Synthesis of a Multi-Purpose Digital Control Law for the Furuta Pendulum
Abstract
This paper investigates the problem of designing digital feedback, which should provide stabilizing control of the Furuta pendulum for various operating regimes. The Furuta pendulum is chosen because it is a non-linear mechanical system with an unstable equilibrium position, and it is widely used in the scientific literature as a test object in experiments with various control algorithms. The regimes of operation of the pendulum are considered as follows: its own motion, motion under the influence of a constant disturbance, and motion caused by an oscillatory disturbance. For each of these regimes a set of the specific requirements on the quality of control system functioning in a closed loop are imposed. Taking into account the set of these requirements, it is very difficult to solve the problem of control law synthesis within the framework of classical methods. In this regard, this paper proposes another approach, which is based on the use of feedback with a specialized multi-purpose structure, that include the basic control law, an asymptotic observer, and a dynamic corrector. The adjustable elements of this structure are subject to search during the control synthesis process. Such approach allows us to decompose the general problem of control law design into a sequence of local sub-problems, which relates to one of the regimes of object operation. At the same time, in practice, modern control algorithms are implemented by digital computers, that implies the discreteness of the processed information flows. Therefore, the paper considers the problem of synthesizing a digital controller for Furuta's pendulum.
As a result of the research, the problems of searching the adjustable elements of the multi-purpose structure of the digital control law are formalized and solved, and the corresponding computational algorithms are developed. Numerical modeling of control processes has been carried out. The results of the experiments showed the efficiency and effectiveness of the proposed multi-purpose approach.
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