Robust Boundary Control for an Euler Bernoulli Beam Subject to Unknown Harmonic Disturbances With a Focus on Resonance

2017 ◽  
Author(s):  
Dimitri Karagiannis ◽  
Verica Radisavljevic-Gajic
Keyword(s):  
Steady State ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Open Loop ◽  
Bernoulli Beam ◽  
Harmonic Vibrations ◽  
The Face ◽  
State Position ◽  
Backstepping Controller ◽  
Euler Bernoulli Beam

In this paper, a sliding mode backstepping controller for a pinned-pinned Euler-Bernoulli beam is briefly reviewed and its efficacy in the presence of unknown bounded harmonic disturbances at arbitrary frequencies is analyzed. A brief discussion of the open-loop unstable response to harmonic excitations at resonant frequencies is provided. Motivated by this, particular attention is given to excitations at the natural frequencies of the system. It is shown that in the face of such resonant disturbances, the sliding mode backstepping controller is able to eliminate the vibrations in the beam system where backstepping control alone cannot. Indeed it is shown that if the disturbances are not accounted for, the closed loop system exhibits large (relative to the initial conditions) steady state harmonic vibrations. When the unknown resonant harmonic disturbances are accounted for via the sliding mode backstepping technique, the steady state position is constant and does not exhibit any vibrations, and furthermore it reaches this steady state exponentially at an arbitrarily selected rate.

Sliding Mode Control for a Membrane Mirror Strip Actuated Using Multiple Smart Actuators

2007 ◽  
Author(s):  
Jamil M. Renno ◽  
C. Konda Reddy ◽  
Daniel J. Inman ◽  
Eric J. Ruggiero
Keyword(s):  
Sliding Mode ◽  
Fiber Composite ◽  
Tensile Load ◽  
Control Law ◽  
Bernoulli Beam ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Euler Bernoulli Beam ◽  
Mode Technique ◽  
Membrane Strip

The sliding mode technique is used to control the deformation of a membrane mirror strip. A membrane mirror strip is augmented with two macro fiber composite (MFC) bimorphs. The first bimorph is actuated in bending whereas the second is actuated in tension. Membrane strips are usually tensioned uniformly. However, the presence of the tension bimorphs induces a local tension at its location. The membrane strip is modeled as an Euler-Bernoulli beam under tensile load, whereas the MFCs are modeled as monolithic piezoceramics. To cast the system into a finite dimensional state space form, the finite elements method (FEM) is used. The control action is switched when the membrane strip approaches its original undeformed shape. Simulation results demonstrate the effectiveness of the proposed control law.

scholarly journals Modeling of vibration for functionally graded beams

2016 ◽  
Vol 14 (1) ◽  
pp. 661-672 ◽  
Author(s):  
Gülsemay Yiğit ◽  
Ali Şahin ◽  
Mustafa Bayram
Keyword(s):  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Fourier Series Expansion ◽  
Bernoulli Beam ◽  
Adomian Decomposition ◽  
Graded Material ◽  
Euler Bernoulli Beam

AbstractIn this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.

Dynamics of Eccentric Shafts Under Linearly Varying Tension Rotating in a Viscous Medium

1974 ◽  
Vol 96 (4) ◽  
pp. 1285-1290
Author(s):  
V. Prodonoff ◽  
C. D. Michalopoulos
Keyword(s):  
Steady State ◽  
Beam Theory ◽  
Viscous Medium ◽  
Bernoulli Beam ◽  
Axial Coordinate ◽  
Simply Supported ◽  
Deterministic Function ◽  
Mass Eccentricity ◽  
Bending Stresses ◽  
Euler Bernoulli Beam

Using Euler-Bernoulli beam theory an investigation is made of the dynamic behavior of an eccentric vertical circular shaft rotating in viscous medium. The shaft is subjected to linearly-varying tension and has distributed mass and elasticity. The mass eccentricity is assumed to be a deterministic function of the axial coordinate. The solution is obtained by modal analysis. An example is considered wherein the shaft is simply supported at the top and vertically guided at the bottom. Steady-state deflections and bending stresses are computed for a particular eccentricity function over a range of speeds of rotation which includes a resonant frequency.

scholarly journals Optimizing the Parameters of Sliding Mode Controllers for Stepper Motor through Simulink Response Optimizer Application

2021 ◽  
Vol 1 (2) ◽  
pp. 209-225
Author(s):  
Magdi Sadek Mahmoud ◽  
Ali H. AlRamadhan
Keyword(s):  
Steady State ◽  
Sliding Mode ◽  
Open Loop ◽  
Step Response ◽  
Stepper Motor ◽  
Model Parameters ◽  
Response Requirement ◽  
Load Torque ◽  
Sliding Mode Controllers ◽  
Motor Model

This paper will focus on optimizing parameters of sliding mode controllers (SMC) for hybrid stepper motor models simulated in Matlab/Simulink. The main objective is to achieve a smooth transient and robust, steady-state to track reference rotor position when the stepper motor is subjected to load disturbances. Two different structures of SMC controllers will be studied, which are based on the flat system concept that is applicable to the stepper motor model. The hassle to determine controller parameters will be optimized using the Simulink Response Optimizer application.  The performance of the controllers will be evaluated by considering load torque and variation in the model parameters. Although the results showed that an open-loop controller could move the rotor to the desired position, however, the transient response had undesired oscillations before the output settled at the steady state. The response was improved by optimizing SMC controllers’ parameters to meet the desire step response requirement. Despite both SMC methods have successfully tracked the reference, there are some challenges to deal with each method in regard to the state measurements, the number of optimized controllers’ parameters, and the scattering of control inputs.

Sliding mode boundary control for vibration suppression in a pinned-pinned Euler–Bernoulli beam with disturbances

2016 ◽  
Vol 24 (6) ◽  
pp. 1109-1122 ◽  
Author(s):  
Dimitri Karagiannis ◽  
Verica Radisavljevic–Gajic
Keyword(s):  
Sliding Mode Control ◽  
Boundary Conditions ◽  
Sliding Mode ◽  
Bending Moment ◽  
Control Technique ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Mode Control ◽  
Control Functions ◽  
Euler Bernoulli Beam

This work addresses the control of a pinned-pinned beam represented by the fourth order partial differential equation commonly known as the Euler–Bernoulli beam model. The system under consideration has pinned boundary conditions on one end (displacement and bending moment fixed at zero) and controlled boundary conditions on the other end (displacement and bending moment are prescribed by control functions). There are also unknown bounded disturbances included on the controlled boundary. A backstepping control technique which introduces arbitrary damping into the system is discussed, and a method for applying this control in the presence of unknown disturbances is developed using sliding mode control theory. Sliding mode controllers are developed in a way that does not create a chattering effect, which is a common issue with sliding mode control. Simulation results are presented to show how the system dampens out vibrations at an arbitrarily determined rate and how the control functions respond to unmodeled disturbances.

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