A method for calculating all periodic solutions and their domains of attraction for flexible systems under nonlinear feedback control is presented. The systems considered consist of mechanical systems with multiple flexible modes and a relay type controller coupled with a linear or nonlinear control law operating in a feedback configuration. The proposed approach includes three steps. First, limit cycle frequencies and periodic fixed points are computed exactly, using a block-diagonal state-space modal representation of the plant dynamics. Then the relay switching surface is chosen as the Poincaré mapping surface and is discretized using the cell mapping method. Finally, the region of attraction for each limit cycle is computed using the cell mapping algorithm and employing an error based convergence criterion. The method is demonstrated on four application examples, each with a different type of relay and/or control law to demonstrate the versatility and accuracy of the method.
|Commitee:||Ioannou, Petros, Yang, Bingen|
|School:||University of Southern California|
|School Location:||United States -- California|
|Source:||DAI-B 72/10, Dissertation Abstracts International|
|Keywords:||Discontinuous control, Flexible structures, Limit cycles, Relay feedback control|
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