Tag Archives: nonlinear control

Phase plane analysis and Matlab code toolbox

How to draw?

Given,

$\dot{x}_1=f_1(x_1,x_2)$

$\dot{x}_2=f_2(x_1,x_2)$

we can find the below equation

$\frac{dx_2}{dx_1}=\frac{f_2(x_1,x_2)}{f_1(x_1,x_2)}$

From $\frac{dx_2}{dx_1}$ , we can find the direction of the phase change at the point of $(x_1, x_2)$ .

Advantage:

It is an exact method. We can see the change of system’s state including transient response.
Simple graphical method. It is very intuitive and easy to understand its characteristics.

Limit:

Limited to the 2nd order system. It is expandable, but hard to visualize.

Reference

1. Lecture of Prof. Fernadez in Mech. Eng, The Univ. of Texas at Austin.

Feedback linearization control (FBL) for nonlinear system control proof, practical implementation, and easy example part 2

Feedback linearization control (FBL) for nonlinear system control proof, practical implementation, and easy example part1

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This article explains about Feedback linearization control (FBL) method for control of a nonlinear system. This is one of the easiest strategy to control nonlinear systems, but pretty powerful. The basic idea is that we can cancel control input by manipulating control input. The below is its proof.

This is the most basic concept to explain easily. If the nonlinear system is not fully controllable, we should use another strategy which finds reduced order manifold (ROM). About the more advanced technique and examples will be explained in the next articles.

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I am Youngmok Yun, and writing about robotics theories and my research.

My main site is http://youngmok.com, and Korean ver. is http://yunyoungmok.tistory.com.

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Youngmok Yun: Roboticist in Austin

Tag Archives: nonlinear control

Phase plane analysis and Matlab code toolbox

How to draw?

Advantage:

Limit:

Reference

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Feedback linearization control (FBL) for nonlinear system control proof, practical implementation, and easy example part 2

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Feedback linearization control (FBL) for nonlinear system control proof, practical implementation, and easy example part1

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How to draw?

Advantage:

Limit:

Reference

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