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Baozhu Guo - One of the best experts on this subject based on the ideXlab platform.

  • boundary output tracking for an euler bernoulli Beam Equation with unmatched perturbations from a known exosystem
    Automatica, 2019
    Co-Authors: Feng Fei Jin, Baozhu Guo
    Abstract:

    Abstract In this paper, we consider boundary output regulation for an Euler–Bernoulli Beam Equation which can describe typically the flexible arm of robots. The reference signal and disturbance are generated by a finite-dimensional exosystem. The measurements are angular and angular velocity of the right end where the control is imposed. However, the performance output is on the left end which is non-collocated with control, a difficult case in practice where the control takes time to perform its force from the right end to the left. The objective is to design an output feedback controller to regulate the displacement of the left end to track the reference signal. We first design a state feedback regulator to make the performance output track the reference signal exponentially. An observer is then constructed to recover the state, with which, an output feedback regulator is designed by replacing state feedback with its estimation. The closed-loop system is shown to admit a unique bounded solution and the tracking error converges to zero exponentially. Some numerical simulations are presented to illustrate the effectiveness of the proposed output feedback regulator.

  • riesz basis generation comparison method
    2019
    Co-Authors: Baozhu Guo, Junmin Wang
    Abstract:

    This chapter provides a panoramic view on the comparison method. It discusses systematically how the comparison method is used to derive the Riesz basis generation for systems described by partial differential Equations. A basic assumption for comparison method to be working is that the feedback can be considered as a perturbation of the system itself, that is, the order of the feedback is lower than the order of original system, which is clear from the spectrum or transfer function point of view. It starts with a constant Beam Equation with collocated boundary feedback control, and then the Beam Equation with variable coefficients. A Beam Equation with span pointwise control is presented to show its Riesz basis and exponential stability. A one-dimensional thermoelastic system is fully discussed. The Riesz basis property has been developed for these systems, which implies particularly that the dynamics of the system is completely determined by vibration frequencies. Mathematically, all the operators are of compact resolvent. In the last section, however, an example of the Boltzmann integral model is presented where the resolvent is not compact and the continuous spectrum exists. Two different types of Boltzmann integrals for the dynamics of vibrating systems are discussed and the Riesz basis property has been developed.

  • uniform convergence for eigenvalues of euler bernoulli Beam Equation with structural damping via finite difference discretization
    Chinese Control Conference, 2018
    Co-Authors: Baozhu Guo, Hanjing Ren
    Abstract:

    In the last two decades, there is a big discovery about the numerical realization of feedback control of systems described by partial differential Equations (PDEs) that for an exponentially stable hyperbolic PDEs, after semi-discretization on the spatial variable, the semi-discrete system is not uniformly decaying with respect to the step size. This prevents obviously the application of feedback control of PDEs in engineering, in particular, in computer digitalization. It is also found that with some vanishing viscosity term in the discrete scheme, the decay rate of semi-discrete scheme becomes uniform in step size. In this paper, we try to understand this problem from mathematical point of view. We first consider an Euler-Bernoulli Beam Equation without the viscosity term. It is found that the semi -discrete eigenvalues are not convergent to the continuous counterparts. However, when the continuous system has structural damping term, then the semi-discrete eigenvalues are uniformly convergent. The reason behind we believe is that the solution of the system without structural damping is not smooth enough, whereas for the system with structural damping, the solution is analytic. Many engineering control researchers are wondering about the smoothness of the solution of PDEs. This paper severs as an example for importance of smoothness of PDEs in control design.

  • lyapunov approach to output feedback stabilization for the euler bernoulli Beam Equation with boundary input disturbance
    Automatica, 2015
    Co-Authors: Feng Fei Jin, Baozhu Guo
    Abstract:

    We propose a boundary output feedback control law for a one-dimensional Euler-Bernoulli Beam Equation with general external disturbance entering the control end. A Galerkin approximation scheme is constructed to show the existence of solution to the closed-loop system. The exponential stability of the closed-loop system is obtained by the Lyapunov functional method. Numerical simulations are presented for illustration.

  • lyapunov approach to the boundary stabilization of a Beam Equation with boundary disturbance
    Chinese Control Conference, 2013
    Co-Authors: Baozhu Guo, Wen Kang
    Abstract:

    In this paper, we are concerned with the boundary output feedback stabilization of an Euler-Bernoulli Beam Equation with free boundary at one end and control and disturbance at the other end. A variable structure output feedback stabilizing controller is designed by the Lyapunov function approach. It is shown that the resulting closed-loop system without disturbance is associated with a nonlinear semigroup and is asymptotically stable. In addition, we show that this controller is robust to the external disturbance in the sense that the vibrating energy of the closed-loop system is also convergent to zero as time goes to infinity in the presence of finite sum of harmonic disturbance at the control end.

Antonina Pirrotta - One of the best experts on this subject based on the ideXlab platform.

  • implicit analytic solutions for a nonlinear fractional partial differential Beam Equation
    Communications in Nonlinear Science and Numerical Simulation, 2020
    Co-Authors: K B Liaskos, Athanasios A Pantelous, Ioannis A Kougioumtzoglou, Antonios T Meimaris, Antonina Pirrotta
    Abstract:

    Abstract Analytic solutions in implicit form are derived for a nonlinear partial differential Equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli Beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential Equation in a Hilbert space. Next, by employing the cosine and sine families of operators, a variation of parameters representation of the solution map is introduced. Due to the presence of a nonlinear term, a local fixed point theorem is employed to prove the local existence and uniqueness of the solution. Relying on the regularity properties of cosine and sine families, taking into account the form of the nonlinear term, and considering the properties of the fractional derivative, the solution map of the abstract problem is cast into a derivative-free analytic solution in implicit-form for the initial boundary value problem. Results corresponding to the limiting purely elastic and purely viscous cases are also provided. The herein developed technique and derived implicit form solutions can be construed as generalizations of available results in the literature to account for fractional derivative elements. This is of significant importance given the vast utilization of fractional calculus modeling in modern engineering mechanics, and in viscoelastic material behavior in particular.

Feng Fei Jin - One of the best experts on this subject based on the ideXlab platform.

  • boundary output tracking for an euler bernoulli Beam Equation with unmatched perturbations from a known exosystem
    Automatica, 2019
    Co-Authors: Feng Fei Jin, Baozhu Guo
    Abstract:

    Abstract In this paper, we consider boundary output regulation for an Euler–Bernoulli Beam Equation which can describe typically the flexible arm of robots. The reference signal and disturbance are generated by a finite-dimensional exosystem. The measurements are angular and angular velocity of the right end where the control is imposed. However, the performance output is on the left end which is non-collocated with control, a difficult case in practice where the control takes time to perform its force from the right end to the left. The objective is to design an output feedback controller to regulate the displacement of the left end to track the reference signal. We first design a state feedback regulator to make the performance output track the reference signal exponentially. An observer is then constructed to recover the state, with which, an output feedback regulator is designed by replacing state feedback with its estimation. The closed-loop system is shown to admit a unique bounded solution and the tracking error converges to zero exponentially. Some numerical simulations are presented to illustrate the effectiveness of the proposed output feedback regulator.

  • lyapunov approach to output feedback stabilization for the euler bernoulli Beam Equation with boundary input disturbance
    Automatica, 2015
    Co-Authors: Feng Fei Jin, Baozhu Guo
    Abstract:

    We propose a boundary output feedback control law for a one-dimensional Euler-Bernoulli Beam Equation with general external disturbance entering the control end. A Galerkin approximation scheme is constructed to show the existence of solution to the closed-loop system. The exponential stability of the closed-loop system is obtained by the Lyapunov functional method. Numerical simulations are presented for illustration.

  • the active disturbance rejection and sliding mode control approach to the stabilization of the euler bernoulli Beam Equation with boundary input disturbance
    Automatica, 2013
    Co-Authors: Baozhu Guo, Feng Fei Jin
    Abstract:

    In this paper, we are concerned with the boundary feedback stabilization of a one-dimensional Euler-Bernoulli Beam Equation with the external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) are adopted in investigation. By the ADRC approach, the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed-loop. It is shown that the external disturbance can be attenuated in the sense that the resulting closed-loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity. In the second part, we use the SMC to reject the disturbance by removing the condition in ADRC that the derivative of the disturbance is supposed to be bounded. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the ''reaching condition'' is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. The numerical simulations validate the effectiveness of both methods.

  • backstepping approach to the arbitrary decay rate for euler bernoulli Beam under boundary feedback
    International Journal of Control, 2010
    Co-Authors: Baozhu Guo, Feng Fei Jin
    Abstract:

    In this article, we are concerned with the boundary stabilisation of the Euler–Bernoulli Beam Equation for which all eigenvalues of the (control) free system are located on the imaginary axis of the complex plane. The fourth-order system in spacial variable is transformed into a coupled heat-like system. This enables us to make a natural backstepping transformation in vector form to transform the system into a target system which has arbitrary decay rate. The state feedback is thus designed. It is shown that the original closed-loop system is exponentially stable with the given arbitrary decay rate.

Antonios T Meimaris - One of the best experts on this subject based on the ideXlab platform.

  • implicit analytic solutions for a nonlinear fractional partial differential Beam Equation
    Communications in Nonlinear Science and Numerical Simulation, 2020
    Co-Authors: K B Liaskos, Athanasios A Pantelous, Ioannis A Kougioumtzoglou, Antonios T Meimaris, Antonina Pirrotta
    Abstract:

    Abstract Analytic solutions in implicit form are derived for a nonlinear partial differential Equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli Beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential Equation in a Hilbert space. Next, by employing the cosine and sine families of operators, a variation of parameters representation of the solution map is introduced. Due to the presence of a nonlinear term, a local fixed point theorem is employed to prove the local existence and uniqueness of the solution. Relying on the regularity properties of cosine and sine families, taking into account the form of the nonlinear term, and considering the properties of the fractional derivative, the solution map of the abstract problem is cast into a derivative-free analytic solution in implicit-form for the initial boundary value problem. Results corresponding to the limiting purely elastic and purely viscous cases are also provided. The herein developed technique and derived implicit form solutions can be construed as generalizations of available results in the literature to account for fractional derivative elements. This is of significant importance given the vast utilization of fractional calculus modeling in modern engineering mechanics, and in viscoelastic material behavior in particular.

  • implicit analytic solutions for the linear stochastic partial differential Beam Equation with fractional derivative terms
    Systems & Control Letters, 2018
    Co-Authors: K B Liaskos, Athanasios A Pantelous, Ioannis A Kougioumtzoglou, Antonios T Meimaris
    Abstract:

    Abstract Analytic solutions in implicit-form are derived for a linear stochastic partial differential Equation (SPDE) with fractional derivative terms, which can model the dynamics of a stochastically excited Euler–Bernoulli Beam resting on a viscoelastic foundation. Specifically, the original initial–boundary value problem of the SPDE is reduced to an initial value problem of a second-order stochastic differential Equation in an appropriate Hilbert space. Next, addressing the abstract Cauchy problem, employing cosine and sine families of operators, and representing the fractional derivative term in a suitable form, a variation of parameters treatment yields the solution in implicit-form. The limiting purely viscous and purely elastic modeling cases are also studied within the same framework. The herein proposed technique and derived implicit-form solutions can be construed as an extension of available results in the literature to account for fractional derivative terms. This generalization is of significant importance given the vast utilization of fractional calculus modeling in engineering mechanics, and in viscoelastic material behavior in particular. In this regard, the herein proposed analytical treatment also supplements existing more numerically oriented solution schemes available in the engineering mechanics literature.

Leonardo Tolomeo - One of the best experts on this subject based on the ideXlab platform.

  • unique ergodicity for a class of stochastic hyperbolic Equations with additive space time white noise
    Communications in Mathematical Physics, 2020
    Co-Authors: Leonardo Tolomeo
    Abstract:

    In this paper, we consider a certain class of second order nonlinear PDEs with damping and space-time white noise forcing, posed on the d-dimensional torus. This class includes the wave Equation for $$d=1$$ and the Beam Equation for $$d\le 3$$. We show that the Gibbs measure is the unique invariant measure for this system. Since the flow does not satisfy the strong Feller property, we introduce a new technique for showing unique ergodicity. This approach may be also useful in situations in which finite-time blowup is possible.

  • unique ergodicity for stochastic hyperbolic Equations with additive space time white noise
    arXiv: Analysis of PDEs, 2018
    Co-Authors: Leonardo Tolomeo
    Abstract:

    In this paper, we consider a certain class of second order nonlinear PDEs with damping and space-time white noise forcing, posed on the $d$-dimensional torus. This class includes the wave Equation for $d=1$ and the Beam Equation for $d\le 3$. We show that the Gibbs measure of the Equation without forcing and damping is the unique invariant measure for the flow of this system. Since the flow does not satisfy the Strong Feller property, we introduce a new technique for showing unique ergodicity. This approach may be also useful in situations in which finite-time blowup is possible.

  • unique ergodicity for a class of stochastic hyperbolic Equations with additive space time white noise
    arXiv: Analysis of PDEs, 2018
    Co-Authors: Leonardo Tolomeo
    Abstract:

    In this paper, we consider a certain class of second order nonlinear PDEs with damping and space-time white noise forcing, posed on the $d$-dimensional torus. This class includes the wave Equation for $d=1$ and the Beam Equation for $d\le 3$. We show that the Gibbs measure of the Equation without forcing and damping is the unique invariant measure for the flow of this system. Since the flow does not satisfy the Strong Feller property, we introduce a new technique for showing unique ergodicity. This approach may be also useful in situations in which finite-time blowup is possible.