Unusual response of my state space model when the correct sign of gain is followed

Hi everyone,

I have a state space model as shown below and uses a simulink model as attached. I placed my poles on p1 = -0.2 + 10j; p2 = -0.2 - 10j; p3 = -0.4; p4 = -1 where poles p1 and p2 are computed from the specifications (i.e. settling time and overshoot). So I use the "place" command to achieve my K as given below. I checked the graph in Simulink but when I properly set K as positive (which will be fed to minus sign) I will then have a graph of my state variables as attached which have a very large oscillations. But when I reverse the sign of my K to be negative, I then get a more acceptable response of my state variables which should converge to zero with fewer oscillations. Do you have any idea why I am having this kind of scenario?

Will appreciate your reply on this.

if true
  A = 
          x1       x2       x3       x4
 x1   -7.249  -0.0399    -5.15    3.585
 x2   -4.574    4.502   -4.366   -1.568
 x3     3.77    16.12   -15.61    4.494
 x4   -9.898    8.374   -4.433   -6.432

B = 
          u1       u2
 x1   0.1564   0.0319
 x2  0.01735    -0.02
 x3    4.494    2.336
 x4   -1.427   -0.273

C = 
          x1       x2       x3       x4
 y1   -3.299   -2.166    0.037  -0.0109
 y2   0.2742   -2.151  -0.0104   0.0163

D = 
     u1  u2
 y1   0   0
 y2   0   0

K =

   23.9911  -14.8621   17.8311    2.2935
  -48.6838   31.9688  -43.0547    2.0584 
end

[Birdman]

Share the simulink model(Export to r2017a)

[Mr. NailGuy]

Hi cvklpstunc! I just shared the model to you. Thanks

[Walter Roberson]

The model did not get attached?

[Mr. NailGuy]

Hi Mr. Walter, I attached both the m file and the simulink model. Here, I am trying to get the response of my state space model in the m file. The model I discussed was to get the response of my 4 state variables in a step input of [1 0] and another [0 1] with non-zero initial conditions, meaning it needs to drive the system from non-zero to zero. It was fairly good when the feedback K was a negative sign, but when I reversed it, a very large oscillation occurs. The model below in this file is to get the 2 outputs, here the response should be from 0 to a steady state value, however, the oscillation are too big for the response. Would appreciate if you can look onto this.

[Mr. NailGuy]

Thanks everyone! I already solved it. Change my poles to a more valid one :)

Answer 1

[Birdman]

The reason for changing the system's response against assignment of poles can be understood from the attachment figure. What we want to see from this figure is the speed of the poles. The response goes to 2.5 and 1 belongs to the poles -0.4 and -1 respectively. Their settling times are seen in the figure. They are slow enough to disturb the dominant pole behaviour so that when the dominant poles can not show their effect as it should be. The response goes to 0.25 and 0.1 belongs to the poles -4 and -10 respectively. Now, this poles settles so quickly(0.1 times than the initial poles) they do not show any negative effect on the dominant poles. Therefore it is emphasized that additional poles have to be assigned 5 times further from the real part of the dominant poles.

[Mr. NailGuy]

Thanks cvklpstunc! You've helped a lot to make me understand the concepts better.