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16 Vibration Reduction via the Boundary Control Method 16.1 16.2 16.3 Siddharth P. Nagarkatti Lucent Technologies Introduction Cantilevered Beam System Model • Model-Based Boundary Control Law • Experimental Trials Axially Moving Web System Model • Model-Based Boundary Control Law • Experimental Trials 16.4 16.5 Flexible Link Robot Arm System Model • Model-Based Boundary Control Law • Experimental Trials Darren M. Dawson Clemson University Summary 16.1 Introduction The dynamics of flexible mechanical systems that require vibration reduction are usually mathematically represented by partial differential equations (PDEs). Specifically, flexible systems are modeled by a PDE that is satisfied over all points within a domain and a set of boundary conditions. These static or dynamic boundary conditions must. | 16 Vibration Reduction via the Boundary Control Method Siddharth P. Nagarkatti Lucent Technologies Darren M. Dawson Clemson University 16.1 Introduction 16.2 Cantilevered Beam System Model Model-Based Boundary Control Law Experimental Trials 16.3 Axially Moving Web System Model Model-Based Boundary Control Law Experimental Trials 16.4 Flexible Link Robot Arm System Model Model-Based Boundary Control Law Experimental Trials 16.5 Summary 16.1 Introduction The dynamics of flexible mechanical systems that require vibration reduction are usually mathematically represented by partial differential equations PDEs . Specifically flexible systems are modeled by a PDE that is satisfied over all points within a domain and a set of boundary conditions. These static or dynamic boundary conditions must be satisfied at the points bounding the domain. Traditionally PDE-based models for flexible systems have been discretized via modal analysis in order to facilitate the control design process. One of the disadvantages of using a discretized model for control design is that the controller could potentially excite the unmodeled high-order vibration modes neglected during the discretization process i.e. spillover effects and thereby destabilize the closed-loop system. In recent years distributed control techniques using smart sensors and actuators e.g. smart structures have become popular however distributed sensing actuation is often either too expensive to implement or impractical. More recently boundary controllers have been proposed for use in vibration control applications. In contrast to using the discretized model for the control design boundary controllers are derived from a PDE-based model and thereby avoid the harmful spillover effects. In contrast to distributed sensing actuation control techniques boundary controllers are applied at the boundaries of the flexible system and as a result require fewer sensors actuators. In this chapter we introduce the reader to the concept .
