A Single-Mode Smooth Wave-Form Command Shaping Control Applied on a Flexible Rotating Beam

2018 ◽  
Author(s):  
Khaled A. Alhazza
Keyword(s):  
Single Mode ◽  
Wave Form ◽  
Rotating Beam ◽  
Command Shaping

Command Shaping Control of a Vertically Rotating Flexible Beam

2019 ◽  
Author(s):  
Khaled A. Alhazza
Keyword(s):  
Initial Conditions ◽  
Equation Of Motion ◽  
Wave Form ◽  
Flexible Beam ◽  
Beam Length ◽  
Rotating Beam ◽  
Double Step ◽  
Higher Modes ◽  
Command Shaping ◽  
System Equation

Abstract Vertically rotating flexible beam under the effect of gravity adds some challenges to the existing input- and command shaping techniques. Classical shapers usually have zero initial conditions while vertically rotating beam may have initial or final deflections. These conditions may introduce large residual vibrations at the end of rest-to-rest maneuvers. Furthermore, the system contains some nonlinearities that may reduce the effectiveness of classical input- and command-shapers. In this work, a waveform command shaping profile is used initially and then optimized to reduce rest-to-rest residual vibrations of a vertically rotating flexible beam. The system equation of motion is determined, discretized, and then linearized to find an initial command shaper. The parameters of the proposed command shaper is then optimized to find a better performance. Only the first mode is considered in this work since higher modes usually have negligible amplitudes. To show the importance of the proposed work, comparisons between the uncontrolled shaper, double step shaper, smooth wave form command shaping, and the optimized command shaping are performed. The proposed technique is tested numerically using two cases, with different maximum velocities, flexible beam length, and acceleration times. Results show that the effectiveness of the proposed technique in reducing residual vibrations in rest-to-rest maneuvers.

Multi-Wave Flutter Vibrations in Mistuned Cascades with Tip-Shroud Friction

2020 ◽  
Author(s):  
Johann Gross ◽  
Malte Krack
Keyword(s):  
Single Mode ◽  
Wave Form ◽  
Modal Interaction ◽  
Modal Interactions ◽  
Multiple Wave ◽  
Aero Engine ◽  
Wave Forms ◽  
Nonlinear Modal Interaction ◽  
The Rich ◽  
Tip Shroud

Abstract Measurements taken during aero engine tests and in the field showed that flutter vibrations of shrouded blades can feature rich wave content (multi-wave flutter vibrations). In a previous work, we demonstrated that this behavior can be explained by the nonlinear interaction of aeroelastically unstable traveling wave modes. The resulting vibrations are quasi-periodic. In the present work, we show that the nonlinear modal interaction is not strictly needed, but actually mistuning alone can explain the multi-wave form of flutter vibrations. The resulting vibrations are periodic and dominated by only a single mode shape of the mistuned system. However, unrealistically high mistuning intensities are needed to obtain significant contributions of multiple wave forms under the considered strong inter-blade coupling. Thus, we conclude that mistuning cannot explain the rich wave content observed in the measurements. Moreover, mistuning tends to hamper the nonlinear modal interactions and, thus, the occurrence of quasi-periodic multi-wave flutter vibrations. This implies that intentional mistuning is not only useful to stabilize flutter, but might also play an important role in developing flutter-tolerant blade designs.

Simplification of the Maxwell-Bloch Equation of Standing Wave Lasers

2013 ◽  
Vol 760-762 ◽  
pp. 8-14
Author(s):  
Li Cheng Sun ◽  
Zheng Wu
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Standing Wave ◽  
Light Field ◽  
Single Mode ◽  
Bloch Equation ◽  
Wave Form ◽  
Wave Laser ◽  
Mathematical Evaluation ◽  
New Equation

In order to make a numerical simulation of the chaos in standing wave lasers, a dynamic equation that is feasible to mathematical evaluation is required. There is a summation symbol in the well known Haken laser equation, and it results in a tremendously heavy quantity of evaluation. In order to simplify the evaluation, the light field in the Haken laser equation was expanded in the standing wave form. Two macroscopic variables were brought in to eliminate the summation symbol in terms of single mode and homogeneously broadening. Therefore, a simplified Maxwell-Bloch equation was gained. Then by normalizing, a new equation was obtained. This equation is in a simple form. Its every variable has unambiguous meaning and every coefficient is only related to gain or dissipation and is easy to obtain. Moreover, the equation is used in two MATLAB numerical simulations of a CO2laser and a chaotic attractor is obtained. So the equation could be a mathematical model in numerical simulations of standing wave laser chaos.

A Novel Wave-Form Command-Shaping Control With Application on Overhead Cranes

2010 ◽  
Author(s):  
Khaled A. Alhazza ◽  
Ziyad N. Masoud
Keyword(s):  
Harmonic Oscillator ◽  
Control Strategy ◽  
Wave Form ◽  
Overhead Crane ◽  
Command Shaping ◽  
Overhead Cranes ◽  
Simple Harmonic Oscillator

In this work, a novel continuous command-shaping control strategy for a simple harmonic oscillator is proposed and implemented on an overhead crane model. A Wave-Form (WF) acceleration command profile is derived analytically, and its performance is validated numerically. To enhance the performance of the proposed command-shaping control strategy, a Modulated Wave-Form (MWF) acceleration command profile is derived. It was determined that the proposed Wave-Form and Modulated Wave-Form command profiles are capable of eliminating the travel and residual oscillations. Furthermore, unlike traditional impulse and step command-shaping, the proposed command profiles have smoother intermediate acceleration, velocity, and displacement profiles.

Command-Shaping Control System for Double-Pendulum Gantry Cranes

2011 ◽  
Author(s):  
Ziyad N. Masoud ◽  
Khaled A. Alhazza
Keyword(s):  
Closed Loop ◽  
Single Mode ◽  
Feedback System ◽  
Mode Frequency ◽  
Gantry Crane ◽  
Necessary Condition ◽  
Double Pendulum ◽  
Double Step ◽  
Scaled Model ◽  
Command Shaping

Traditionally, multi-mode command-shaping controllers are tuned to the system frequencies. This work suggests an opposite approach. A frequency-modulation (FM) strategy is developed to tune the system frequencies to match the frequencies eliminated by a single-mode command-shaper. The shaper developed in this work is based on a double-step command-shaping strategy. Using the FM Shaper, a simulated feedback system is used to modulate the closed-loop frequencies of a simulated double-pendulum model to the point where the closed-loop second mode frequency becomes an odd multiple of the closed-loop first mode frequency, which is the necessary condition for a satisfactory performance of a single-mode command-shaper. The double-step command-shaper is based on the closed-loop first mode frequency. The input commands to the plant of the simulated closed-loop system are then used to drive the actual double-pendulum. Performance is validated experimentally on a scaled model of a double-pendulum gantry crane.

A Smooth Multimode Waveform Command Shaping Considering the Effect of Hoisting

2016 ◽  
Author(s):  
Khaled A. Alhazza
Keyword(s):  
Equations Of Motion ◽  
Optimization Technique ◽  
Large Body ◽  
Single Mode ◽  
Input Shaping ◽  
Double Pendulum ◽  
Scaled Model ◽  
Command Shaping ◽  
Varying Coefficients ◽  
Time Varying Coefficients

Input shaping and command shaping control techniques are the subject of large body of research in the past several decades. Most of the research is dedicated to time invariant single-mode systems. For a double pendulum hoisting system, hoisting results in a complex system of equations of motion. For rest-to-rest maneuvers, it is a common practice in research to split maneuvers into three consecutive independent stages; hoisting up the payload from an initial position, moving it horizontally, and finally lowering it to a final location. Input shaping is used is the horizontal travel motion stage to eliminate inertia excited vibrations. Although, this approach is effective, significant time penalties are involved due to the split motion approach. Further, traditional input shaping techniques involve significant jerks in the motion commands. To overcome these drawbacks, a new smooth waveform command shaping technique is proposed to enable concurrent hoisting and travel actions. The equations of motion including time varying coefficients are derived and used to determine the coefficients of an optimum waveform shaped command profile. Genetic algorithm optimization technique is used to find the optimal values of the command parameters. The initial values of these parameters are determined assuming a constant cable length. The effectiveness of the shaped command is demonstrated through numerical simulations and experiments on a scaled model of double pendulum using different maneuvers involving simultaneous travel and linear hoisting.

Adjustable maneuvering time wave-form command shaping control with variable hoisting speeds

2016 ◽  
Vol 23 (7) ◽  
pp. 1095-1105 ◽  
Author(s):  
Khaled A Alhazza
Keyword(s):  
Continuous Wave ◽  
Equation Of Motion ◽  
Approximation Technique ◽  
Wave Form ◽  
Input Shaping ◽  
Overhead Crane ◽  
Algorithm Optimization ◽  
Optimization Scheme ◽  
Command Shaping ◽  
Pendulum Model

Classical input shaping is based on convolving a general input signal with a sequence of timed impulses. These impulses are chosen to match certain modal parameters of the system under control to eliminate residual vibrations in rest-to-rest maneuvers. This type of input shaping is strongly dependent on the system period. In this work, an adjustable maneuvering time wave form command shaper is presented. The equation of motion of a simple pendulum model of a crane is derived and solved in order to eliminate residual vibrations at the end of motion. Several cases are simulated numerically and validated experimentally on an experimental model of an overhead crane. Results show that the proposed command shaper is capable of eliminating residual vibrations effectively with a single continuous wave form command. The work is extended to include the effect of hoisting on the shaper performance. Several functions are used to simulate hoisting. To overcome the added complexity of hoisting on the system, an approximation technique is used to determine initial shaped command parameters, which are later used in a genetic algorithm optimization scheme. Numerical and experimental results prove that the proposed command shaper can effectively eliminate residual vibrations in rest-to-rest maneuvers.

A Smooth Wave-Form Command Shaping Control

2013 ◽  
Author(s):  
Khaled A. Alhazza ◽  
Ziyad N. Masoud ◽  
Nehal Alotaibi
Keyword(s):  
Experimental Results ◽  
Harmonic Oscillators ◽  
Wave Form ◽  
Overhead Crane ◽  
Scaled Model ◽  
Smoothing Techniques ◽  
Command Shaping ◽  
Shaping Technique ◽  
Multi Mode ◽  
Smooth Acceleration

To avoid excitation of higher modes of flexible and multi-mode systems, it is important to eliminate sudden and jerky inputs. To achieve this goal, researchers tend to use different smoothing techniques to reduce the effect of the command roughness. In this work, a new smooth command-shaping technique for oscillation reduction of simple harmonic oscillators is proposed. A continuous smooth wave-form acceleration command-shaper is proposed. The shaper parameters are tuned to eliminate residual vibrations in rest-to-rest maneuvers. The performance of the proposed shaper is determined analytically, simulated numerically, and validated experimentally on a scaled model of an overhead crane. Results obtained show that the proposed smooth wave-form shaper is capable of eliminating travel and residual oscillations. Furthermore, unlike traditional step command shapers, the proposed command profiles have completely smooth acceleration, velocity, and displacement profiles. Experimental results demonstrate the ability of our proposed smooth wave-form commands to eliminate residual vibrations at the end of rest-to-rest maneuvers.

A Continuous Modulated Wave-Form Command Shaping for Damped Overhead Cranes

2011 ◽  
Author(s):  
Khaled A. Alhazza ◽  
Asmahan H. Al-Shehaima ◽  
Ziyad N. Masoud
Keyword(s):  
Control Strategy ◽  
Damping Ratio ◽  
Harmonic Oscillators ◽  
Wave Form ◽  
Double Step ◽  
Command Shaping ◽  
Overhead Cranes ◽  
Input Shaper ◽  
Displacement Profile ◽  
System Properties

A new command-shaping control strategy for oscillation reduction of damped harmonic oscillators is derived and implemented on damped overhead cranes. The effect of damping on the shaper frequency and duration is investigated. The performance of the proposed simper is simulated numerically and compared with the classical double-step input-shaper for different system properties. It was shown that, the proposed wave-form command profiles are capable of eliminating the travel and residual oscillations for systems with different damping ratio. Further, unlike traditional impulse and step command shapers, the proposed command profiles have smoother intermediate acceleration, velocity, and displacement profile.

Experimental and Numerical Validation on a Continuous Modulated Wave-Form Command Shaping Control Considering the Effect of Hoisting

2013 ◽  
Author(s):  
Khaled A. Alhazza
Keyword(s):  
Optimization Technique ◽  
Large Body ◽  
Initial Point ◽  
Pattern Search ◽  
Wave Form ◽  
Input Shaping ◽  
Time Varying ◽  
Scaled Model ◽  
Command Shaping ◽  
Cable Length

A large body of research has been dedicated to input-shaping control techniques. Most of the research assumes constant cable length, due to the complexity of the dynamics associated with changing cable length (hoisting). Current techniques tend to split maneuvers into three consecutive stages, raising the payload from an initial point, then moving it horizontally using input-shaping, and finally lowering it to a final location. These techniques are effective, however, they involve significant time penalties. In this work, a new modulated wave-form command shaping technique is proposed to enable concurrent hoisting and travel maneuvers. The time varying ordinary differential equation of motion is derived and used to determine the parameters and frequency of the proposed shaped-command. Assuming linear hoisting, the equation is solved analytically by assuming small changes in the time varying terms. This approach results in some error which can be corrected by using pattern search optimization technique. It is shown that, the proposed method is capable of eliminating the travel and residual oscillations for different maneuvers involving linear hoisting. Performance is simulated numerically and validated experimentally on a scaled model of an overhead crane.

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