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.

Optimal Vibration Feedback Control of an Euler-Bernoulli Beam: Toward Realization of the Active Sink Method

1999 ◽  
Vol 121 (2) ◽  
pp. 174-182 ◽  
Author(s):  
N. Tanaka ◽  
Y. Kikushima
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Control Point ◽  
Control Law ◽  
Bernoulli Beam ◽  
Control Laws ◽  
Reflected Waves ◽  
Feedback Control Systems ◽  
Active Wave ◽  
Euler Bernoulli Beam

This paper discusses the optimal vibration feedback control of an Euler-Bernoulli beam from a viewpoint of active wave control making all structural modes inactive (more than suppressed). Using a transfer matrix method, the paper derives two kinds of optimal control laws termed “active sink” which inactivates all structural modes; one obtained by eliminating reflected waves and the other by transmitted waves at a control point. Moreover, the characteristic equation of the active sink system is derived, the fundamental properties being investigated. Towards the goal of implementing the optimal control law that is likely to be non-causal, a “classical” velocity feedback control law (Balas, 1979) widely used in a vibration control engineering is applied, revealing a substantial shortcoming. Introduction of a “classical” displacement feedback to the velocity is found to realize the optimal control law in a restricted frequency range. Finally, two kinds of stability verification for closed feedback control systems are presented for distributed parameter structures.

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.

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.

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