Thursday, December 22, 2011

How to Analyze a Control System, Using Matlab Part 1

To analyse a system either mechanical or electrical circuits needseveral stages, as follows: 
  1. Determining the mathematical model of the system,
  2. Determining the Laplace equation of mathematical models,
  3. Illustrate the diagram blocks,
  4. Simplify the block diagram (optional),
  5. Analyze the characteristics of the system to the test signal (Transient-Response Analysis). Either mathematically or using Matlab. 

Here's an example of an electrical circuit analysis: 
An RLC Circuit indicated as shown below, and we will analyze the capacitor voltageas of the output. The following stages of completion: 

1. Determine the mathematical model of the system 
    By using Kirchhoff's voltage law on the left of the closed circuit path, obtained :

ei (t) = 10 i(t) + 4 di(t)/dt + eo(t)

    and capacitor voltage: 
eo (t) = 1/0.05 ∫ i(t) dt

2. Determine the Laplace equation, with zero initial conditions:

Ei (s) = (10 + 4s) I(s) + Eo (s)

I (s) = ( 1 / 4s+10 ) ( Ei (s) - Eo (s) )

Eo (s) = (1/0,05s) I(s)

3. From the Laplace equation that we get, can be illustrated a block diagram of the relationship of each equation that we get. Block Diagram images can be seen in the image below.

4. Simplify the block diagram (optional)
The simplified goal is to obtain transfer function from the system. To simplify the block diagram, there are several methods:
a. The simplification method is mathematically
b. Block Diagram Reduction
c. Signal flow

For this occasion I did not simplify the block diagram has been obtained due to the analysis in the next post I will be using MATLAB, so without a simplified we can still see the relationship between input and output.
5. Analyze the characteristics from the system against test signals (Transient Response Analysis)
Either mathematically or using Matlab.

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