Coriolis Force Sliding Mode Control Method for the Rotary Motion of the Central Rigid Body-Flexible Cantilever Beam System in TBM

Beam slab structure is often encountered in a complex tunnel boring machine. Beam slab structure is subject to dynamic load, which is easy to cause fatigue damage and affect its service life. Therefore, it is necessary to control the vibration of this kind of beam slab structure. In this study, the central rigid body-flexible beam model is established for the rotating beam and plate rotating around the y-axis. Based on the Hamilton variational principle, the dynamic equation of the central rigid body-flexible beam system is established, and the dynamic model of the central rigid body-flexible beam system considering the influence of Coriolis force and centrifugal force is given. The vibration control of the central rigid body-flexible beam system is studied. The vibration mode of the rotating Euler Bernoulli beam is determined by using the elastic wave and vibration mode theory. The influence of the rotating motion on the beam vibration is analyzed, and the variable structure control law is designed to suppress the beam vibration. Numerical simulation results show that the control method can effectively suppress the first-order and second-order vibration of the beam and verify the effectiveness of the control strategy.

Effective Placement of a Cantilever Resonator on Flexible Primary Structure for Vibration Control Applications—Part 1: Mathematical Modeling and Analysis

In this Part 1 of a two-part series, the theoretical modeling and optimization are presented. More specifically, the effect of attachment location on the dynamics of a flexible beam system is studied using a theoretical model. Typically, passive/active resonators for vibration suppression of flexible systems are uniaxial and can only affect structure response in the direction of the applied force. The application of piezoelectric bender actuators as active resonators may prove to be advantageous over typical, uniaxial actuators as they can dynamically apply both a localized moment and translational force to the base structure attachment point. Assuming unit impulse force disturbance, potential actuator/sensor performance for the secondary beam can be quantified by looking at fractional root-mean-square (RMS) strain energy in the actuator relative to the total system, and normalized RMS strain energy in the actuator over a frequency band of interest with respect to both disturbance force and actuator beam mount locations. Similarly, by energizing the actuator beam piezoelectric surface with a unit impulse, one can observe RMS base beam tip velocity as a function of actuator beam position. Through such analyses, one can balance both sensor/actuator performance and make conclusions about optimally mounting the actuator beam sensor/actuator. Accounting for both sensing and actuation requirements, the actuator beam should be mounted in the following nondimensionalized region: 0.4≤e≤0.5.

Adaptive Robust Tip Tracking Control for Single-Link Flexible Beam

This paper presents an inversion-based adaptive robust tip tracking control strategy that results in high tracking performance while guaranteeing the robustness for a class of linear motor driven single-link flexible beam. To address the non-minimum phase characteristics of the system, the inversion control is achieved by applying output redefinition technique as well as defining the new output at the tip of the flexible beam. In addition, the adaptive robust control (ARC) is introduced to deal with the parameter uncertainties and model uncertainties and to guarantee transient and steady state tracking performance. Comparative simulations and actual experiments based on linear motor driven flexible beam system are carried out to verify the effectiveness of the proposed control strategy.

Experimental Study of Active Vibration Control of a Flexible Beam System Using Iterative Learning Algorithm

Experimental studies are conducted on active vibration control using self-tuning proportional integral derivative and self-tuning proportional iterative learning algorithm control schemes to suppress vibration on a flexible beam via real-time computer control. An experimental rig is developed to investigate controller performance when a change in the dynamic behavior of the flexible beam system occurs. The performance of the self-tuning control schemes is validated experimentally and compared with that of conventional control schemes through the use of an iterative learning algorithm. Experimental results clearly reveal the effectiveness and robustness of the self-tuning control schemes over conventional control schemes.

Dynamic System Modeling of Flexible Beam System Using Multi-Objective Optimization Differential Evolution Algorithm

This paper proposes an algorithm called multi-objective optimization using differential evolution (MOODE) for providing the optimal mathematical model of flexible beam system. The main reason of developing a flexible beam system is to find an appropriate controller to control the vibration produced by this system. This dynamic system is treated as a black box where the acquired input-output data is used in the modeling processes. Two objective functions are considered for optimization; minimizing the number of term of a model structure and minimizing the mean square error between actual and predicted outputs. Nonlinear auto-regressive with exogenous input (NARX) model is used to represent the mathematical model of the investigated system. To obtain an optimal model for representing the dynamic behavior of flexible beam system, the model validity tests have been applied.