At present, nonlinear synthesis methods that use the original nonlinear model are gaining popularity. Such an approach makes it possible to form a control not only in the vicinity of the linearization point, but in a larger domain of change in the state variables, which makes it possible to take into account the behavior of the object most fully in the control law. Linear synthesis methods, such as the modal synthesis method, synthesis methods using polynomial decomposition, optimization algorithms, construction of PID regulators, and others are used for models linearized in the vicinity of a certain point. But this representation does not describe all the properties of the operation of the source object. In order to apply linear synthesis methods for nonlinear objects, it is more appropriate to use feedback linearization, which leads the behavior of the original object to a linear form. The essence of the method lies in the search for such compensating control, in which the behavior of a closed system will correspond to the behavior of the system described by linear differential equations. Then, for the synthesized system, it becomes possible to calculate the regulator by linear synthesis methods. In the present work a review of previous works on this topic was carried out. Various single-channel nonlinear objects are considered; an object containing a trigonometric function; the possibility of obtaining a different solution of the problem of linearization by nonlinear feedbacks for the same object is shown. Using the example of the pendulum subsystem of the object model, an inverted pendulum on the trolley produces a synthesis of the control system with a modal regulator and a full-order observer, where in one case the higher derivative of the output quantity was used, and in the other there is not; the possibility of using this method for multichannel objects (two and three channel), nonlinear on the output, is shown; and also shows a formalized method for finding linearizing controls based on algebra and Lie brackets.

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