Abstract
This paper presents a study of linear control systems based on exact feedback linearization and approximate feedback linearization. As exact feedback linearization is applied, a linear controller can perform the control objectives. The approximate feedback linearization is required when a nonlinear system presents a noninvolutive property. It uses a Taylor series expansion in order to compute a nonlinear transformation of coordinates to satisfy the involutivity conditions.
Highlights
The control theory of nonlinear system has been receiving increasing attention in recent years, both for its technical importance as well as for its impact in various fields of application
Among the possible techniques used to deal with the nonlinear control problem, this paper studies the approximate feedback linearization technique for controlling nonlinear systems
It can be seen that for the Taylor linearization, the controller managed to stabilize the inverted pendulum for x3 0 ≤ 41◦, while with the approximate linearization, the controller managed the stabilization for x3 0 ≤ 53◦, which represents an increase in the inverted pendulum operation region
Summary
The control theory of nonlinear system has been receiving increasing attention in recent years, both for its technical importance as well as for its impact in various fields of application. When the nonlinear effects of systems become significant, nonlinear control techniques generally fail to produce the desired performance. Among the possible techniques used to deal with the nonlinear control problem, this paper studies the approximate feedback linearization technique for controlling nonlinear systems. The applications of these techniques are illustrated through some examples. The first condition indicates the system controllability in which the vector fields {g, adfg, · · · , adfn−1g} are equivalent to the controllability matrix for linear systems b Ab A2b · · · An−1b 1. The second involutivity condition enables to find out a new vector of linear state through the states feedback
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