Vibration Control of a Rotating Shaft: An Analytical Solution

1999 ◽  
Vol 66 (1) ◽  
pp. 254-259 ◽  
Author(s):  
S. M. Yang ◽  
G. J. Sheu
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Feedback Gain ◽  
Beam Model ◽  
Vibration Modes ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Rayleigh Beam ◽  
Sensor Actuator ◽  
Whirl Speed

It has been shown that a rotating shaft in the Rayleigh beam model has only a finite number of whirl speeds and vibration modes when the rotating speed is higher than half of the whirl speed. The system’s unbalanced response can therefore be written analytically by the vibration modes and the generalized coordinates. This paper presents an analytical controller design of optimal sensor/actuator location and feedback gain for minimizing the steady-state unbalanced response. Because all of the critical speeds and vibration modes are included in the controller design, there will be no residual mode, hence no spillover. An example is used to illustrate that the controller design in collocated or noncollocated configuration not only guarantees the closed-loop stability but also effectively suppresses the unbalanced response.

On the Spillover of Steady State Unbalance Response of a Rotating Shaft Under Velocity Feedback

2005 ◽  
Vol 128 (2) ◽  
pp. 143-147 ◽  
Author(s):  
S. M. Yang ◽  
G. J. Sheu
Keyword(s):  
Steady State ◽  
Controller Design ◽  
System Stability ◽  
Feedback Gain ◽  
Beam Model ◽  
Rotating Shaft ◽  
Velocity Feedback ◽  
Reduced Order ◽  
Rayleigh Beam ◽  
Unbalance Response

It has been stated that a uniform rotating shaft in the Rayleigh beam model has only a finite number of critical speeds and precession modes. This paper presents a controller design of optimal sensor/actuator location and feedback gain for steady state unbalance response of a rotating shaft operating in a speed range. For systems under order-limit constraint such that only part of the precession modes can be included in the reduced-order controller design, the system stability can be evaluated. The example of a hinged-hinged rotating shaft is employed to illustrate the controller design of velocity feedback in collocated and noncollocated senor/actuator configuration. Analyses show that the reduced-order controller not only guarantees the closed loop system stability but also effectively suppress the unbalance response.

scholarly journals Analytical Solution of Whirl Speed and Mode Shape for Rotating Shafts

1996 ◽  
Author(s):  
S. M. Yang ◽  
G. J. Sheu ◽  
C. D. Yang
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Mode Shape ◽  
Slenderness Ratio ◽  
Common Belief ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Rayleigh Beam ◽  
Whirl Speed ◽  
Gyroscopic Effects

The analytical solution of whirl speed and mode shape of a rotating shaft in six boundary conditions is presented in this paper. The shaft is modelled by a Rayleigh beam with rotatory inertia and gyroscopic effects, and the boundary conditions are (1) short-short, (2) long-long, (3) long-free, (4) free-free, (5) long-short, and (6) short-free bearings. It is shown that the whirl speed can be written analytically by a function of the whirl ratio (λ) defined by the rotating speed over the whirl speed and the slenderness ratio (l) defined by the length of the shaft over its radius. The number of whirl speeds, contrary to common belief, is finite when λ > 1/2. For the first time, the rotating system’s unbalanced response can be written analytically in an exact form by a finite number of vibration modes with the corresponding generalized coordinates.

scholarly journals Gain scheduled controller design for thermo-optical plant

2014 ◽  
Vol 24 (3) ◽  
pp. 333-349 ◽  
Author(s):  
Vojtech Veselý ◽  
Jakub Osuský ◽  
Ivan Sekaj
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Feedback Gain ◽  
Small Gain ◽  
Gain Scheduled Controller ◽  
The Stability ◽  
Gain Scheduled ◽  
Siso Systems

Abstract This paper presents a gain scheduled controller design for MIMO and SISO systems in the frequency domain using the genetic algorithms approach. The proposed method is derived from the M-delta structure of closed loop MIMO (SISO) systems and the small gain theory is exploited to obtain the stability condition. An example of real system illustrates the effectiveness of the proposed output feedback gain scheduled controller design method and also the possibility to improve its performance using the genetic algorithm

scholarly journals Effects of Discrete Damping on the Dynamic Behaviour of Rotating Shaft through Extended Lagrangian Formulation

2016 ◽  
Vol 46 (3) ◽  
pp. 35-64
Author(s):  
Vikas Rastogi
Keyword(s):  
Excitation Frequency ◽  
Continuous System ◽  
Lagrangian Formulation ◽  
Beam Model ◽  
Rotating Shaft ◽  
One Dimensional ◽  
Rotor Shaft ◽  
Rayleigh Beam ◽  
Increase With Increase ◽  
Simulation Results

Abstract The main focus of the paper is touted as effects of discrete damping on the dynamic analysis of rotating shaft. The whole analysis is being carried out through extended Lagrangian formulation for a discrete – continuous system. The variation formulation for this system is possible, considering the continuous system as one-dimensional. The generalized formulation for one dimensional continuous rotary shaft with discrete external damper has been obtained through principle of variation. Using this extended formulation, the invariance of umbra-Lagrangian density through extended Noether’s theorem is achieved. Rayleigh beam model is used to model the shaft. Amplitude equation of rotor is obtained theoretically and validated through simulation results. The simulation results reveal the important phenomena of limiting dynamics of the rotor shaft, which is due to an imbalance of material damping and stiffness of the rotor shaft. The regenerative energy in the rotor shaft, induced due to elasticity/stiffness of the rotor shaft, is dissipated partially through the in-span discrete damper and also through the dissipative coupling between drive and the rotor shaft. In such cases, the shaft speed will not increase with increase in excitation frequency of the rotor but the slip between the drive and the shaft increases due to loading of drive.

Modal Controllability and Observability of General Mechanical Systems

1995 ◽  
Vol 117 (4) ◽  
pp. 510-515 ◽  
Author(s):  
B. Yang
Keyword(s):  
Closed Loop ◽  
Linear Independence ◽  
Transfer Functions ◽  
Controller Design ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Vibration Modes ◽  
Trial And Error ◽  
Root Locus ◽  
Controllability And Observability

Controllability and observability are studied for general mechanical systems with combined effects of damping, gyroscopic and circulatory forces. A new modal analysis is proposed to represent the system transfer functions by the nonorthogonal eigenvectors that are associated with the original equations of motion. Investigation of linear independence of the rows and columns of the transfer functions yields the modal controllability and observability conditions. Because of their explicit relationships with the vibration modes, the controllability and observability tests require less computation than the conventional criteria, avoid trial and error in selection and positioning of actuators and sensors, and can be applied to systems with unidentified parameters. Moreover, the closed-loop root locus sensitivity coefficients are examined to give insights into modal controllability and observability, and to provide useful guidance for active controller design.

Study on Chaotic Operation and Control System of Ultrasonic Motor

2013 ◽  
Vol 462-463 ◽  
pp. 782-787
Author(s):  
Xun Zhong Quan ◽  
Xiao Wei Liao ◽  
Yan Wu ◽  
Li Wang
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Ultrasonic Motor ◽  
Open Loop ◽  
Feedback Signal ◽  
Motor Speed ◽  
Rotating Speed ◽  
Neural Network Controller ◽  
The Neural Network ◽  
And Control

Ccording to the running speed of ultrasonic motor instability, design a motor testing system, the closed-loop controller embedded improved neural networkalgorithm, to suppress chaos. In open-loop state, input constant parameters to the motor, the motor rotating speed detection, the test data is chaotic analysis,found the speed has chaotic characteristics; in the closed-loop state, the feedback signal through the controller for processing, effectively inhibited theultrasonic motor speed jitter phenomenon, so as to improve the smoothness of motion motor. Experimental results show that, the neural network controller design not only significantly inhibited motor chaotic jitter phenomenon, but also has good anti-interference ability.

Mode-Based Controller Design for Hammerstein Models Using Closed-Loop Tranjent Response Data

2016 ◽  
Vol 136 (5) ◽  
pp. 625-632
Author(s):  
Yoshihiro Matsui ◽  
Hideki Ayano ◽  
Shiro Masuda ◽  
Kazushi Nakano
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Response Data ◽  
Hammerstein Models

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

Impedance Reduction Controller Design for Mechanical Systems

2013 ◽  
Author(s):  
Hanseung Woo ◽  
Kyoungchul Kong
Keyword(s):  
Case Studies ◽  
Closed Loop ◽  
Controller Design ◽  
Mechanical Impedance ◽  
Open Loop ◽  
Mechatronic Systems ◽  
Closed Loop Systems ◽  
Guaranteed Stability ◽  
Reaction Forces ◽  
Definition Of

Safety is one of important factors in control of mechatronic systems interacting with humans. In order to evaluate the safety of such systems, mechanical impedance is often utilized as it indicates the magnitude of reaction forces when the systems are subjected to motions. Namely, the mechatronic systems should have low mechanical impedance for improved safety. In this paper, a methodology to design controllers for reduction of mechanical impedance is proposed. For the proposed controller design, the mathematical definition of the mechanical impedance for open-loop and closed-loop systems is introduced. Then the controllers are designed for stable and unstable systems such that they effectively lower the magnitude of mechanical impedance with guaranteed stability. The proposed method is verified through case studies including simulations.

A Note on Pole Placement of Mechanical Systems

1991 ◽  
Vol 113 (3) ◽  
pp. 420-421 ◽  
Author(s):  
C. Minas ◽  
D. J. Inman
Keyword(s):  
Least Squares ◽  
Canonical Form ◽  
Output Feedback ◽  
Closed Loop ◽  
Weighted Least Squares ◽  
Mechanical Systems ◽  
Pole Placement ◽  
Feedback Gain ◽  
Closed Loop System ◽  
Feedback Method

An output feedback method is developed, that systematically places a desired number of poles of a closed-loop system at or near desired locations. The system is transformed to its equivalent controllable canonical form, where the output feedback gain matrix is calculated in a weighted least squares scheme, that minimizes the change of the remaining modes of the system. The advantage of this method over other pole placement routines is the fact that the influence on the remaining unplaced modes of the system is minimum, which is particularly important in preserving closed-loop stability.

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