Re: [python-control-discuss] Implementation of lsim, step, initial, impulse

[Richard M. <mu...@cd...>]

Hi Eike.  Thanks for your interest in python-control!

I'll take a look at your patches as soon as possible (developers: if anyone else wants to volunteer, just let me know!).  We have had some discussion about the output formats and have a plan for how to implement that, so might have to sort through some of the changes below if they are not consistent with the current plan (see the discussion list archives for more info).

Will respond to the parameter convention suggestion a bit later (busy few weeks ahead).  I've added you to the discuss list so that we can have a conversation about it.

-richard

On 12 May 2011, at 16:11 , Eike Welk wrote:

> Hello!
> 
> I have written a patch for the Python Control Systems Library with the 
> following contents:
> 
> * An implementation of the four simulation functions ``lsim``, ``step``, 
> ``initial``, and ``impulse`` of the module ``matlab``. 
> 
> * It also adds a function ``dcgain`` to the ``matlab`` module, which computes 
> the gain of a linear system for steady state and constant input.
> 
> * The patch contains a bug fix for class ``StateSpace``, which enables it to 
> work properly together with Scipy's ``signal`` module. 
> 
> * The simulation functions' return values are changed (back?) to arrays, 
> because matrices confuse Matplotlib.
> 
> http://sourceforge.net/tracker/?func=detail&aid=3301246&group_id=282523&atid=1198311
> 
> 
> Would you include my patch into the library? 
> 
> What do you think about the parameter convention below? IMHO a detailed 
> section that explains the used convention should be included in the module's 
> documentation. The documentation of the individual functions should link to 
> it. 
> 
> What is the proper communication channel for the library's developers?
> 
> If you include my patch, my next step would be to extend ``lsim`` to MIMO 
> systems (by copying the code from ``scipy.signal.lsim2``); and to convert the 
> module's documentation to proper reStructuredText.
> 
> 
> Implementation Notes
> -------------------
> 
> The implementation is centered around ``lsim``, which checks the parameters 
> thoroughly, and generates useful error messages. It then calls 
> ``scipy.signal.lsim2`` to solve the differential equations. The other 
> simulation functions (``step``, ``initial``, ``impulse``) are small and call 
> ``lsim``.
> 
> 
> Parameter Convention
> --------------------
> 
> The new convention for parameters and return values harmonizes with the way 
> how the system equations are written. It can be generalized to MIMO systems, 
> and it also works well with Matplotlib:
> 
> All parameters can be arrays, matrices, or nested lists. 
> 
> The time vector is either 1D, or 2D with shape (1, n)::
> 
>      T = [[t1,     t2,     t3,     ..., tn    ]]  
> 
> Input, state, and output all follow the same convention. Columns are different 
> points in time, rows are different components. When there is only one row, a 
> 1D object is accepted or returned, which adds convenience for SISO systems::
> 
>      U = [[u1(t1), u1(t2), u1(t3), ..., u1(tn)]
>           [u2(t1), u2(t2), u2(t3), ..., u2(tn)]
>           ...
>           ...
>           [ui(t1), ui(t2), ui(t3), ..., ui(tn)]]
> 
>      Same for X, Y
> 
> The initial conditions are either 1D, or 2D with shape (j, 1)::
> 
>     X0 = [[u1]
>           [u2]
>           ...
>           ...
>           [uj]]
> 
> So, U[:,2] is the system's input at the third point in time; and U[1] or 
> U[1,:] is the sequence of values for the system's second input. 
> 
> As all simulation functions return array plotting is convenient::
> 
>    t, y = step(sys)
>    plot(t, y)
> 
> The output of a MIMO system would be plotted like this::
> 
>    t, y, x = lsim(sys, u, t)
>    plot(t, y[0], label='y_0')
>    plot(t, y[1], label='y_1')
> 
> 
> Yours,
> Eike.
> <make-matlab-work.patch>