Cross term constructed Lyapunov function based two-time scale controller design and vibration suppression for a rotating hub-beam system

2019 ◽  
Vol 42 (3) ◽  
pp. 551-564
Author(s):  
Ghasem Khajepour ◽  
Ramin Vatankhah ◽  
Mohammad Eghtesad ◽  
Mohsen Vakilzadeh
Keyword(s):  
Lyapunov Function ◽  
Vibration Suppression ◽  
Controller Design ◽  
Equations Of Motion ◽  
Angular Position ◽  
Pole Placement ◽  
Cross Term ◽  
Modeling And Control ◽  
Beam System ◽  
Flexible Arm

In this article, modeling and control of a rotating hub-beam system are studied. The system consists of a solid rotating cylinder and an attached flexible arm with a payload at the end. The rotation is supposed to be in the presence of gravity and the flexible arm is assumed to be a Euler-Bernoulli beam. To derive the equations of motion of the system, Lagrange’s method is applied. Moreover, Galerkin’s technique is employed to discretize the equations of motion. Furthermore, designing an appropriate two-time (slow and fast) scale controller in the presence of uncertainties is considered in order to track the desired hub angular position and suppress vibrations of the arm simultaneously. For the so-called slow subsystem, a novel controller design is proposed as two different cases, with and without the presence of uncertainties in system dynamics are considered; and accordingly, a control law for tracking the desired path is introduced based on the idea of using the cross-term constructed Lyapunov function. For the fast subsystem, a pole placement technique is used to suppress vibration of the beam. The simulation results indicate notable effectiveness of the proposed controller.

Active Damping of a Large Flexible Manipulator With a Short-Reach Robot

1996 ◽  
Vol 118 (4) ◽  
pp. 704-713 ◽  
Author(s):  
I. Sharf
Keyword(s):  
Vibration Suppression ◽  
Controller Design ◽  
Reaction Force ◽  
Control Variable ◽  
Active Damping ◽  
Flexible Manipulator ◽  
Design Problems ◽  
Flexible Arm ◽  
Six Degree Of Freedom ◽  
Small Robot

This paper deals with manipulator systems comprising a long-reach manipulator (LRM) with a short-reach dextrous manipulator (SRM) attached to its end. The former, due to its size, is assumed to have significant structural flexibility, while the latter is modeled as a rigid robot. The particular problem addressed is that of active damping, or vibration suppression, of the LRM by using SRM specifically for that purpose Such a scenario is envisioned for operations where the large manipulator is used to deploy the small robot and it is necessary to damp out vibrations in LRM prior to operating SRM. The proposed solution to the problem uses the reaction force from SRM to LRM as a control variable which allows to effectively decouple the controller design problems for the two manipulators. A two-stage controller is presented that involves first, determining the trajectory of the short manipulator required to achieve a desired damping wrench to the supporting flexible arm and subsequently, brings the small manipulator to rest. Performance of the active damping algorithm developed is illustrated with a six-degree-of-freedom rigid manipulator on a flexible mast. Comparison to an independent derivative joint controller is included. The paper also discusses how the proposed methodology can be extended to address other issues related to operation of long-reach manipulator systems.

scholarly journals A Review on Eigenstructure Assignment Methods and Orthogonal Eigenstructure Control of Structural Vibrations

2009 ◽  
Vol 16 (6) ◽  
pp. 555-564 ◽  
Author(s):  
Mohammad Rastgaar ◽  
Mehdi Ahmadian ◽  
Steve Southward
Keyword(s):  
Vibration Suppression ◽  
Controller Design ◽  
Pole Placement ◽  
Structural Vibration ◽  
Eigenstructure Assignment ◽  
Large Space ◽  
Mode Localization ◽  
The Past ◽  
Recent Developments ◽  
Design Freedom

This paper provides a state-of-the-art review of eigenstructure assignment methods for vibration cancellation. Eigenstructure assignment techniques have been widely used during the past three decades for vibration suppression in structures, especially in large space structures. These methods work similar to mode localization in which global vibrations are managed such that they remain localized within the structure. Such localization would help reducing vibrations more effectively than other methods of vibration cancellation, by virtue of confining the vibrations close to the source of disturbance. The common objective of different methods of eigenstructure assignment is to provide controller design freedom beyond pole placement, and define appropriate shapes for the eigenvectors of the systems. These methods; however, offer a large and complex design space of options that can often overwhelm the control designer. Recent developments in orthogonal eigenstructure control offers a significant simplification of the design task while allowing some experience-based design freedom. The majority of the papers from the past three decades in structural vibration cancellation using eigenstructure assignment methods are reviewed, along with recent studies that introduce new developments in eigenstructure assignment techniques.

Dynamic Modeling of a Piggybacked Cantilever Beam System

2014 ◽  
Author(s):  
Troy Lundstrom ◽  
Nader Jalili
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Continuous System ◽  
Element Model ◽  
System Response ◽  
Structure Response ◽  
Beam System ◽  
Geometric Boundary ◽  
Primary Base ◽  
Base Structure

Typically, 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 torque and translational force to the base structure attachment point; this minimizes the likelihood that the attachment location is the node of a mode (rotary or translational). In this paper, Hamilton’s Principle is used to develop the equations of motion for a continuous two-beam system composed of a cantilevered, primary base beam with a secondary piezoelectric bender mounted to its surface. A disturbance force is applied near the fixture location of the base beam and the system response is estimated using a sufficient quantity of assumed eigenfunctions that satisfy the geometric boundary conditions. A theoretical study is performed to compared the continuous system eigenfunctions to a finite element model (FEM) of the two-beam structure and the required number of eigenfunctions required to yield a convergent solution for an impulse excitation is explored. In addition, the frequency response function for the dynamic system is presented and compared to that of a FEM.

scholarly journals Fuzzy Descriptor System Modeling and Control of Lagrange Dynamics with Regional Pole-Placement Constraint

2004 ◽  
Vol 8 (4) ◽  
pp. 362-368
Author(s):  
Jin-Shig Kang ◽  
Keyword(s):  
Controller Design ◽  
System Modeling ◽  
Fuzzy Model ◽  
Pole Placement ◽  
Descriptor System ◽  
Linear Matrix ◽  
Simple Extension ◽  
Design Algorithm ◽  
Modeling And Control ◽  
Regional Pole Placement

We present a descriptor fuzzy model for Lagrange dynamics and a controller design algorithm based on state feedback pole placement. The fuzzy descriptor system (FDS) model is a simple extension of the original Takagi-Sugeno fuzzy model for which a new controller is designed based on the linear matrix inequality (LMI) theory. We show that LMI-based regional pole-placement design for the FDS is easily solved. Two examples explain the controller’s simplicity and easy design.

VIBRATION SUPPRESSION OF A ROTATING HUB-BEAM SYSTEM WITH A FLEXIBLE SUPPORT USING FRACTIONAL ORDER SLIDING MODE CONTROL

2017 ◽  
Vol 41 (4) ◽  
pp. 627-643 ◽  
Author(s):  
Mohsen Vakilzadeh ◽  
Mohammad Eghtesad ◽  
Mohammad Rahim Nami ◽  
Ghasem Khajepour
Keyword(s):  
Fractional Order ◽  
Vibration Suppression ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Angular Position ◽  
Industrial Applications ◽  
Superior Performance ◽  
Sensors And Actuators ◽  
Flexible Support ◽  
Wide Range

In this paper, a rotating hub-blade system with a flexible support which represents a wide range of industrial applications is considered for modelling and control. The flexible blade is assumed as an Euler–Bernoulli beam. In addition, three piezoelectric layers are mounted on the blade as sensors and actuators to reduce vibrations of the blade attached to the hub. For modelling, the Lagrange’s method is utilized to obtain the equations of motion of the system. In order to simultaneously suppress vibrations of the system and track the desired angular position of the hub, designing an appropriate controller is carried out. In this regard, a fractional order sliding mode (FOSM) controller is proposed to fulfil these objectives and then the comparison between FOSM controller and the classical sliding mode controller is presented in order to investigate the effectiveness of the proposed controller. The simulation results indicate the superior performance of the fractional order controller in compare to the integer order sliding.

Modeling and Control of Elastic Joint Robots

1987 ◽  
Vol 109 (4) ◽  
pp. 310-318 ◽  
Author(s):  
M. W. Spong
Keyword(s):  
Controller Design ◽  
Nonlinear Models ◽  
Integral Manifold ◽  
Equations Of Motion ◽  
Joint Stiffness ◽  
Nonlinear Feedback ◽  
Static State ◽  
Modeling And Control ◽  
Elastic Joint ◽  
And Control

In this paper we study the modeling and control of robot manipulators with elastic joints. We first derive a simple model to represent the dynamics of elastic joint manipulators. The model is derived under two assumptions regarding dynamic coupling between the actuators and the links, and is useful for cases where the elasticity in the joints is of greater significance than gyroscopic interactions between the motors and links. In the limit as the joint stiffness tends to infinity, our model reduces to the usual rigid model found in the literature, showing the reasonableness of our modeling assumptions. We show that our model is significantly more tractable with regard to controller design than previous nonlinear models that have been used to model elastic joint manipulators. Specifically, the nonlinear equations of motion that we derive are shown to be globally linearizable by diffeomorphic coordinate transformation and nonlinear static state feedback, a result that does not hold for previously derived models of elastic joint manipulators. We also detail an alternate approach to nonlinear control based on a singular perturbation formulation of the equations of motion and the concept of integral manifold. We show that by a suitable nonlinear feedback, the manifold in state space which describes the dynamics of the rigid manipulator, that is, the manipulator without joint elasticity, can be made invariant under solutions of the elastic joint system. The implications of this result for the control of elastic joint robots are discussed.

Observer-based controller for floor vibration control with optimization algorithms

2016 ◽  
Vol 23 (3) ◽  
pp. 345-360 ◽  
Author(s):  
Donald S Nyawako ◽  
Paul Reynolds
Keyword(s):  
Vibration Suppression ◽  
Controller Design ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Pi Controller ◽  
Pole Placement ◽  
Algorithm Optimization ◽  
Single Input Single Output ◽  
Reduced Order ◽  
Output Controller

This study presents the results of vibration suppression of a walkway bridge structure with a single actuator and sensor pair by using a proportional-integral (PI) controller and observer-based pole-placement controllers. From the results of experimental modal analysis, reduced-order models of the walkway are identified. These are used for the design of a PI controller as well as for state estimation procedures that are necessary for the development of reduced-order observer controllers. The respective orders of the latter are dependent on the number of plant modes used for their designs. They are formulated from plant and observer feedback gains that are obtained from the specification of desired floor closed-loop eigenvalues and observer eigenvalues. There are numerous solutions possible with the observer-based controller design procedures whereas the PI controller defaults to a particular solution. There is also the flexibility for isolation and control of target vibration modes with the observer-based controllers for higher controller orders from a purely single-input single-output controller scheme as demonstrated in the analytical and experimental studies presented. Further, in this work, a design space of potential feedback gains is specified, where only a single plant mode has been used for the observer-based controller design process, and a multi-objective genetic algorithm optimization scheme is used to search for an optimal solution within some pre-defined constraint conditions. The best solution here is regarded as one that offers the greatest vibration mitigation performance amongst the solutions identified.

The Trajectory Tracking Control of 2-Link Flexible Arm Using Tendon Mechanism

1995 ◽  
Author(s):  
Hui Cao ◽  
Kazuo Yoshida
Keyword(s):  
Trajectory Tracking ◽  
Tracking Control ◽  
Control Method ◽  
Equations Of Motion ◽  
Real Time Control ◽  
Trajectory Tracking Control ◽  
Modeling And Control ◽  
Time Control ◽  
Flexible Arm ◽  
Resolved Acceleration Control

Abstract This paper deals with the trajectory tracking control of a 2-link flexible arm using tendon control mechanism. The purpose of this research is to establish modeling and control method for flexible arm. First, the equations of kinematic relationship and equations of motion are derived by using static deflection curve. From these equations, the relationship between tip trajectory and joint input torque is established. Second, a trajectory tracking controller is designed for real-time control of the flexible arm by using the resolved acceleration control method. Then the controller is carried out to track the designed straight line and circular trajectory. The simulation results show the effectiveness of the proposed method. To summarize these results, it was demonstrated that the tendon mechanism can be used to solve the tracking problem of the flexible arms and it also has a higher tracking precision than traditional method.

Design of a slender turning cutting tool via a vibration absorber equipped with piezoelectric ceramic

2021 ◽  
pp. 107754632110144
Author(s):  
Yiqing Yang ◽  
Haoyang Gao ◽  
Qiang Liu
Keyword(s):  
Piezoelectric Ceramic ◽  
Cutting Tool ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Electrical Energy ◽  
Diameter Ratio ◽  
Vibration Absorber ◽  
Machined Surface ◽  
Structural Part ◽  
Machined Surface Roughness

Turning cutting tool with large length–diameter ratio has been essential when machining structural part with deep cavity and in-depth hole features. However, chatter vibration is apt to occur with the increase of tool overhang. A slender turning cutting tool with a length–diameter ratio of 7 is developed by using a vibration absorber equipped with piezoelectric ceramic. The vibration absorber has dual functions of vibration transfer to the absorber mass and vibration conversion to the electrical energy via the piezoelectric effect. Equations of motion are established considering the dual damping from the piezoelectric ceramic and rubber gasket. The equivalent damping of piezoelectric ceramic is derived, and the geometries are optimized to achieve optimal vibration suppression. The modal analysis demonstrates that the cutting tool with the vibration absorber can reach 80.1% magnitude reduction. Machining tests are carried out in the end. The machining acceleration and machined surface roughness validate the vibration suppression of the VA, and the output voltage by the piezoelectric ceramic demonstrates the ability of vibration sensing.

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