Linear Matrix Inequalities in multivariable ship’s steering

Abstract

This paper explains the basics of the Linear Matrix Inequalities (LMI), with examples of simulations and calculations created in Matlab/Simulink programming environment where the controlled plant is the “Blue Lady” ship model. First chapter of this paper gives a short overview of publications describing the use of Linear Matrix Inequalities method. Second chapter contains basic definitions and equations for the LMI method. Chapter three presents the use of LMI method for ship control by describing controller synthesis for the “Blue Lady”. Chapter four compares the operation of two controllers, the first one consisting of three independent proper adjusted PID controllers and the second one being a multivariable LMI controller. Finally conclusions from the above comparison are drawn.

Improvement of control precision for ship movement using a multidimensional controller

“…The simulation model is based on papers of W. Gierusz as shown in [19,20]. It belong to 3DOF class, and takes into account movement on a single plane without including list, trim and draught during Silm Lake trials as described in [21,22].…”

Consistent Design of PID Controllers for an Autopilot

“…The other factors require the application of nonlinear control methods developed in academic communities and tested on models or training ships. The first group of such methods applies control theory extensions, namely (sample references given only): model reference adaptive control [3], linearization by feedback [4], H∞ robust control and matrix inequalities [5,6], sliding mode [7,8], and backstepping [9,10]. The second group refers to solutions acquired from artificial intelligence, such as: fuzzy logic [11], neural networks [12] or other [13].…”

Control of Dynamic Positioning System with Disturbance Observer for Autonomous Marine Surface Vessels

“…The further development of control algorithms used in dynamic positioning systems was associated with the emergence of alternative control strategies such as robust control [55][56][57][58][59][60][61][62][63], modal control [64,65], adaptive control [66] and model predictive control [46,[67][68][69]. Other solutions for control systems were related to the developments taking place in non-linear control [70,71] using methods such as backstepping [72][73][74][75][76][77][78], dynamic surface control [79,80], active direct surface control [81], nonlinear PID control [18,82,83], port-Hamiltonian framework [84] and sliding mode control [85][86][87].…”