Modal synthesis of observers of state variables of ship dynamical systems

Abstract

The purpose of the work is to increase the information content of ship control systems through the use of dynamic observers, which are, in essence, mathematical information sensors and allow you to fully restore the vector of state variables of the object model with high accuracy by measuring the output vector of a smaller dimension. An algorithm for the synthesis of observers based on the modal method of parametric evaluation of their model is proposed. It provides obtaining the parameters of the regulator according to the given spectra of the matrices of the state of the observed system and the object by means of the Control Toolbox of the MATLAB computing environment. The use of the modal method (subject to the conditions of observability and controllability) guarantees the stability of observers, which allows them to be used for stable and unstable observed objects and systems. The algorithm of modal synthesis of observers is suitable for increasing the information content of a wide range of ship dynamic systems and, above all, control systems for ship energy complexes and their components. These include autopilots, control systems for ship power plants and their elements, dynamic complexes of satellite and inertial navigation systems and positioning of moving objects in remote control conditions, monitoring and safety tools, identifiers, etc. It has been shown that in the conditions of digital transformation, the use of observers dramatically improves the quality and reduces the time for modeling the dynamics of ship systems and energy complexes operated under conditions of external disturbances, which makes it possible to improve the algorithms for estimating state variables of a class of autonomous objects modeled by nonlinear equations that allow the transition in the working area to quasi linear models with time-invariant parameters. The proposed algorithm is demonstrated by the example of the synthesis of a three-dimensional observer for the control system of a supertanker with deadweight of 150 thousand tons. The simulation of the control object is performed with an input signal of triangular shape, which most fully corresponds to the real control signal, and it is implemented in the form of a program compiled in MATLAB codes. The obtained values of state variables and errors of their recovery correspond to the specified speed and the required stability of the control system.