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Modal synthesis of estimator of unmeasured state variables for ship course stabilization system

The purpose of the study is to apply automation technologies and digitalization in estimating the unmeasurable variables of the ship course stabilization system to control the high-tech software and hardware and, thus, to intensify the use of ships at a qualitatively new level, as well as to improve the reliability and efficiency of their operation. It has been stated that estimating the vector of state variables in real time requires to use methods and computational algorithms 
of stochastic and, in particular, binomial filtering. It is emphasized that for improving the reliability and accuracy of estimating the parameters of the system under perturbations of the roll angle, angular rotation speed or measurement noise there are required compromise solutions that take into account the required values of the system's speed and stability. It is shown that digitalization of mathematical and physical ship models, producing the adequate decisions, taking into account a wide range of environmental influences and navigation conditions allow to synthesize ship control complexes in the class of digital predictive systems with a transition to the control of unmanned objects. There has been considered the modal method of synthesis of the vector estimator of the state of full dimension (Kalman observer) which can obtain estimates of unmeasured state variables of the course stabilization system with measured output and input of the system by developing a model of the state of the extended system ‘object–observer’, which ensures stability of the ship on the course. A model and an algorithm for estimating unmeasured state variables by using binomial filtering algorithms, matrix laboratory tools and computer modeling technologies in the MATLAB environment are proposed. The proposed algorithm for the synthesis of a vector evaluator of unmeasured state variables is implemented in the form of a program compiled in MATLAB codes and demonstrated in calculating a two-dimensional dynamic observer for an unstable object of control. The obtained estimates of unmeasured variables, as well as the results of modeling the dynamic reactions of the course stabilization system correspond to the specified speed and stability transient processes of the ship object when transferring it into the steady state under the new initial conditions.