H ∞ control design to include nonlinearities. Second report: nonlinearities in equations of motion

Abstract

In our first report, a method to deal with the nonlinearity of saturation was proposed. A method of dealing with nonlinearity in equations of motion is proposed in this paper. The nonlinear equations of motion are expressed as variations of linear equations of motion. The nonlinear equations can be linearized around a specific point with a tangential plane or line. Accordingly, nonlinear equations effective in a certain domain can be obtained by variations in this tangential line. A control system with varying elements can be designed using the general H∞ control theory. As an example, we present a speed and heading changing system for large vessels at low speeds during berthing maneuvers, where the equation will vary during motion. The nonlinearity of the equations is caused by the speeds. The control system is essentially designed to be robust in disturbance and noise. In this example, the saturation in the propeller is also considered using the method proposed in the first report. The results show that the method proposed in this paper is effective.