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Course keeping for ships is the core of automatic navigation in sea transportation. Much work has concentrated on developing novel control strategies for closed loop systems. We have turned our attention the other way to improve the control performance of marine autopilots in this work by "modulating" the control error using a sine function while the construction of the controller is not changed. The nonlinear feedback signal thus obtained is sent to the controller to replace the control error itself, which used to be the deviation between the output response and the reference input of the system. Such a control scheme is called "nonlinear feedback control" hereafter. Theoretical analysis by using a describing function and robust control theory shows that the same control quality is guaranteed with minor control actions for the nonlinear feedback scheme. Simulation experiments were carried out for the ship Yulong of Dalian Maritime University. It is shown that the method postulated in this paper has advantages of safety and energy saving in navigation; the maximum initial rudder angle is reduced by 31·2% with satisfactory control effect.2. Closed-loop gain shaping. 3. Course keeping. 4. Nonlinear feedback. 5. Sine function.6. Describing function.

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Course keeping for ships is vital for automatic navigation in marine transportation. To improve the control effect and reduce the energy output of the controller, this article proposes an improved concise backstepping controller based on a Lyapunov candidate function by introducing a nonlinear function of course error to replace the course error itself in the feedback loop. The procedure of nonlinear controller design has been reduced from two steps to one step using information from controlled plant to construct the Lyapunov candidate function. Compared with the pure backstepping control, the proposed improved algorithm reserves the nonlinear item of the system, and possesses a strong disturbance rejection ability and robustness to the mathematical model uncertainty. The algorithm given here has advantages of simplified construction method, satisfactory control effect, robustness and energy saving.