A Computer-Oriented, Parameter-Space Approach to the Synthesis of Nonlinear Control Systems

1971 ◽  
Vol 93 (2) ◽  
pp. 67-72 ◽  
Author(s):  
D. P. Garg
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Control Systems ◽  
Parameter Space ◽  
Limit Cycles ◽  
Nonlinear Control Systems ◽  
Digital Computation ◽  
Synthesis Procedure ◽  
Systematic Synthesis ◽  
Space Approach

A systematic synthesis procedure is developed for ensuring an absence of limit cycles in nonlinear systems. Compensator parameter plots, subject to specified constraints, are generated in parameter planes. These plots can be combined to yield design surfaces. The proposed approach is oriented for digital computation but can be adapted easily to a paper and pencil equivalent. The procedure is illustrated by two design examples.

Stabilität von Grenzschwingungen bei nichtlinearen Regelungssystemen mit zwei Nichtlinearitäten / Stability of limit-cycles in nonlinear control systems with two-nonlinearities

1974 ◽  
Vol 22 (10) ◽  
Author(s):  
L. Sebastian ◽  
Μ. Voicu
Keyword(s):  
Nonlinear Control ◽  
Control Systems ◽  
Limit Cycles ◽  
Nonlinear Control Systems ◽  
Wird Eine

In der Arbeit wird eine graphisch-analytisch anwendbare Methode aufgezeigt, die es ermöglicht, Aussagen über das Stabilitätsverhalten von Grenzschwingungen zu machen. Die auftretenden Grenzschwingungen selbst werden nach der Methode der harmonischen Balance [1] bestimmt

A New Approach to Popov Criterion for Stability Analysis of Nonlinear Control Systems

2012 ◽  
Vol 463-464 ◽  
pp. 1549-1552
Author(s):  
Ivan Svarc
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Control Systems ◽  
Transfer Functions ◽  
Sufficient Conditions ◽  
Nonlinear Control Systems ◽  
Engineering Practice ◽  
The Stability ◽  
The Given

The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The tables includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically. Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.

scholarly journals Towards Design of Quasilinear Gurvits Control Systems

2019 ◽  
Vol 18 (3) ◽  
pp. 678-705
Author(s):  
Anatoly Gaiduk
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Equilibrium Point ◽  
Control Systems ◽  
Design Problem ◽  
Systems Design ◽  
Nonlinear Control Systems ◽  
Proved Theorem ◽  
Control Systems Design ◽  
Nonlinear Plants

The design problem of control systems for nonlinear plants with differentiated nonlinearity is considered. The urgency of this problem is caused by the big difficulties of practical design of nonlinear control systems with the help of the majority of known methods. In many cases, even provision by these methods of just stability of equilibrium point of a designing system represents a big challenge. Distinctive feature of the method of nonlinear control systems design considered below is the use of the nonlinear plants models represented in a quasilinear form. This form of the nonlinear differential equations exists, if nonlinearities in their right parts are differentiated across all arguments. The quasilinear model of the controlled plant allows reducing the design problem to the solution of an algebraic equations system, which has the unique solution if the plant is controlled according to the controllability condition provided in the article. This condition is similar to the controllability condition of the Kalman’s criterion. Procedure of the nonlinear control systems design on a basis of the plant’s quasilinear models is very simple. Practically, it is close to the known polynomial method of the linear control systems design. The equations of the nonlinear systems designed with application of the plant’s quasilinear models also can be represented in the quasilinear form. The basic result of this article is the proof of the theorem and the corollary from it about conditions of the asymptotical stability at whole of the equilibrium point of the nonlinear control systems designed on a basis of the plant’s quasilinear models. For the proof of the theorem and consequence, the properties of simple matrixes and known theorems of stability of the indignant systems of the differential equations are used. A way of the stability research of the equilibrium point of the quasilinear control systems based on the proved theorem is illustrated by numerical examples. Computer simulation of these systems verifies correctness of the hypoyhesis of the proved theorem. Obtained results allow applying the method of nonlinear systems design on a basis of the quasilinear models for creation of various control systems for plants in power, aviation, space, robotechnical and other industries.

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