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Modeling, Analysis, and Control of Dynamical Systems with Friction and Impacts

Ethan Mitchell

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Published in Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts (World Scientific On Nonlinear Science A 92)

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Dynamical systems with friction and impacts are ubiquitous in engineering and science. They arise in a wide variety of applications, including robotics, automotive systems, and manufacturing processes. The presence of friction and impacts can significantly alter the behavior of these systems, making them more difficult to control and predict.

In recent years, there has been a growing interest in the development of modeling, analysis, and control techniques for dynamical systems with friction and impacts. This interest has been driven by the increasing use of these systems in safety-critical applications, such as autonomous vehicles and medical devices.

Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts (World Scientific On Nonlinear Science A 92)

Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts (World Scientific Series On Nonlinear Science Series A Book 92)

by Jan Awrejcewicz

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Language	:	English
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This article provides an overview of the current state of the art in modeling, analysis, and control of dynamical systems with friction and impacts. We begin by discussing the different types of friction and impact models that are available. We then discuss the challenges associated with modeling and analyzing these systems. Finally, we present an overview of the different control techniques that have been developed for these systems.

Types of Friction and Impact Models

There are a wide variety of friction and impact models that can be used to represent the behavior of these systems. The choice of model depends on the specific application and the desired level of accuracy.

Some of the most common friction models include:

* Coulomb friction: This is the simplest friction model, and it assumes that the friction force is proportional to the normal force between the two surfaces in contact. * Viscous friction: This model assumes that the friction force is proportional to the relative velocity between the two surfaces in contact. * Stribeck friction: This model is a combination of the Coulomb and viscous friction models. It is often used to represent the behavior of friction at low velocities.

Some of the most common impact models include:

* Perfectly elastic impact: This model assumes that the impact is perfectly elastic, meaning that there is no loss of energy during the impact. * Perfectly plastic impact: This model assumes that the impact is perfectly plastic, meaning that all of the energy is lost during the impact. * Viscoelastic impact: This model is a combination of the perfectly elastic and perfectly plastic impact models. It is often used to represent the behavior of impacts at intermediate velocities.

Challenges in Modeling and Analyzing Dynamical Systems with Friction and Impacts

Modeling and analyzing dynamical systems with friction and impacts is challenging for a number of reasons. First, the presence of friction and impacts can introduce nonlinearities into the system dynamics. This can make it difficult to predict the behavior of the system, even for simple systems.

Second, friction and impacts can lead to discontinuous behavior in the system dynamics. This can make it difficult to analyze the system using traditional methods.

Third, friction and impacts can introduce time delays into the system dynamics. This can make it difficult to control the system in real time.

Control Techniques for Dynamical Systems with Friction and Impacts

There are a number of different control techniques that have been developed for dynamical systems with friction and impacts. These techniques can be divided into two main categories:

* Open-loop control: This type of control does not use any feedback from the system. Instead, the control input is determined based on a model of the system. * Closed-loop control: This type of control uses feedback from the system to adjust the control input. This allows the controller to compensate for disturbances and uncertainties in the system.

Some of the most common open-loop control techniques for dynamical systems with friction and impacts include:

* Bang-bang control: This is a simple control technique that switches between two fixed control inputs. * Sliding mode control: This is a more sophisticated control technique that uses a sliding surface to control the system.

Some of the most common closed-loop control techniques for dynamical systems with friction and impacts include:

* PID control: This is a simple feedback control technique that is often used to control linear systems. * State feedback control: This is a more sophisticated feedback control technique that uses the state of the system to determine the control input. * Optimal control: This is a control technique that minimizes a cost function over a specified time period.

Modeling, analysis, and control of dynamical systems with friction and impacts is a challenging but important area of research. The techniques that have been developed for these systems have the potential to improve the safety and performance of a wide variety of applications.

As the use of these systems continues to grow, the need for effective modeling, analysis, and control techniques will only increase.

Dynamical Systems With Friction And Impacts Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts (World Scientific On Nonlinear Science A 92)