Block Manipulation and LTI Viewer Tutorial PDF

Preview

Summary

Block Manipulation and LTI Viewer Tutorial...

Description

University of Hertfordshire School of Engineering & Technology

Block Manipulation using MATLAB and Unit Step Responses with the LTI VIEWER .

MATLAB can manipulate Block Diagrams using a set of rules in much the same way as has been shown in lectures. The LTI Viewer (Linear Time Invariant) enables you to see the step response of a system given the transfer function without the need to develop a Simulink model. In this tutorial you will use MATLAB and the LTI Viewer to plot the step response of the following system.

G2 2

G4

G1 u +

+ 3 1+s

s+5 s

+

y

4 2+s

G3

1

2

Instruction Start MATLAB either by using the programme menu which you can get to by clicking the “start” button in the bottom left corner of the screen or by using the MATLAB shortcut button if available. Define G1 Syntax is: G=tf([num coef’s],[den coef’s])

3

4

where coefficients are in descending powers of s. Define G2, G3 and G4 Note G2 is actually a simple “gain” term so you do not strictly need to define the denominator. Since the numerators of G3 and G4 only have a constant term you do not need the square brackets. Start in the middle of the diagram and work outwards joining blocks together. e.g.

G2

+

G3

Single left click

In the “Command window” type: G1=tf([1 5],[1 0]) Remember to leave a space between coefficients otherwise MatLab would read the numerator as 15! Also note the 0 is required since the coefficient for s0 does not exist. Type: G2=tf(2) G3=tf(3,[1 1]) G4=tf(4,[1 2])

Type: G23=parallel(G2,G3) The result should read:

2 3 1+s

Command

+

2s + 5 ------s +1 Check the answer by hand using the block manipulation parallel rule given in lectures.

5

6

Now introduce G1 e.g.

Type:

G1

G23

G123=series(G1,G23)

s+5 s

2s + 5 1+s

NB the series command only allows two transfer functions in series to be joined together.

Introduce G4

Type: G1234=series(G123,G4)

7

Incidentally this is called the OPEN loop transfer function. Type:

Finally introduce the feedback y

u +

G=feedback(G1234,1)

G1234

8

Now open the LTI Viewer (LTI = Linear TimeInvariant)

The reason for the 1 is that there is no transfer function in the feedback path. Alternatively you can imagine a transfer function in the feedback but it would be unity, i.e. it does not change the feedback variable. Type: ltiview(G) After a few seconds the LTI Viewer window will appear with a unit step response.

9

Determine the steady state output (yss), time to maximum (tmax), and the % overshoot.

10

Show the 95% settling time. (i.e. time to settle within ±5% of the Steady State) (NB The default in Matlab is time to settle within ±2% of the steady state!)

11

Determine numerical values for the time response

Right click the white background of the plot again and left click “Steady State” under “Characteristics”. A blue dot will appear on the right of the plot. Move the cursor over the dot and the exact steady state output (“final value”) will be shown. Again right click the white background of the plot and left click the “Peak Response” under “Characteristics”. Another blue dot will appear on the plot corrsponding to the peak output. By moving the cursor over the blue dot the exact time to maximum and the % overshoot will be shown. Right click the white background of the plot follwed by a left click of “Properties…”. A “Property Editor” window will appear. Under the “Characteristics” menu(tab) in the Property Editor window, change “show settling time within” to 5%. (Remember to press enter after typing the new value!) Right click the white background of the plot again and left click “Settling Time” under “Characteristics”. Two dotted lines will appear either side of the steady state output with a blue dot showing the 95% settling time. By moving the cursor over the blue dot the exact settling time can be determined. Click the blue response curve on the plot (doesn’t matter where) and a box will appear with the time and “amplitude” (i.e. output value) at that point. Drag this point backwards and forwards along the blue response curve by moving the cursor whilst holding the left button down. Note the output values at 0.2 second intervals across the plot.

You should now be able to adapt this procedure to determine the transfer function of any system made up of several subsystems and produce a step response. All it takes is practice. Note the LTI Viewer can do much more as you will see later on your course. DAG...