Modal control of piezolaminated anisotropic rectangular plates .2. Control theory

A general selective modal control design methodology is presented for piezolaminated anisotropic plate systems that utilizes selective modal transducers to realize any number of possible modal control strategies. A selective modal control design procedure is specified that defines a step-by step framework through which the structural and control subdesign processes are effectively integrated. Several conditions that sufficiently ensure asymptotic stability are derived and then discussed in the context of deriving selective modal control methods that are stability robust to modeling and implementation errors. Several selective modal control examples are then given in which selective modal transducers are designed and control laws chosen so as to allow for 1) the contributions of any given mode to the active energy extraction rate to be directly specified and 2) pole locations to be selectively and dynamically varied or 3) both pole locations and selective modal transducer design constants to be optimally determined. A numerical example is presented in which a stability-robust optimal selective modal control method is developed for a cantilevered anisotropic plate. Maintaining a linear feedback law, a single self-sensing selective modal transducer is employed whose design parameters were chosen to optimize the system response to a given initial excitation. Frequency and transient response analyses show a dramatic enhancement in system performance and accurately concur with theoretical predictions. The example serves both to illustrate the design process and to independently validate selective modal transducer and selective modal control theoretical results.