signal.step not working with mimo system

[TobiasGlaubach]

the step function in scipy.signal does not work when the passed system is a MIMO system with integrator.

Reproducing code example:

Consider a simple control system plant in state space form which has 2 inputs, 2 outputs and 3 states.
(Coupled electro mechanical system)

A = np.matrix([     
                [ -R_A/L_A, 0, 0 ],
                [ -K_em / m_rot, K_pm / m_rot, 0 ],
                [ 0, 1, 0 ]
            ]);

B = np.matrix([     
                [ 1/L_A, 0],
                [ 0, 1/m_rot],
                [ 0, 0 ]
            ]);

C = np.matrix([     
                [ k_im, 0, 0 ],
                [ 0, 1, k_zm ]
            ]);

D = np.matrix([     
                [ 0, 0 ],
                [ 0, 0 ]
            ]);

where all given Parameters are real numbers.

Test the dimensions by calculationg with test vectors:

u = np.matrix([     
                [ 1 ],
                [ 1 ],
            ]);
x = np.matrix([     
                [ 1 ],
                [ 1 ],
                [ 1 ],
            ]);

try:
    B @ u
    A @ x
    A @ x + B @ u
    
    C @ x
    D @ u
    C @ x + D @ u
except:
    raise

which works. Now however, when we transform the system to a lti state space system and try to use the step method:

sys = signal.StateSpace(A, B, C, D)
print(sys)
X0 = np.array([0,0,0])
T = np.linspace(0, 0.3, 10000)
t2,y2 = signal.step(sys, T=T, X0=X0)

Error message:

ValueError: System does not define that many inputs.

Traceback (most recent call last):

  File "<ipython-input-36-e3c064c647e9>", line 6, in <module>
    t2,y2 = signal.step(sys, T=T, X0=X0)

  File "C:\Users\...\AppData\Local\Continuum\anaconda3\lib\site-packages\scipy\signal\ltisys.py", line 2269, in step
    vals = lsim(sys, U, T, X0=X0, interp=False)

  File "C:\Users\...\AppData\Local\Continuum\anaconda3\lib\site-packages\scipy\signal\ltisys.py", line 1989, in lsim
    raise ValueError("System does not define that many inputs.")

ValueError: System does not define that many inputs.

Scipy/Numpy/Python version information:

1.1.0 1.15.4 sys.version_info(major=3, minor=6, micro=7, releaselevel='final', serial=0)

[ilayn]

Hi @TobiasGlaubach . Thanks for taking the time to report this. Currently we have a number of missing features regarding MIMO systems, off the top of my head #2862, #4675 and #4794. I'll try to see whether this can be fixed without a major surgery. In the meantime you can use python-control or harold while we fix these.

[dstuartbryant]

I recently had issues getting this to work.

Code

from scipy import signal

A = np.array([[-1,-1],[6.5,0]])
B = np.array([[1,1],[1,0]])
C = np.array([[1,0],[0,1]])
D = np.array([[0,0],[0,0]])

signal.step((A,B,C,D))

Error

ValueError                                Traceback (most recent call last)
~/.../example_malfunction.py in <module>
      7 D = np.array([[0,0],[0,0]])
      8 
----> 9 signal.step((A,B,C,D))

/usr/local/lib/python3.6/site-packages/scipy/signal/ltisys.py in step(system, X0, T, N)
   2407         T = asarray(T)
   2408     U = ones(T.shape, sys.A.dtype)
-> 2409     vals = lsim(sys, U, T, X0=X0, interp=False)
   2410     return vals[0], vals[1]
   2411 

/usr/local/lib/python3.6/site-packages/scipy/signal/ltisys.py in lsim(system, U, T, X0, interp)
   2103 
   2104     if U.shape[1] != n_inputs:
-> 2105         raise ValueError("System does not define that many inputs.")
   2106 
   2107     if not interp:

ValueError: System does not define that many inputs.

Notes

It looks like the n_states = A.shape[0] (line 2054, scipy/signal/ltisys.py) value is not incorporated
in the handling of the U array.

I attempted to fix by defining U (line 2408,scipy/signal/ltisys.py) as

U = ones((T.shape[0],A.shape[0]), sys.A.dtype)

but that did not appear to be a good solution.