STABILITY ANALYSIS AND VIBRATION CONTROL OF A CLASS OF NEGATIVE IMAGINARY SYSTEMS

2015 ◽  
Vol 77 (17) ◽  
Author(s):  
Auwalu M. Abdullahi ◽  
Z. Mohamed ◽  
M. S. Zainal Abidin ◽  
R. Akmeliawati ◽  
Amiru A. Bature
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Vibration Control ◽  
Horizontal Plane ◽  
Closed Loop ◽  
Flexible Manipulator ◽  
The Finite Element Method ◽  
Closed Loop System ◽  
Resonance Modes ◽  
Resonant Controller

This paper presents stability analysis and vibration control of a class of negative imaginary systems. A flexible manipulator that moves in a horizontal plane is considered and is modelled using the finite element method. The system with two poles at the origin is shown to possess negative imaginary properties. Subsequently, an integral resonant controller (IRC) which is a strictly negative imaginary controller is designed for the position and vibration control of the system. Using the IRC, the closed-loop system is observed to be internally stable and simuation results show that satisfactory hub angle response is achieved. Furthermore, vibration magnitudes at the resonance modes are suppressed by 48 dB.

PI Control of HSFDs for Active Control of Rotor-Bearing Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 658-667 ◽  
Author(s):  
J. P. Hathout ◽  
A. El-Shafei
Keyword(s):  
Vibration Control ◽  
Active Control ◽  
Closed Loop ◽  
Rotating Machinery ◽  
Loop System ◽  
Pi Control ◽  
Closed Loop System ◽  
Transient Vibration ◽  
Critical Speeds ◽  
Rotor Bearing

This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDS) for active control of rotor vibrations. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady-state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient runup through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated into the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.

scholarly journals Multiple shooting method in stability analysis of non-prismatic multi-segment columns

2013 ◽  
Vol 12 (4) ◽  
pp. 225-232
Author(s):  
Ryszard Hołubowski ◽  
Andrzej Merena
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Shooting Method ◽  
High Efficiency ◽  
Variable Coefficients ◽  
Multiple Shooting ◽  
System Of Differential Equations ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Multiple Shooting Method

The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

A comparative study for collocated and non-collocated sensor/actuator placement in vibration control of a maneuvering flexible satellite

2014 ◽  
Vol 229 (8) ◽  
pp. 1415-1424 ◽  
Author(s):  
Morteza Shahravi ◽  
Milad Azimi
Keyword(s):  
Vibration Control ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Lyapunov Analysis ◽  
Closed Loop System ◽  
Sensors And Actuators ◽  
Sensor Actuator ◽  
Attitude Maneuver ◽  
System Equations ◽  
Actuator Placement

This paper presents a study concerning the vibration control of smart flexible sub-structures of satellite during attitude maneuver. A comparison between the collocated and non-collocated piezoceramic patches acting as sensors and actuators is performed in order to investigate their effectiveness to suppress vibrations in flexible substructures. A rigid hub with two elastic appendages containing surface bounded piezoelectric patches is being considered as satellite model. Finite element method and Lagrangian formulation are used for derivation of system equations of motion. Stability proof of the overall closed-loop system is given via Lyapunov analysis. The numerical simulations verify the results of the study.

On the control of a single flexible arm robot via Youla-Kucera parameterization

Robotica ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 150-172 ◽  
Author(s):  
Habib Esfandiar ◽  
Saeed Daneshmand ◽  
Roozbeh Dargahi Kermani
Keyword(s):  
Closed Loop ◽  
Optimization Techniques ◽  
Loop System ◽  
Flexible Manipulator ◽  
Order System ◽  
Flexible Beam ◽  
Closed Loop System ◽  
Stabilizing Controller ◽  
Main Challenge ◽  
Tip Mass

SUMMARYIn this paper, based on the Youla-Kucera (Y-K) parameterization, the control of a flexible beam acting as a flexible robotic manipulator is investigated. The method of Youla parameterization is the simple solution and proper method for describing the collection of all controllers that stabilize the closed-loop system. This collection comprises function of the Youla parameter which can be any proper transfer function that is stable. The main challenge in this approach is to obtain a Youla parameter with infinite dimension. This parameter is approximated by a subspace with finite dimensions, which makes the problem tractable. It is required to be generated from a finite number of bases within that space and the considered system can be approximated by an expansion of the orthonormal bases such as FIR, Laguerre, Kautz and generalized bases. To calculate the coefficients for each basis, it is necessary to define the problem in the form of an optimization problem that is solved by optimization techniques. The Linear Quadratic Regulator (LQR) optimization tool is employed in order to optimize the controller gains. The main aim in controller design is to merge the closed-loop system and the second order system with the desirable time response characteristic. The results of the Youla stabilizing controller for a planar flexible manipulator with lumped tip mass indicate that the proposed method is very efficient and robust for the time-continuous instances.

Sign in / Sign up

Export Citation Format

Share Document