How to give a step input with special shape?

Hi everyone, I am trying to give a step tracking input for an aircraft pitch transfer function. Attached you can find the type of input I am looking for. I don't know how to define this input to Matlab. Thanks in advance.

Answer 1

[John BG]

1.

As you may have already considered when writing your question, attempting to define the step the way you have, without considering first the system to test, has certain elemental uncertainty:

have you included enough samples so that the system you want to test really sees a step, not a pulse?

is the transition edge sharp enough?

2.

To prevent this, MATLAB has the function step that focuses on correctly defining the system, rather than the step itself:

following, MATLAB start example for command step

define the system

a = [-0.5572,-0.7814;0.7814,0];
b = [1,-1;0,2];
c = [1.9691,6.4493];
sys = ss(a,b,c,0);

test the system with a step

step(sys)

3.

MATLAB includes a Linear System Analyser that you can launch with command linearSystemAnalyzer

4.

Among the many functions of interest in the Control System Toolbox, stepinfo displays the step related parameters at the output of the system, for instance the system defined with the following transfer function (from MATLAB help)

sys = tf([1 5],[1 2 5 7 2]);
S = stepinfo(sys,'RiseTimeLimits',[0.05,0.95])

modifies the ideal input step resulting into a real step with the following parameters

S = 

          RiseTime: 7.4454
      SettlingTime: 13.9378
       SettlingMin: 2.3737
       SettlingMax: 2.5201
         Overshoot: 0.8032
        Undershoot: 0
              Peak: 2.5201
          PeakTime: 15.1869

5.

A few links of interest:

step:

https://uk.mathworks.com/help/ident/ref/step.html?searchHighlight=step&s_tid=doc_srchtitle

transfer function:

https://uk.mathworks.com/help/control/ref/tf.html?>searchHighlight=tf&s_tid=doc_srchtitle

stepinfo

https://uk.mathworks.com/help/control/ref/stepinfo.html?s_tid=srchtitle

state space model

https://uk.mathworks.com/help/control/ref/ss.html

specify discrete transfer functions with filt

https://uk.mathworks.com/help/control/ref/filt.html

.

if you find these lines useful would you please mark my answer as Accepted Answer?

To any other reader, if you find this answer of any help please click on the thumbs-up vote link,

thanks in advance for time and attention

John BG

<mailto:[e-mail] [e-mail]>

Answer 2

[hosein Javan]

hello. I have attached a simulink file. unzip it and open it. you only have to define your transfer function.

[hosein Javan]

also you can do it by matlab code:

syms s t
laplace(heaviside(-t+10))    %heaviside=u(t):step
tf=1/(s+1)   %define your transfer function here
response=ilaplace(((1-exp(-10*s))/s)*tf)
ezplot(t,response)