Dynamic modeling and nonlinear boundary control of hybrid Euler–Bernoulli beam system with a tip mass

Mohammadpour

2018

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This paper investigates the control of a single-link flexible robot manipulator with a tip payload appointed to rotate about 2 perpendicular axes in space. The control objective is to regulate the rigid body rotation of the manipulator with guaranteeing the stability of its vibration in the presence of exogenous disturbances. To achieve this, a Lyapunov-based control design procedure is used and accomplished in some steps. First, the partial differential equation (PDE) dynamic model governing the rigid-flexible hybrid motion of the arm is derived by applying Hamilton's principle. Next, based on the developed PDE model, an adaptive robust boundary control is established using the Lyapunov redesign approach. To this end, an adaptation mechanism is proposed so that the robust boundary control gains are dynamically updated online and there is no need for prior knowledge of disturbance upper bounds. The actuators and sensors are fully implemented at the arm boundary without using distributed actuators or sensors. Furthermore, in order to avoid control errors resulting from the spillover, control design is directly based on infinite-dimensional PDE model without resorting to model truncation. Simulation results illustrate the efficacy of the considered method. KEYWORDS adaptive upper bound, boundary control, distributed parameter systems, flexible arm, robust control Int J Adapt Control Signal Process. 2018;32:891-907.wileyonlinelibrary.com/journal/acs

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic modeling and adaptive robust boundary control of a flexible robotic arm with 2‐dimensional rigid body rotation

Mohammadpour

2018

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“…Therefore, this paper considers the velocity and slope of the beam at the controlled boundary as the outputs of the control system and uses them as the measured signals. From a practical point of view, this is essentially an advantage because the existing boundary control schemes [1,2,[4][5][6][28][29][30][31], proposed for different beam-type structures, mostly entail the additional feedback from shear force. The main contributions of the article can be summarized in three parts as follows.…”

Section: Introductionmentioning

confidence: 99%

“…Krstic et al solved different boundary control problems in connection with the beam vibration using the backstepping approach [25][26][27]. Tavasoli [28] proposed nonlinear boundary control of a hybrid Euler-Bernoulli beam with coupled rigid-flexible motion in the plane.The aforementioned works neglect the effect of external disturbances, which is a significant factor that degrades the system performance [5]. Therefore, Ge et al investigated vibration control of the Euler-Bernoulli beam under unknown spatiotemporally varying disturbance [29].…”

mentioning

confidence: 99%

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Adaptive robust boundary control of coupled bending‐torsional vibration of beams with only one axis of symmetry

Enjilela

2016

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In control design for vibration of beams in literature, the beam section is considered to have two axes of symmetry so that the bending and torsional vibrations are uncoupled; thus, the bending vibration is controlled independently without twisting the beam. However, if the cross section of a beam has only one axis of symmetry, the bending and torsional vibrations become coupled and the beam will undergo twisting in addition to bending. This paper addresses Lyapunov-based boundary control of coupled bending-torsional vibration of beams with only one axis of symmetry. The control strategy is based on applying a transverse force and a torque at the free end of the beam. The control design is directly based on the system partial differential equations (PDEs) so that spillover instabilities that are a result of model truncation are avoided. Three cases are investigated. Firstly, it is shown that when exogenous disturbances do not affect the beam, a linear boundary control law can exponentially stabilize the coupled bending-torsional vibration. Secondly, a nonlinear robust boundary control is established that exponentially stabilizes the beam in the presence of boundary and spatially distributed disturbances. Thirdly, to rule out the need for prior knowledge of disturbances upper-bound, the proposed robust control is redesigned to achieve an adaptive robust control that stabilizes the beam in the presence of disturbances with unknown upper-bound. The efficacy of the proposed controls is illustrated by simulation results.A. TAVASOLI AND V. ENJILELA Figure 1. Channel section as a common example of beams with only one axis of symmetry.The need for high speed and low energy consumption has increased the application of lightweight flexible beams in various mechanical systems, such as marine risers [1,2], rotors [3], wind turbine towers [4], flexible robots [5], and space mechanisms [6]. Because beams are made as slender as possible to avoid the penalties attached to excessive weight and cost, they lack sufficient rigidity and damping properties to effectively operate under applied loads [7]. Therefore, active control techniques [8] have been employed to suppress vibration of beam structures. Flexible beams are continuous mechanical systems [9, 10] with infinite degrees of freedom and are modeled through PDEs. This makes both practical and theoretical challenges in controlling beams. Because the control synthesis techniques for systems represented by PDEs have not been developed, the conventional approaches for controlling beams mainly rely on discretizing the system PDEs into some ordinary differential equations (ODEs) [11]. Although the mathematical complexities in dealing with PDEs are avoided by discretizing the model, a control system designed based on model truncation can incur spillover instabilities [12,13] because of excitation of residual modes. In addition, a finite-state approximation to a PDE may wrongly render fundamental system theoretic properties like controllability and observability into functions of the ...

Robust boundary stabilization of a vibrating rectangular plate using disturbance adaptation

2016

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This paper considers robust boundary control with disturbance adaptation to stabilize the vibration of a rectangular plate under disturbances with unknown upper-bounds. Disturbances are considered to be distributed both over the plate interior domain and along the boundary (in-domain and boundary distributed disturbances). Applying Hamilton's principle, the dynamics of the plate is represented in the form of a fourth-order partial differential equation subject to static and dynamic boundary conditions. The proposed model considers the membrane effect of axial force and the effect of actuator mass dynamics on the plate vibration. A robust boundary control is established that stabilizes the plate in presence of both in-domain and boundary disturbances. A rigorous Lyapunov stability analysis shows that the vibration of the plate is uniformly ultimately bounded and converges to the vicinity of zero by proper selection of control gains. For the vanishing in-domain disturbances, it is seen that exponential stability is achieved by the proposed control. Next, a disturbance adaptation law is introduced to stabilize the plate vibration in response to disturbances with unknown bounds, and the stability of the robust boundary control with disturbance adaptation is studied using Lyapunov. Simulation results verify the efficiency of the suggested control.