is it possible to use step for a state space dynamic system with multi input?

Hi all I have a dynamic system with A, B, C, and D that identify the state space model, this system has two inputs one is a constant value while the other is a vector with data that changes with time. can i use step function for two input channel or can I identify the two inputs directly to B and C matrices. Thanks in advance

   A = [0 1 0 0;a1 a2 a3 a4;0 -1 0 1;0 a5 a5 a7];
   B = [-1 0 0 0]';
   C = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1; 0 -1 0 1]; 
   D = 0;
   q = ss(A,B,C,D);

where a1,....., a7 are a constant values.

Answer 1

[Sebastian Castro]

Yes. You can use stepDataOptions to define an option set and then pass it into the step function.

For a 2-input system, you can say:

opts = stepDataOptions('InputOffset',[1 0],'StepAmplitude',[0 2])
step(sys,opts)

This means that the first input is a constant value (offset 1, amplitude 0), and the second input is a step that starts at 0 and ends at 2.

Alternatively, you could use the lsim function to define your own input vector and have it do whatever you'd like.

Sebastian

[Muna Shehan]

Thanks for your response. what can I do if one input is a force (constant value) and the other input is displacement (with a certain amplitude value). I appreciate your kindly help. Regards

[Sebastian Castro]

I think whatever the inputs map to would depend on your state-space model.

Either way, you should be able to either use stepDataOptions/step or lsim to define an input trajectory.

[Muna Shehan]

Thanks for your response. So in my state-space model, can I use the first input channel (the constant force ( f) directly in the state-space model) and identify the second input channel ( step input ( r) with amplitude 0.1 m) directly in the state space model. and in this case B matrix will be

B = [-f 0; 0 0;0 r; f 0 ]

 Can I do that ?. Thanks in advance

[Sebastian Castro]

Yeah, you can do that. Each column of the B matrix is a separate input, and it makes sense that they act on separate states (rows).

[Muna Shehan]

Thanks again for your help. When I try to fit B matrix I get this error. Kindly, can you assist me to figure out the error. Best Regards

ms = 325;              
mus = 65; 
|monospaced| kus = 232.5e3;             
k=20954;
c=1366.47;
Aqcar = [0        1      0     0;...
        -kus/mus -c/mus  k/mus c/mus;...
         0       -1      0     1;...
         0        c/ms  -k/ms -c/ms];

      Bqcar=[0     -0.1;...
            -100/mu 0;...
             0      0; ...
             100/ms 0];

      Cqcar = [1 0 0 0;...
               0 1 0 0;...
               0 0 1 0;...
               0 0 0 1];
      Dqcar = 0;
      qcar = ss(Aqcar,Bqcar,Cqcar,Dqcar);

the error:

Warning:    usage:  [bnds,rowd,sens,rowp,rowg] = mu(matin,blk,opt) 
> In mu at 45
  In RobustControlofanActiveSuspension at 53
Error in ==> mu at 44
if nargin < 1 | nargin > 4

??? Output argument "bnds" (and maybe others) not assigned during call to
"E:\Program
Files\MATLAB\R2011a\toolbox\robust\rctobsolete\mutools\commands\mu.m>mu".

Error in ==> RobustControlofanActiveSuspension at 53
    Bqcar=[0     -0.1;...

[Sebastian Castro]

You are attempting to use a variable mu which you didn't define (you defined mus)... instead, it finds a built-in function mu.

[Muna Shehan]

Thanks Sebastian for your answer and for all your comments. I appreciate your help. All the best for you Best regards