scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Structural Control Considering Time Delay Effect

1985 ◽  
Vol 9 (4) ◽  
pp. 224-227 ◽  
Author(s):  
Mohamed Abdel-Rohman
Keyword(s):  
Time Delay ◽  
Active Control ◽  
Theoretical Consideration ◽  
Structural Control ◽  
Control Mechanism ◽  
Structural Response ◽  
Delay Effect ◽  
Numerical Example ◽  
Control Forces ◽  
Time Delay Effect

The time delay between measuring the structural response, and applying the designed active control forces may affect the controlled response of the structure if not taken into consideration. In this paper it is shown how to design the control forces to compensate for the delay effect. It is also shown that the time delay effect can be used as a criterion to judge the effectiveness of the proposed control mechanism. As an illustration of the theoretical consideration, a numerical example in which a tall building is controlled by means of active tendons is presented.

Seismic Control Effect for Nonlinear Benchmark Building Using Passive or Semi-Active Damper

2002 ◽  
Author(s):  
Akira Fukukita ◽  
Tomoo Saito ◽  
Keiji Shiba
Keyword(s):  
Active Control ◽  
Passive Control ◽  
Feedforward Control ◽  
Electrical Power ◽  
Control Device ◽  
Control Effect ◽  
Damping Force ◽  
Active Device ◽  
Seismic Control ◽  
Control Forces

We study the control effect for a 20-story benchmark building and apply passive or semi-active control devices to the building. First, the viscous damping wall is selected as a passive control device which consists of two outer plates and one inner plate, facing each other with a small gap filled with viscous fluid. The damping force depends on the interstory velocity, temperature and the shearing area. Next, the variable oil damper is selected as a semi-active control device which can produce the control forces by little electrical power. We propose a damper model in which the damping coefficient changes according to both the response of the damper and control forces based on an LQG feedback and feedforward control theory. It is demonstrated from the results of a series of simulations that the both passive device and semi-active device can effectively reduce the response of the structure in various earthquake motions.

Optimized Design of Vibration Controllers for Steady and Transient Excitation of Flexible Rotors

1995 ◽  
Vol 209 (3) ◽  
pp. 155-168 ◽  
Author(s):  
P S Keogh ◽  
C Mu ◽  
C R Burrows
Keyword(s):  
Measurement Error ◽  
Controller Design ◽  
Optimized Design ◽  
Rotor Vibration ◽  
Transient Vibration ◽  
Flexible Rotors ◽  
Vibration Attenuation ◽  
Measured Displacement ◽  
Control Forces ◽  
Shaft Surface

Controller designs for the attenuation of rotor vibration are investigated. Disturbance inputs leading to vibration are classified and related to control forces and defined control states. Optimization based on the H∞ norm is then used to minimize the influence of forcing disturbances, modelling error and measurement error. The practicalities of applying the method to an experimental rotor-bearing system, with hardware constraints on controller order, are stated. The controller was implemented experimentally to conduct steady state and mass loss tests. Steady synchronous, non-synchronous and transient vibration attenuation was demonstrated. It was also shown that measurement error, caused by shaft surface roughness, can be incorporated into the controller design without the need to remove the roughness component from the measured displacement signals. If the roughness influence is not included in the design and the uncontrolled vibration is small, unnecessary control forces may result, causing an increase in vibration.

Active Vibration Control of a Multimode Rotor-Bearing System Using an Adaptive Algorithm

1986 ◽  
Vol 108 (2) ◽  
pp. 230-231 ◽  
Author(s):  
A. V. Metcalfe ◽  
J. S. Burdess
Keyword(s):  
Active Vibration Control ◽  
Rotation Frequency ◽  
External Control ◽  
Electromagnetic Actuators ◽  
Mass Unbalance ◽  
Rotor Bearing ◽  
Active Vibration ◽  
Control Forces ◽  
Bearing System ◽  
Uncontrolled System

A method for minimizing forced harmonic vibration of a rotor-bearing system by the application of external control forces is presented. The frequency of the vibration is assumed known. In cases of mass unbalance or bend in the shaft this will be shaft rotation frequency and can usually be monitored without difficulty. The control forces could be provided by electromagnetic actuators. The control strategy presented does not require any knowledge of the system parameters and, provided the uncontrolled system is stable, cannot destablize the system. Results from a simulation are shown.

Vibration Control Using Combined Independent Modal Space Control and Fuzzy Logic

1995 ◽  
Author(s):  
Mehran Asdigha ◽  
Robert Greif
Keyword(s):  
Physical Space ◽  
Fuzzy Rule ◽  
Fuzzy Reasoning ◽  
Performance Criterion ◽  
Active Damping ◽  
Rule Base ◽  
Control Law ◽  
Traditional Algorithm ◽  
Control Forces ◽  
Modal Space

Abstract Independent Modal Space Control (IMSC) is an established technique in active suppression of vibrations, in which the control law is developed exclusively in the modal space, allowing for independent design of the modal control forces. These forces can be transformed to the physical domain through modal transformation. The resulting controller is fixed-gain, with the active damping introduced to the system determined independently for each mode and is a function of the velocity for the under-damped case. In this work we propose to modify IMSC using fuzzy reasoning. The result is a new non-linear control law, embedding fuzzy reasoning and an implicit fuzzy rule-base that transforms the traditional algorithm from a fixed-gain to a variable-gain controller. The algorithm uses information about the displacement profile across the sensed locations to distribute the active damping rationally among the modal controllers. This new algorithm complements the “local” view of the traditional algorithm in the modal space, with a “global” view of the displacements in the physical space. The results show significant improvement in the settling time as the performance criterion.

Spatial Actuation Effectiveness of Segmented Actuators on Parabolic Cylindrical Panels

2012 ◽  
Author(s):  
S. D. Hu ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Shape Control ◽  
Cylindrical Panel ◽  
Design Parameters ◽  
Modal Control ◽  
Control Force ◽  
Optimal Position ◽  
Meridional Direction ◽  
Cylindrical Panels ◽  
Active Vibration ◽  
Control Forces

With the distinct capability of line-focusing, open parabolic cylindrical panels are commonly used as key components of radar antennas, space reflectors, solar collectors, etc. These structures suffer unexpected vibrations from the fluctuation of base structure, non-uniform heating and air flow. The unwanted vibration will reduce the surface reflecting precision and even result in structure damages. To explore active vibration and shape control of parabolic cylindrical panels, this study focuses on actuation effectiveness induced by segmented piezoelectric patches laminated on a flexible parabolic cylindrical panel. The mathematical model of a parabolic cylindrical panel laminated with distributed actuators is formulated. The segmentation technique is developed and applied to parabolic cylindrical panels, and the piezoelectric layer is segmented uniformly in the meridional direction. The distributed actuator patches induced modal control forces are evaluated. As the area of actuator patch varies in the meridional direction, modal control force divided by actuator area, i.e., actuation effectiveness, is investigated. Spatial actuation effectiveness, including its membrane and bending components are evaluated with respect to design parameters: actuator size and position, shell curvature, shell thickness and vibration mode in case studies. The actuation component induced by the membrane force in the meridional direction mainly contributes to the total actuation effectiveness for lower modes. Average and cancellation effect of various actuator sizes and the optimal actuator position are also discussed. Results suggest that for odd vibration modes, the maximal actuation effectiveness locates at the ridge of the panel; while for even modes, the peak/valley closest to the ridge is the optimal position to obtain the maximal actuation effectiveness. A segmentation scheme of the meridian interval angle 0.0464rad for the investigated standard panel is a preferred tradeoff between the actuation effectiveness and practical feasibility. The modal actuation effectiveness increases with the shell curvature, whereas decreases when the shell thickens.

Mechanical Design of a Variable Pitch Fan for Turbofan Engines

2010 ◽  
Author(s):  
John A. Violette ◽  
Eric S. Loos
Keyword(s):  
Mechanical Design ◽  
High Strength ◽  
Variable Pitch ◽  
Fuel Savings ◽  
Turbofan Engines ◽  
Change Mechanism ◽  
Engine Efficiency ◽  
Retention System ◽  
Fan Blade ◽  
Control Forces

The mechanical design of a new variable pitch fan system for high bypass turbofan engines is presented, offering 10–14% fuel savings for next generation turbofan engines. Comparable in weight to current fans, the new design incorporates a compact pitch change mechanism that fits within a current fan’s center body. The key to compactness is the use of multiple high strength tension/torsion straps, which support blade centrifugal loads with unique structural efficiency and redundancy, while allowing ten to fifteen degrees of blade pitch rotation. The new retention system also offers significant reduction of pitch control forces by balancing blade centrifugal twisting loads with strap restoring moments, achieving a desired pitch setting. The use of a pin root fan blade facilitates on-wing blade replacement. Fan blade incidence angles are decreased at low aircraft speeds to avoid fan stall flutter problems. Therefore, advanced engines no longer need the addition of a variable area nozzle to the exit of the fan duct to prevent flutter, saving additional weight, complexity, and cost. This new fan system offers the best solution for achieving a major improvement in turbofan engine efficiency, at the lowest weight.

Vibration Control for the Rotor-Bearing System and Calculation of the Optimum Control Forces

1989 ◽  
Vol 111 (4) ◽  
pp. 366-369
Author(s):  
Lie Yu ◽  
You-Bai Xie ◽  
Jun Zhu ◽  
Damou Qiu
Keyword(s):  
Linear Equations ◽  
Mode Analysis ◽  
Constrained Control ◽  
Optimum Control ◽  
Numerical Examples ◽  
Rotor Bearing ◽  
Optimum Response ◽  
Control Forces ◽  
Complex Methods ◽  
Bearing System

The objective function applied to express the optimum response of the rotor-bearing system is presented based on the complex mode analysis. Two kinds of problems about the calculation of control forces are solved: in the nonconstraint condition the optimization of control forces is treated as the evaluation of a set of linear equations; and the Powell and complex methods are used to calculate the constrained control forces. Numerical examples are also given.

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