[python-control-discuss] forced response problem for large dt

[Ryan K. <rk...@si...>]

Apparently I don't know which email list is subscribed.  Sorry if this
comes through more than once.

I am teaching a classical controls class for mechanical engineering
undergraduates.  Up till now, I have tried to gloss over state-space.  My
students need to do an initial condition simulation for a system that
includes actuator saturation.  I have them do this by integrating for one
time step at a time using control.forced_response inside a for loop.  We
are essentially doing a continuous time approximation of ZOH with the input
held constant for each time step.  As the time step gets too large, sp.
linalg.expm has to use a higher order pade approximation and eventually
throws this error:

ValueError                                Traceback (most recent call last)

/Users/rkrauss/git/python-control/zumo_PID_simulation_modified_ss.py
in <module>()

    103     t0 = dt*(i-1)

    104     t1 = dt*i

--> 105
  to, yo, xo = control.forced_response(G_int, [t0,t1], [v[i],v[i]], X0=X0)

    106     X0 = xo[:,-1]#<-- save for next time through for loop

    107     x[i] = squeeze(X0)


/Users/rkrauss/git/python-control/control/timeresp.pyc in forced_response(sys,
T, U, X0, transpose)

    374                          [np.zeros((n_inputs, n_states + 2 *
n_inputs))]])

    375             print('M=' + str(M))

--> 376             expM = sp.linalg.expm(M)

    377             Ad = expM[:n_states, :n_states]

    378             Bd1 = expM[:n_states, n_states+n_inputs:]


/usr/local/lib/python2.7/site-packages/scipy/linalg/matfuncs.pyc in expm(A,
q)

    258     # Input checking and conversion is provided by
sparse.linalg.expm().

    259     import scipy.sparse.linalg

--> 260     return scipy.sparse.linalg.expm(A)

    261

    262


/usr/local/lib/python2.7/site-packages/scipy/sparse/linalg/matfuncs.pyc
in expm(A)

    580

    581     """

--> 582     return _expm(A, use_exact_onenorm='auto')

    583

    584


/usr/local/lib/python2.7/site-packages/scipy/sparse/linalg/matfuncs.pyc
in _expm(A,
use_exact_onenorm)

    635     if structure == UPPER_TRIANGULAR:

    636         # Invoke Code Fragment 2.1.

--> 637         X = _fragment_2_1(X, h.A, s)

    638     else:

    639         # X = r_13(A)^(2^s) by repeated squaring.


/usr/local/lib/python2.7/site-packages/scipy/sparse/linalg/matfuncs.pyc
in _fragment_2_1(X,
T, s)

    753     exp_diag = np.exp(scale * diag_T)

    754     for k in range(n):

--> 755         X[k, k] = exp_diag[k]

    756

    757     for i in range(s-1, -1, -1):


ValueError: setting an array element with a sequence.


This is probably ultimately a problem for the scipy people, but my
students' project is due in 6 days.  Any suggestions to quickly get the
attached simulation code to work for 60Hz simulation, i.e. dt = 1.0/60?


Thanks,


Ryan

--
Ryan Krauss, Ph.D.
Associate Professor
Mechanical Engineering
Southern Illinois University Edwardsville