Synchronization of non-identical dynamic systems with robust equivalent control

Relevance of the study is caused by the need to improve the effectiveness of approaches to synchronization of non-identical interconnected dynamical systems under conditions of considerable uncertainty. The main aim of the study is to design a robust tracking system for the slave systems the reference the trajectory (task) for which is a synchronized output signal of the master system; to evaluate the implementation of specific dynamic and static parameters, such as settling time of the transient component and the allowable synchronization error; to study robust properties at deviation of slave system parameters from the nominal ones by ±50 %. Method of study: the method of Lyapunov function, automatic control theory, the elements of synchronization and chaos theory; simulation on Matlab/Simulink. The main feature of the method is the use of a new type of controls - "robust equivalent control" - to design robust control systems and to interchange interconnected slave systems without compensators of joints cross channels. Robust controller is the PDn-1 controller with adjustable gain. The possibility of infinite gain magnification without loss of stability allows suppressing general components of uncertain models of slave systems to an arbitrarily small value. This ensures a high tracking (timing) accuracy of the reference trajectory for a wide range of uncertainties. Results and conclusions. Numerical modeling of synchronization systems with different internally regular and chaotic oscillators has shown simplicity and high efficiency of the proposed approach. Really, the synchronization error can be reduced to an arbitrarily small value. However, this requires the use of high gain values ??of the regulator. High performance of robust dynamic mode is achieved. This is proved by the high concentration of beams of transient characteristics of slave systems in the vicinity of the nominal trajectory. The author managed to avoid the mathematical difficulties occur when synthesizing robust tracking systems. The disadvantages of the proposed methodology are reinforcement of the high-frequency interferences having immediate access to the controller as well as the use of output derivative to form PDn-1 controller. Moreover, not every object is capable of implementing the high gain.