Optimum control of a flexible single link manipulator with Artificial Bee Colony Algorithm

This paper presents a stable control for a single link flexible manipulator. The flexible manipulator is considered as Euler–Bernoulli beam, and its dynamic model is developed based on assumed mode method. Position and vibration control are realised with a single controller as motor torque. The controller has three parameters that must be selected. In this paper, the main motivation is to find the suitable parameter values to generate optimum torque values in every sampling time. In order to achieve this goal, Artificial Bee Colony Algorithm is performed, and the controller parameters are optimised simultaneously in every sampling period. Simulations verify that the manipulator achieves the position control objective, and the vibration is suppressed simultaneously even with different payloads with the proposed optimisation method.

Passive Walking Biped Robot Model with Flexible Viscoelastic Legs

To simulate the complex human walking motion accurately, a suitable biped model has to be proposed that can significantly translate the compliance of biological structures. In this way, the simplest passive walking model is often used as a standard benchmark for making the bipedal locomotion so natural and energy-efficient. This work is devoted to a presentation of the application of internal damping mechanism to the mathematical description of the simplest passive walking model with flexible legs. This feature can be taken into account by using the viscoelastic legs, which are constituted by the Kelvin–Voigt rheological model. Then, the update of the impulsive hybrid nonlinear dynamics of the simplest passive walker is obtained based on the Euler–Bernoulli’s beam theory and using a combination of Lagrange mechanics and the assumed mode method, along with the precise boundary conditions. The main goal of this study is to develop a numerical procedure based on the new definition of the step function for enforcing the biped start walking from stable condition and walking continuously. The study of the influence of various system parameters is carried out through bifurcation diagrams, highlighting the region of stable period-one gait cycles. Numerical simulations clearly prove that the overall effect of viscoelastic leg on the passive walking is efficient enough from the viewpoint of stability and energy dissipation.

Component-based Modeling and Simulation of Nonlinear Drill-string Dynamics

In this paper, we present a dynamic model for a generic drill-string. The model is developed with the intention for component-based simulation with coupling to external subsystems. The performance of the drill-string is vital in terms of efficient wellbore excavation for increased hydrocarbon extraction. Drill-string vibrations limit the performance of rotary drilling; the phenomenon is well-known and still a subject of interest in academia and in industry. In this work, we have developed a nonlinear flexible drill-string model based on Lagrangian dynamics, to simulate the performance during vibrations. The model incorporates dynamics governed by lateral bending, longitudinal motion and torsional deformation. The elastic property of the string is modeled by the assumed mode method, representing the elastic deformation, with a finite set of modal coordinates. By developing a bond graph model from the equations of motion, we can ensure correct causality of the model towards interacting subsystems. The model is analyzed through extensive simulations in case studies, comparing the qualitative behavior of the model with state-of-the art models. The flexible drill-string model presented in this paper can aid in developing system simulation case studies and parameter identification for offshore drilling operations.

PZT Actuators’ Effect on Vibration Control of the PRRRP 2-DOF Flexible Parallel Manipulator

Thanks to their advantages over rigid ones, interest for lightweight parallel manipulator was increased. Besides, structural flexibility effects at high operational speeds are more significant. Thus, developing an appropriate model for the assessment of the dynamic properties of flexible mechanisms and linkages to gain effective vibration control will raise high demand. Therefore, this paper represents the dynamic and kinematic modeling using the assumed mode method and first-type Lagrange equations of the 2-DOF planar parallel manipulator with two flexible links. To truly predict vibrations of the manipulator without any major simplifying assumptions, nonlinear dynamic modeling, which thoroughly attempts to represent the flexible behavior of the links, is considered. As a result, an active damping approach is being studied with PZT actuators. The results show that this approach is effective in damping the vibrations of the links that give accurate trajectory control.

Reduced-Order Modeling and the Physics Governing Flapping Wing Fluid-Structure Interaction

Flapping, flexible insect wings deform during flight from aerodynamic and inertial forces. This deformation is believed to enhance aerodynamic and energetic performance. However, the predictive models used to describe flapping wing fluid-structure interaction (FSI) often rely on high fidelity computational solvers such as computational fluid dynamics (CFD) and finite element analysis (FEA). Such models require lengthy solution times and may obscure the physical insights available to analytical models. In this work, we develop a reduced order model (ROM) of a wing experiencing single-degree-of-freedom flapping. The ROM is based on deformable blade element theory and the assumed mode method. We compare the ROM to a high-fidelity CFD/FEA model and a simple experiment comprised of a mechanical flapper actuating a paper wing. Across a range of flapping-to-natural frequency ratios relevant to flying insects, the ROM predicts wingtip deflection five orders of magnitude faster than the CFD/FEA model. Both models are resolved to predict wingtip deflection within 30% of experimentally measured values. The ROM is then used to identify how the physical forces acting on the wing scale relative to one another. We show that, in addition to inertial and aerodynamic forces, added mass and aerodynamic damping influence wing deformation nontrivially.

Electrostatically actuated double walled piezoelectric nanoshell subjected to nonlinear van der Waals effect: nonclassical vibrations and stability analysis

In this paper, nonlinear vibration and frequency response analysis of double walled piezoelectric nanoshell (DWPENS) is investigated using nonclassical approach of the Gurtin–Murdoch surface/interface (GMSIT) theory. The piezoelectric nanoshell is simultaneously subjected to visco-Pasternak medium, the nonlinear van der Waals and electrostatic forces. Hamilton’s principles, the assumed mode method combined with Lagrange–Euler’s are used for the governing equations and boundary conditions. Complex averaging method combined with Arc-length continuation is used to achieve the nonlinear frequency response and stability analysis of the DWPENS. It is found that the electrostatic and piezoelectric voltages, the length to radius ratio, the nanoshell gap width, van der Waals (vdW) coefficients and other parameters can effectively change the flexural rigidity of the system which in turn affects the nonlinear frequency response. And also, increasing or decreasing of some parameters lead to increasing or decreasing the resonance amplitude, resonant frequency, the system’s instability, nonlinear behavior, and bandwidth.

Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and pole placement strategy to suppress the rotation angle fluctuations. The RBF neural network is used to identify uncertain items caused by the manipulator’s flexibility and the time-varying characteristics of dynamic parameters. Besides, the pole placement strategy is used to optimize the PD (Proportional Differential) controller’s parameters to improve the response speed and stability. Firstly, a dynamic model of flexible manipulators considering gravity is established based on the assumed mode method and Lagrange’s principle. Then, the system’s control characteristics are analyzed, and the pole placement strategy optimizes the parameters of the PD controllers. Next, the control method based on the RBF neural network is proposed, and the Lyapunov stability theory demonstrates stability. Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy.

Development of Polynomial Mode Shape Functions for Continuous Shafts with Different End Conditions

Common methods used to determine the solutions for vibration response of continuous systems are assumed mode method, Rayleigh-Ritz method, Galerkin Method, finite element method, etc. Each of these methods requires the shape functions which satisfy the boundary conditions. Shape functions derived in most of the classical textbooks are simple trigonometric functions for some end conditions but are very complex transcendental functions for many end conditions. It is very difficult to determine the vibration response of a continuous system analytically by using such transcendental shape functions. Hence this paper presents a method to develop polynomial shape functions required to solve the vibration of continuous shafts with different end conditions. The natural frequencies obtained from the developed polynomial shape functions are compared to those obtained from the classical transcendental shape functions and found very close for the first three modes.

A composite controller for manipulator with flexible joint and link under uncertainties and disturbances

In this article, a composite controller is proposed for the manipulator with the flexible joint and link under uncertainties and time-varying disturbances. The dynamic of the system is developed by the Euler–Lagrange and assumed mode method, which is a nonlinear, strong coupling, and underacted system. Therefore, based on the singular perturbation theory, the dynamic is decomposed into a slow and fast subsystem. For the slow dynamic, a novel adaptive-gain super-twisting sliding mode controller is designed to guarantee joint tracking under the uncertainties and disturbances. For the fast dynamics, adaptive dynamic programming is used to deal with the uncertainty. The simulation result shows that the proposed composite controller can effectively track the trajectory and suppress the vibration simultaneously.