on system theoretic properties such as pole and zero locations, properness, relative degree and minimum phase. It is sometimes possible to design a controller using the irrational transfer function, and several such techniques are outlined. More often, the irrational transfer function is approximated by a rational one for the purpose of controller design. Various approximation techniques and their underlying theory are briefly discussed. (C) 2009 Elsevier Ltd. All rights reserved.
A framework is presented to facilitate the formulation of control strategies for nonlinear DPS. The key contribution is the generalized quantitative expression of the stability condition for any nonlinear DPS. The met...
详细信息
A framework is presented to facilitate the formulation of control strategies for nonlinear DPS. The key contribution is the generalized quantitative expression of the stability condition for any nonlinear DPS. The methodology derives from the use of symmetry groups that determine the group-invariant solutions of a differential system. An invariance condition in the prolonged space of the differential system provides the framework for the distributed control law. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations (PDEs). Both distrib...
详细信息
This paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations (PDEs). Both distributed measurement form and collocated boundary measurement form are considered. A Takagi-Sugeno (T-S) fuzzy PDE model is first applied to accurately represent the semilinear parabolic PDE system. Based on the T-S fuzzy PDE model, two types of fuzzy boundary controllers, which are easily implemented since only boundary actuators are used, are proposed to ensure the exponential stability of the resulting closed-loop system. Sufficient conditions of exponential stabilization are established by employing the Lyapunov direct method and the vector-valued Wirtinger's inequality and presented in terms of standard linear matrix inequalities. Finally, the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples.
暂无评论