Difference between revisions of "Scilab/C4/Control-systems/English"

1. Define a continuous time system: second and higher order
2. Plot response to step and sine inputs
3. Do a Bode plot
4. Study numer and denom Scilab functions
5. Plot poles and zeros of a system

• Ubuntu 12.04 as the operating system and
• Scilab 5.3.3 version

For Scilab, please refer to the Scilab tutorials available on the Spoken Tutorial website.

So, first we have to define complex domain variable 's'.

s = poly(0, ’s’)

Here type:

s equal to poly open paranthesis zero comma open single quote s close single quote close paranthesis

and press Enter.

s = %s

and press Enter.

On the console window, type:

s equal to percentage s

and press Enter.

Use the Scilab function ’syslin’ to define the continuous time system.

G of s is equal to 2 over 9 plus 2 s plus s square

Use csim with step option, to obtain the step response and then plot the step response.

sysG = syslin(’c’,2/(sˆ2+2*s+9))

Here type:

sys capital G equal to syslin open paranthesis open single quote c close single quote comma two divided by open paranthesis s square plus two asterik s plus nine close paranthesis close paranthesis

Here c is used, (because) as we are defining a continuous time system.

Press Enter.

2 over 9 plus 2 s plus s square

t=0:0.1:10;

Press Enter.

t equal to zero colon zero point one colon ten semicolon

Press Enter.

y1 = csim(’step’, t, sysG);

Press Enter.

y one is equal to c sim open paranthesis open single quote step close single quote comma t comma sys capital G close the paranthesis semicolon

Press Enter.

plot(t, y1);

Press Enter.

plot open paranthesis t comma y one close paranthesis semicolon

Press Enter.

Sine inputs can easily be given as inputs to a second order system to a continuous time system.

u2=sin(t);

Press Enter.

Type

U two is equal to sine open paranthesis t close paranthesis semicolon

Press Enter.

Press Enter.

y two is equal to c sim open paranthesis u two comma t comma sys capital G close the bracket semicolon

Press Enter.

Here we are using sysG, the continuous time second order system we had defined earlier.

Press Enter.

plot open paranthesis t comma open square bracket u two semicolon y two close square bracket close paranthesis

Make sure that you place a semicolon between u2 and y2 because u2 and y2 are row vectors of the same size.

Press Enter.

This plot shows the response of the system to a step input and sine input. It is called the response plot.

As expected,

• the output is also a sine wave, and
• there is a phase lag between the input and output

• Amplitude is different for the input and the output, as it is being passed through a transfer function.
• This is a typical under-damped example.

Please note command 'f r e q' is a Scilab command for frequency response.

Do not use f r e q as a variable !!

fr = [0.01:0.1:10]; // Hertz

Press Enter.

f r is equal to open square bracket zero point zero one colon zero point one colon ten close square bracket semicolon.

Press Enter.

The frequency is in Hertz.

bode open paranthesis sys capital G comma fr close paranthesis

and press Enter.

The bode plot is shown

We have an over-damped system p equal to s square plus nine s plus nine

Let us plot step response for this system.

p=s^2 +9*s+9

Press Enter.

Type this on your Scilab console.

p is equal to s square plus nine asterik s plus nine

and then press Enter.

Press Enter.

sys two is equal to syslin open paranthesis open single quote c close single quote comma nine divided by p close paranthesis

and press Enter.

Then type

t equal to zero colon zero point one colon ten semicolon

Press Enter.

y is equal to c sim open paranthesis open single quote step close single quote comma t comma sys two close the paranthesis semicolon

Press Enter.

Then type plot open paranthesis t comma y close paranthesis

Press Enter.

The response plot for over damped system is shown.

and press Enter.

Roots of p

and press Enter.

These roots are the poles of the system sys two

G of s is equal to 2 over 9 plus 6 s plus s square which is a critically damped system

Then G of s is equal to two over 9 plus s square which is an undamped system

G of s is equal to 2 over 9 minus 6 s plus s square which is an unstable system

Check response to sinusoidal inputs for all the cases and plot bode plot too.

Switch to the Scilab Console Window and type this on your Scilab Console

--> sys3 = syslin(’c’,s+6,sˆ2+6*s+19) and press Enter

Alternatively:

Type this on your Console

--> g = (s+6)/(sˆ2+6*s+19) and press Enter

Then type this on your Scilab Console

--> sys4 = syslin(’c’,g) and press Enter

For a general transfer function, the numerator and denominator can be specified separately. Let me show you how.

Type on your console

sys three is equal to syslin open paranthesis open single quote c close single quote comma s plus six comma s square plus six asterik s plus nineteen close paranthesis

Press Enter

Another way of defining a system, is to type

g is equal to open paranthesis s plus six close paranthesis divided by open paranthesis s square plus six asterik s plus nineteen close paranthesis

Press Enter.

Then type this on your console

sys four is equal to syslin open paranthesis open single quote c close single quote comma g close paranthesis

Press Enter.

six plus s over 19 plus six s plus s square

Its numerator and denominator can be extracted by various ways.

Sys of two , numer of sys or numer of g gives the numerator.

The denominator can be calculated using sys(3) or denom of sys functions.

The syntax is p l z r of sys

The plot shows x for poles and circles for zeros.

--> sys3(2) and press Enter

Type this on your Scilab console.

sys three open paranthesis two close paranthesis

Press Enter.

This gives the numerator of the rational function 'sys three' that is 6 + s

numer open paranthesis sys three close paranthesis

The numerator of sys three is shown.

sys three open paranthesis three close paranthesis. Press Enter.

The denominator of the function is shown.

denom(sys3) >> Press Enter.

Press Enter.

plzr(sys3) >> Press Enter.

Press Enter.

It shows cross and circle' for poles and zeros of the system respectively.

It is plotted on the complex plane.

• Define a system by its transfer function.
• Plot step and sinusoidal responses.
• Extract poles and zeros of a transfer function.

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