Modeling and Control of Flexible Second Order Systems With Damped Boundaries

2012 ◽  
Author(s):  
Lea Sirota ◽  
Yoram Halevi
Keyword(s):  
Vibration Suppression ◽  
Transfer Functions ◽  
Initial Conditions ◽  
Modeling And Control ◽  
Sum Of Products ◽  
Second Order Systems ◽  
The Time Domain ◽  
And Control ◽  
Infinite Sum ◽  
Insight Into

This paper considers the problem of modeling and control of non-conservative flexible systems, whose dynamics is described by the wave equation. Classical modal analysis failed so far when the boundaries included dampers. A new insight into the problem was obtained by infinite dimension transfer functions models, developed in previous works. Their special structure, consisting of delays and low order rational terms lead to the time domain interpretation of traveling waves. In this paper the Laplace modeling approach is used to represent the solution in a modal like fashion, i.e. an infinite sum of products of spatial and temporal functions. While this form is closely related to standing waves, it was shown to lead also to a traveling wave representation. The response is then used to investigate the behavior of the system under control with the absolute vibration suppression (AVS) controller, which was originally designed for tracking control. It is shown that the vibration suppression properties of this controller apply also to nonzero initial conditions.

Modeling and Control of Interconnected Dimensionless Dynamic Systems

2009 ◽  
Author(s):  
Scott Manwaring ◽  
Andrew Alleyne
Keyword(s):  
Dimensional Analysis ◽  
Dynamic Systems ◽  
Controller Design ◽  
Fluid Power ◽  
Modeling And Control ◽  
Initial Investigation ◽  
And Control ◽  
Insight Into ◽  
Original Dynamic

Previous work has found benefit in using dimensional analysis in the modeling and control of dynamic systems. What has not been explored is how multiple dimensionless dynamic systems would interconnect and interact with one another. This work presents an initial investigation into the interconnection of dimensionless dynamic systems, including an analysis of the differences between interconnecting dimensioned and dimensionless systems. A strategy is developed to interconnect dimensionless dynamic systems and explored using models of multiple fluid power components. The interconnection strategy is tested through controller design and simulation, which reveals insight into the dimensionless transformation of the original dynamic systems.

Vibration Suppression of a Linear Oscillator Force-Excited by Random Excitation via an Inerter Pendulum Vibration Absorber

2021 ◽  
Author(s):  
Joel A. Cosner ◽  
Wei-Che Tai
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Qualitative Change ◽  
Random Excitation ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Nonlinear Energy Transfer ◽  
Mass Damper ◽  
The Time Domain ◽  
Insight Into

Abstract In this theoretical study, the vibration suppression and nonlinear energy transfer, as a function of a dimensionless pendulum length parameter, is investigated for an Inerter Pendulum Vibration Absorber (IPVA) attached to a linear single-degree-of-freedom spring-mass-damper system, subject to white noise excitation. Stochastic differential equations of motion are first developed and integrated to determine the evolution of the response and associated mean and mean square values for long integration times. Dynamic statistical moment equations are then developed, while arc-length continuation is used to track stationary the moments as a function of the pendulum length. Two noise intensity and damping configurations are analyzed and a critical parameter value, in both cases, is found to produce a qualitative change in the system dynamics accompanied by optimal vibration suppression. The results are compared to the response of a linear system without an IPVA to quantify the vibration suppression. Realizations in the time domain are finally calculated to provide validation for the results and gain insight into the changing dynamics of the system as a function of the pendulum length, leading to the discovery of intermittent rotation for sufficiently large pendulum length.

scholarly journals Passenger car active braking system: Model and experimental validation (Part I)

2017 ◽  
Vol 232 (4) ◽  
pp. 585-594 ◽  
Author(s):  
Antonio Tota ◽  
Enrico Galvagno ◽  
Mauro Velardocchia ◽  
Alessandro Vigliani
Keyword(s):  
Stability Control ◽  
Strategy Development ◽  
Hardware In The Loop ◽  
Modeling And Control ◽  
Pulse Width Modulated ◽  
Braking System ◽  
Pressure Dynamics ◽  
Outlet Valve ◽  
Second Order Systems ◽  
And Control

This paper introduces a method to characterize the dynamic behavior of a normal production hydraulic brake system through experiments on a hardware-in-the-loop test bench for both modeling (part I) and control (part II) tasks. The activity is relative to the analysis, modeling, and control of anti-lock braking system and electronic stability control digital valves, and is aimed at obtaining reference tracking and disturbance-rejection performance similar to that achievable when using pressure proportional valves. The first part of this two-part study is focused on the development of a mathematical model that emulates the pressure dynamics inside a brake caliper when the inlet valve, outlet valve, and motor pump are controlled by digital or pulse width modulated signals. The model takes into account some inherent nonlinearities of these systems, e.g. the variation of fluid bulk modulus with pressure, while inlet and outlet valves together with the relay box are modeled as second-order systems with variable gains. The hardware-in-the-loop test rig is used for both parameter estimation and model validation; the parameters and model will be used for the control strategy development presented in the second part of this study.

Quantitative Analysis of Singularities for Fractional Order Systems

2015 ◽  
Author(s):  
Yan Li ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Intrinsic Property ◽  
Time Domain Analysis ◽  
Order System ◽  
Fractional Order Systems ◽  
Stability And Control ◽  
Practical Strategy ◽  
The Time Domain ◽  
And Control

The singularity is an intrinsic property for various fractional order systems. This paper focuses on the time domain analysis of typical “non-proper” fractional order transfer functions, which plays the crucial role in the implementation, stability and control of fractional order systems. To this end, the fractional order system is converted into a weak singularity integro-differential equation, where the non-proper property can be clearly presented. A practical strategy is shown to find out the poles in the first Riemann plane, which is especially applicable to small commensurate order problems. The distributed order and order sensitivity problems are discussed as well. A number of examples are illustrated by using some reliable fractional order numerical methods.

Modal Representation of Second Order Flexible Structures With Damped Boundaries

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Lea Sirota ◽  
Yoram Halevi
Keyword(s):  
Initial Conditions ◽  
Separation Of Variables ◽  
Complete Solution ◽  
Flexible Structures ◽  
Second Order ◽  
Free Response ◽  
Laplace Domain ◽  
Boundary Case ◽  
Sum Of Products ◽  
Infinite Sum

The problem of obtaining a modal (i.e., infinite series) solution of second order flexible structures with viscous damping boundary conditions is considered. In conservative boundary systems, separation of variables is well established and there exist closed form modal solutions. However, no counterpart results exist for the damped boundary case and previous publications fall short of providing a complete solution for the series, in particular, its coefficients. The paper presents the free response of damped boundary structures to general initial conditions in the form of an infinite sum of products of spatial and time functions. The problem is attended via Laplace domain approach, and explicit expressions for the series components and coefficients are derived. The modal approach is useful in finite dimension modeling, since it provides a convenient framework for truncation. It is shown via examples that often few modes suffice for approximation with good accuracy.

scholarly journals Modeling and control of a three-phase isolated grid-connected converter for photovoltaic applications

2011 ◽  
Vol 22 (3) ◽  
pp. 215-228 ◽  
Author(s):  
Marcelo Gradella Villalva ◽  
Marcos Fernando Espindola ◽  
Thais Gama de Siqueira ◽  
Ernesto Ruppert
Keyword(s):  
Output Voltage ◽  
Closed Loop ◽  
Transfer Functions ◽  
Voltage Source ◽  
Small Signal ◽  
Modeling And Control ◽  
Photovoltaic Array ◽  
Three Phase ◽  
Photovoltaic Applications ◽  
And Control

This paper describes the modeling and control of a three-phase grid-connected converter fed by a photovoltaic array. The converter is composed of an isolated DC-DC converter and a three-phase DC-AC voltage source inverter The converters are modeled in order to obtain small-signal transfer functions that are used in the design of three closed-loop controllers: for the output voltage of the PV array, the DC link voltage and the output currents. Simulated and experimental results are presented.

Modeling and H2/H∞ MIMO Control of an Earthmoving Vehicle Powertrain

2002 ◽  
Vol 124 (4) ◽  
pp. 625-636 ◽  
Author(s):  
Rong Zhang ◽  
Andrew Alleyne ◽  
Eko Prasetiawan
Keyword(s):  
Power Distribution ◽  
Controller Design ◽  
Operating Conditions ◽  
Robust Controller ◽  
Modeling And Control ◽  
Linearized Model ◽  
The Time Domain ◽  
Representative System ◽  
And Control ◽  
Vehicle Powertrain

Coordination of the power distribution in a Multi-Input Multi-Output (MIMO) electro-hydraulic transmission is investigated for the case of an earthmoving vehicle powertrain. A generalized model of a representative system is presented along with the development of both H2 and H∞ MIMO controller designs. The controllers are developed based on a linearized model of the system about some nominal operating point. Multiple inputs are coordinated to control multiple load outputs simultaneously. Since typical MIMO electrohydraulic transmission systems have significant nonlinear dynamics that vary with system operating conditions, a robust controller design is paramount. The increased robustness of the H∞ controller over the H2 scheme is demonstrated qualitatively in the time domain through both disturbance rejection and trajectory tracking comparisons. A frequency domain criterion quantitatively provides quantifiable comparisons between the two methods. Hardware-in-the-Loop experiments validate the modeling and control performance on an Earthmoving Vehicle Powertrain Simulator (EVPS).

Modeling and Multivariable Control of an Earthmoving Vehicle Powertrain

2001 ◽  
Author(s):  
Rong Zhang ◽  
Eko A. Prasetiawan ◽  
Andrew G. Alleyne
Keyword(s):  
Power Distribution ◽  
Controller Design ◽  
Operating Conditions ◽  
Robust Controller ◽  
Modeling And Control ◽  
Linearized Model ◽  
The Time Domain ◽  
Representative System ◽  
And Control ◽  
Vehicle Powertrain

Abstract Coordination of the power distribution in a Multi-Input Multi-Output (MIMO) electrohydraulic transmission is investigated for the case of an earthmoving vehicle powertrain. A generalized model of a representative system is presented along with the development of both H2 and H∞ MIMO controller designs. The controllers are developed based on a linearized model of the system about some nominal operating point Multiple inputs are coordinated to control multiple load outputs simultaneously. Since typical MIMO electrohydraulic transmission systems have significant nonlinear dynamics that vary with system operating conditions, a robust controller design is paramount The increased robustness of the H∞ controller over the H2 scheme is demonstrated qualitatively in the time domain through both disturbance rejection and trajectory tracking comparisons. A frequency domain criterion quantitatively provides quantifiable comparisons between the two methods. Hardware-in-the-Loop experiments validate the modeling and control performance on an Earthmoving Vehicle Powertrain Simulator (EVPS).

Effect of Payload on the Dynamics of a Flexible Manipulator—Modeling for Control

1991 ◽  
Vol 113 (3) ◽  
pp. 409-418 ◽  
Author(s):  
T. R. Parks ◽  
H. A. Pak
Keyword(s):  
Transfer Functions ◽  
Order Reduction ◽  
Qualitative Change ◽  
Flexible Manipulator ◽  
Flexible Beam ◽  
Model Order ◽  
Modeling And Control ◽  
Prior Literature ◽  
And Control ◽  
Substantial Change

The “exact” and pole/zero transfer functions are developed for a flexible beam-like single link arm with actuator on one end and payload on the other. This model represents a broader class of actuator hub and payload mass properties than is found in prior literature. The dependence of dynamics on the hub and payload inertia characteristics are studied and graphs are provided to facilitate estimation of poles and zeroes for any similar plant. It is shown that a 10:1 reduction in fundamental frequency and substantial change in the zeroes results from variations in payload through a practical range. Payload rotary inertia is shown to cause a qualitative change in the arm tip zeroes resulting in loss of observability/controllability in some cases. Results provide insight into the two-link problem and it is shown that complex values zeroes may result if the second arm is allowed to “fold back.” Implications to plant modeling and control design are discussed including sensor placement and model order reduction issues. Analytical results are compared to those measured on an experimental arm and show very good agreement in modal frequency and shape.

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