TIME-VARYING CONTROLLER SYNTHESIS FOR STRUCTURES SUBJECTED TO PARAMETRIC PERIODIC LOADINGS

摘要

Linear and nonlinear time-varying controller synthesis for systems represented by nonlinear differential equations with periodic coefficients is addressed. A recently developed technique, based on the Liapunov-Floquet (L-F) theorem, is employed so that time-varying control gains can be obtained via time-invariant techniques. Further, a simple time-varying pole-placement approach for the design of linear control has also been devised for linear time-periodic systems. The robustness of the above control designs under structured perturbations of the nominal system matrices is studied. In many cases, the linear control design alone may not meet the desired performance specifications of the nonlinear periodic systems due to the time-varying nature of the problem. Therefore, to improve the controlled response of the nonlinear system, a nonlinear time-varying controller is designed and incorporated. In this paper, three control design methodologies are compared. In the first two methods, linear and nonlinear controllers are used to stabilize and improve the response specifications, respectively. The linear control designs are based on the L-F transformation approach and the time-varying pole-placement approach whereas, the nonlinear controller is obtained using the Liapunov's Direct Method. In the third approach, a purely nonlinear controller is employed to stabilize the system, even though the linear part is unstable. The responses obtained through the above three approaches are compared and the advantages and disadvantages of the methods are discussed. Noticeably, the combination of linear and nonlinear controllers based on L-F transformation approach has been found to have better performance and robustness characteristics than the other approaches. The gains obtained via purely nonlinear control is found to be large and sensitive to initial conditions of the system and therefore, does not represent a robust control design.