Synthesis of a multi-connected digital controller for a robotized vibration isolation platform based on $H_\infty$-optimization

We consider the problem of constructing multi-connected control of a robotic platform designed to protect technological objects and human operators from low-frequency influences on part of the moving base. The platform includes six drive mechanisms with stepper motors. The problem is solved by the methods of the modern theory of robust stabilization and optimal control based on $H_\infty$-optimization in the state space. We construct a mathematical model of the multidimensional system, taking into account the characteristics of electromechanical drives and using signals of feedback sensors as state variables. We give an example of synthesizing a multidimensional optimal stabilizing controller in the form of state feedback for a system with disturbances bounded in $L_2$-norm. We define the feedback control structure and obtain the matrix of feedback coefficients. We also show the results of mathematical modeling.