Linearization Of Nonlinear Control Systems Research Articles

Optimization of driving modes of a diesel train with traction asynchronous drive based on geometric control theory

The need to produce more economical traction rolling stock for the railways of Ukraine led to the creation of a modern diesel train with a traction asynchronous drive and an on-board measurement and information computing system for the transportation of passengers, which improves the performance of the energy equipment of the stock. An attempt was made to optimize the control laws of a diesel train using a geometric control theory, which allows replacing the synthesis of optimal control laws for objects described by nonlinear systems of ordinary differential equations, linearization of nonlinear control systems using feedback and the application of a well-developed linear control theory systems The advantages and disadvantages of the mentioned approach are analyzed. Bibliography: 12 titles. Key words: diesel train, traction asynchronous drive, geometric control theory, linearization of nonlinear control systems using feedback.

State feedback linearization of nonlinear control systems on homogeneous time scales

The paper addresses the state feedback linearization problem for nonlinear systems, defined on homogeneous time scale. Necessary and sufficient solvability conditions are given within the algebraic framework of differential one-forms. The conditions concerning the exact dynamic state feedback linearization are equivalent to the property of differential flatness of the system. An output function which defines a right invertible system without zero-dynamics is shown to exist if and only if the basis of some space of one-forms can be transformed, via polynomial matrix operator over the field of meromorphic functions, into a system of exact one-forms. The results extend the corresponding results for the continuous-time case.

Static state feedback linearization of nonlinear control systems on homogeneous time scales

The paper addresses the problem of static state feedback linearization for nonlinear control systems defined on homogeneous time scales. Necessary and sufficient conditions for generic local linearizability of the considered systems by static state feedback and state transformation are presented in terms of a sequence of subspaces of differential one-forms related to the system.

Obstacle avoidance of manipulators with rate constraints

The paper presents a new control method which achieves autonomous obstacle avoidance for manipulators with rate constraints. More precisely, in order to achieve the autonomous obstacle avoidance, we exploit the freedom of the coordinate transformation for feedback linearization of nonlinear control systems. At the same time, we cope with the rate constraints by adopting the state-dependent time scale transformation. Furthermore, we apply this method to an actual two-link robot manipulator, and evaluate its effectiveness by experiment, which is the most important part of the paper.

Exact linearization of nonlinear systems: trajectory tracking with bounded controls and state constraints

The exact linearization of nonlinear control systems provides a useful method for designing feedback controllers based on the linear model in which the nonlinear plant is transformed. This paper deals with two drawbacks involved in this method when applied to trajectory tracking problems: the control must be bounded, and the evolution of the state variables must lie within a determined region of the state space. Conditions for fulfilling both constraints are given, and an application to a robot manipulator is shown.

Approximate linearization of nonlinear control systems

The paper address the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback. The main result proved is that if the fast k d- relative degrees are equal to each other, then the input-output response of a nonlinear control system can be linearized to degree k. Any system having linear d- relative degree can be linearized to any degree by dynamic feedbacks. One example of signal tracking using dynamic feedback linearization method to improve the performance is also given.

On approximate linearization of nonlinear control systems

AbstractA method for the approximate linearization of nonlinear control systems based on the ‘state‐space exact linearization’ method is presented. An explicit procedure, both for the single‐input and for the multiple‐input case, is given, which is straightforward to implement.

Linearization of Nonlinear Control Systems by Recursive Transformations: An Algebraic Approach

In this paper. a recursive procedure for the algebraic construction of a transformation that linearizes a given nonlinear control systemis proposed. Explicit algebraic formulae for this construction are obtained via a special notation; they allow the construction to be automatically performed in a computer without the resort to symbolic languages. The subject of this paper is of practical interest in the application of transformation theory of nonlinear control systems.

Analysis of Statistical Linearization of Nonlinear Control Systems

Analysis of Statistical Linearization of Nonlinear Control Systems

Statistical Linearization of Non-linear Control Systems

ABSTRACTThe analysis of Non-linear Control Systems with Random inputs is of very great practical interest. In such an analysis statistical linearization techniques are useful since they are simple to use, being based on the linear transformation of random functions. Mathematical methods for this transformation are quite straightforward. This technique results in the non-linear element being replaced by an equivalent linear gain. There are methods available for the analysis of ‘zero-memory’ or interialess non-linearities. A method is proposed for the analysis of an important ‘memory’ type non-linearity, a relay with hysteresis. This type of non-linearity is important in practice since relay or on-off servos are an important class of systems.