Time-Varying Controller Synthesis for Nonlinear Systems Subjected to Periodic Parametric Loadings

Abstract

Linear and nonlinear time-varying controller synthesis for systems represented by nonlinear dif ferential 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. Furthermore, 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 de sign 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. The linear control is used to stabilize and the nonlinear controller is employed to improve the response specifications of the system. The linear control de signs are based on the L-F transformation approach and the time-varying pole-placement approach, whereas the nonlinear controller is obtained using the Liapunov direct method. The responses obtained through the above approaches are compared and the advantages and disadvantages of the methods are discussed. Notice ably, the combination of linear and nonlinear controllers based on the L-F transformation approach has been found to have better performance and robustness characteristics than the other approach.