Nonlinear Iterative Control of Manoeuvring Models for Transport over Water

This chapter addresses the problem of control design and implementation of a nonlinear marine vessel manoeuvring model. The chapter includes a thorough literature review of the current state of the art in the nonlinear control of marine vessels field. Then, the model will be presented; the authors will consider a highly nonlinear vessel 4 DOF model as the basis of the work. The control algorithm will be introduced providing the adequate mathematical description. The control algorithm here proposed consists of a combination of two methodologies: (i) An iteration technique that approximates the original nonlinear model by a sequence of linear time varying equations whose solution converge to the solution of the original nonlinear problem and, (ii) A lead compensation design in which for each of the iterated linear time varying systems generated, the controller is optimized at each time on the interval for better tracking performance. The control designed for the last iteration is then applied to the original nonlinear problem. Simulations and results will be presented and will show an accurate performance of the approximation methodology to the non linear manoeuvring model and also an accurate tracking for certain manoeuvring cases under the control of the designed lead controller. The main characteristics of the nonlinear systems response are the reduction of the settling time and the elimination of the steady state error and overshoot.

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