Fundamentals of Vibrations

There is a high demand for developing effective controllers to perform fast and accurate operations for either flexible link manipulators (FLMs) or rigid link manipulators (RLMs). Thus, this paper is beneficial for such vast field, and it is also advantageous and indispensable for researchers who are interested in robotics to have sufficient knowledge about various controllers of FLMs and RLMs as the controllers’ concepts are elaborated in detail. The paper concentrates in critically reviewing classical controllers, intelligent controllers, robust controllers, and hybrid controllers for both FLMs and RLMs. The advantages and disadvantages of the aforementioned control methods are summarized in this paper; it also has a detailed comparison for the controllers in terms of the design difficulty, performance, and the suitability for controlling FLMs or RLMs.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/77234C86571FA246BCFD0B8331BE37DC/S0263574720000223a.pdf/div-class-title-a-critical-review-of-control-techniques-for-flexible-and-rigid-link-manipulators-div.pdf

A Critical Review of Control Techniques for Flexible and Rigid Link Manipulators

Mathematical modelling plays an important role for robotic manipulators in order to design their particular controllers. Also, it is hard challenge to obtain an accurate mathematical model or obtain a suitable modelling method in such vast field. Thus, this critical review is advantageous and indispensable for researchers who are interested in the area to gain fruitful knowledge on the mathematical modelling methods. This paper is classified based on the type of robotic manipulators such as flexible link manipulators (FLMs), rigid link manipulators (RLMs) and hybrid manipulators which involves rigid links and flexible links. The used modelling methods for FLMs are the assumed mode method, the finite element method, and the lumped parameter method as approximation techniques which are well explained and reviewed. The Lagrangian method has inclusive explanation and review which is widely participated for obtaining the dynamic equations of FLMs, and it is appropriate and commonly employed for modelling RLMs. The Newtonian method, the forward kinematic, and the inverse kinematic are also well discussed and reviewed which are suitable and commonly employed for modelling RLMs. The critical discussion of 170 articles reported in this paper guides researchers to select the suitable method for modelling. This paper reviews the published articles in the period of 2010–2020 except for few older articles for the need of providing essential theoretical knowledge. The advantages and disadvantages of each method are well summarized at the end of the paper. The intelligent identification methods are briefly discussed due to the lack of publications especially on the period of 2010–2020.

A critical review of modelling methods for flexible and rigid link manipulators

Lighter manipulators are used due to reducing power consumption and reaching higher speeds for applications. Composite manipulators can be more desirable for this purpose because they are light weight and have high strength. As it is well known that using flexible manipulators causes high amplitude vibrations and this affects the accuracy of end-point positioning. In this study, a single-link flexible glass fabric reinforced epoxy-glass composite manipulator is analyzed in ANSYS and the residual vibrations are controlled with a new method. The finite element vibration analysis is performed and an experimental system is introduced to verify simulation results. [0/90] lay-up and two different velocity profiles are studied for different case studies. An exponential-harmonic velocity excitation is applied after the end of the trapezoidal velocity profile to control the residual vibrations. It is known that the vibration amplitudes of a system decrease when the system is excited at higher frequency than the natural frequencies. The effect of the amplitude, frequency, the duration of the application and the exponential decay factor on the suppression of the residual vibration are analyzed. Both simulation and experimental analyses are performed and the results are in good agreement. It is concluded that the residual vibration amplitudes of the flexible composite manipulator are suppressed with the proposed method up to 99% for all velocity inputs.

An enhanced method to control the residual vibrations of a single-link flexible glass fabric reinforced epoxy-glass composite manipulator

There is a high interest in research for using flexible link manipulators in industrial robots as flexible link manipulators are more advantageous than heavy and rigid link manipulators. However, flexible link manipulators still have a critical problem of less accuracy due to their tip vibration. Thus, this research contributes to this topic by obtaining a mathematical model and proposing an intelligent optimal controller for a single-flexible link manipulator with variable payload. The study developed the mathematical model of the single-flexible link manipulator using finite element method and Lagrange’s equation, the mathematical model of the flexible link manipulator has been validated with a SimMechamics model. The novel intelligent optimal controller is an integration of a fuzzy logic controller and an optimal linear quadratic regulator controller, the proposed intelligent optimal controller has the advantages of simplicity and effectiveness for position tracking and vibration suppression. The concept of integrating the fuzzy and linear quadratic regulator solves the problem of rules’ explosion of fuzzy control as only uses the minimum and active rules. The proposed controller has shown better position tracking performance and has demonstrated better effectiveness for vibration suppression of the flexible link manipulator than the linear quadratic regulator controller. Furthermore, the proposed controller is more robust than the linear quadratic regulator controller for dealing with uncertainties.

Dynamic Model and Intelligent Optimal Controller of Flexible Link Manipulator System with Payload Uncertainty

http://www.scielo.org.mx/pdf/jart/v13n1/v13n1a6.pdf

J.F. Peza-Solís

Papers

Trajectory Tracking Control in a Single Flexible-Link Robot using Finite Differences and Sliding Modes