Active buckling control of a beam-column with circular cross-section using piezo-elastic supports and integral LQR control

Abstract

Buckling of slender beam-columns subject to axial compressive loads represents a critical design constraint for light-weight structures. Active buckling control provides a possibility to stabilize slender beam-columns by active lateral forces or bending moments. In this paper, the potential of active buckling control of an axially loaded beam-column with circular solid cross-section by piezo-elastic supports is investigated experimentally. In the piezo-elastic supports, lateral forces of piezoelectric stack actuators are transformed into bending moments acting in arbitrary directions at the beam-column ends. A mathematical model of the axially loaded beam-column is derived to design an integral linear quadratic regulator (LQR) that stabilizes the system. The effectiveness of the stabilization concept is investigated in an experimental test setup and compared with the uncontrolled system. With the proposed active buckling control it is possible to stabilize the beam-column in arbitrary lateral direction for axial loads up to the theoretical critical buckling load of the system.

Energy Shaping Control for Robotic Needle Insertion

“…The stability conditions for the equilibrium * , 0 of the closed-loop system (10), (17) are discussed in the following result.…”

“…The application of a lateral force to the needle near the insertion point was proposed in [15], while an optimized path planning procedure for insertions in multi layered tissues was presented in [16]. Notable results in modelling and control of slender beams with tip load, which are representative of needle insertion, include: an integral LQR control for buckling avoidance of columns with piezoelectric actuators at both ends [17]; Hamiltonian models of a beam actuated at the base employing modal decomposition approaches in [18]; energy shaping control of a flexible beam with tip load in [19]- [21]. In practice however, actuators can often be placed only at the needle base, while linear controllers are only intended for small deflection.…”

Approach to Prove the Efficiency of the Monte Carlo Method Combined With the Elementary Effect Method to Quantify Uncertainty of a Beam Structure With Piezo-Elastic Supports

“…The reference structure for the application of the global sensitivity analysis is a beam with piezo-elastic supports that is used for two different applications of passive and active structural control: active buckling control [11] and passive lateral vibration attenuation [12]. Figure 1 shows the beam structure with piezo-elastic supports and the sectional view of the piezoelastic support.…”

“…To calculate the first lateral resonance frequency f 1 of the beam, a finite element (FE) model was derived in [11]. The free vibration of the beam with piezo-elastic supports in Figure 2 is modeled by the homogeneous FE equation of motion…”

Optimal Placement of Active Bars for Buckling Control in Truss Structures under Bar Failures

“…Equation 1 Alternative to passively increasing the maximum bearable compressive load of an individual bar, active buckling control may be used. Active buckling control provides a possibility to increase the maximum bearable load of slender bars by the integration of piezoelectric stack actuators in compact piezo-elastic supports at the bar ends, Fig.2(a), [11,12]. In this particular setup, the circular bar is made of aluminum alloy EN AW-7075 with a length of 400 mm, diameter of 8 mm and Young's modulus 71.0 kN/mm 2 .…”