ABSTRACT
The paper presents an adaptive multivariable control system for a Multi‐Input, Multi‐Output (MIMO) nonlinear dynamic process. The problems under study are exemplified by a synthesis of a course angle and forward speed control system for the nonlinear four‐Degrees‐of‐Freedom (4‐DoF) mathematical model of a single‐screw, high‐speed container ship. The paper presents the complexity of the assumed model to be analyzed and a synthesis method for the multivariable adaptive modal controller. Due to a strongly nonlinear nature of the ship movements equations a multivariable adaptive controller is tuned in relation to changeable hydrodynamic operating conditions of the ship. In accordance with the given operating conditions controller parameters are chosen on the basis of four measured auxiliary signals. The system synthesis is carried out by linearization of the nonlinear model of the ship at its nominal operating points in the steady‐state and by means of a pole placement control method. The final part of the paper includes results of simulation tests of the proposed control system carried out in the MATLAB/Simulink environment along with conclusions and final remarks.
1 INTRODUCTION
Nonlinear control systems are commonly encountered in many different areas of science and technology. In particular, problems difficult to solve arise in motion and/or position control of various vessels such as drilling platforms and ships, sea ferries, container ships, etc. Complex motions and/or complex‐shaped bodies moving in the water, and in the case of ships also at the boundary between water and air, give rise to resistance forces dependent in a nonlinear way on velocities and positions, thus causing the floating bodies to become strongly nonlinear dynamic plants.
5 CONCLUSIONS
In the paper an adaptive control system for the nonlinear MIMO plant was proposed and tested. The utilized adaptive gain scheduling modal controller allows one to control a strongly nonlinear process, here the model of a container vessel. The synthesis of the controller is based on the linearization of a nonlinear ship model in operating points corresponding to the set of 992 typical operating regimes. The adaptive controller parameters vary in a stepwise way on the basis of auxiliary signals measured during ship operation. The presented example of multivariable control of the ship, shows efficiency of this method and the appropriateness of its use to the direct control or as a part of more complex control systems, e.g. a model loop in the MFC control structure (Dworak et al. 2012b).
