Ball, Helton, and Walker (BHW) derived the nonlinear dissipative controller formulas with the assumption implying that no stable mode uncontrollable from the exogenous input. The assumption is more restrictive than that considered in DGKF. In this paper, we address the numerical difficulty encountered by BHW’s controller formulas when the assumption is not satisfied. Next, we propose a modified nonlinear dissipative controller and successfully remove the numerical difficulty. We also show that the linear version of the proposed controller formulas is identical to the DGKF controller. An example is given to demonstrate constructing the proposed controller and simulating the closed-loop pulse responses.
A Computational Issue and Modified Formulas for Nonlinear Dissipative Controllers
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division, November 16, 2000; final revision, November 25, 2002. Associate Editor: S. Nair.
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Hu, S., Yang , P., and Chang , B. C. (September 18, 2003). "A Computational Issue and Modified Formulas for Nonlinear Dissipative Controllers ." ASME. J. Dyn. Sys., Meas., Control. September 2003; 125(3): 475–480. https://doi.org/10.1115/1.1590686
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