In [10]:

    

%pylab inline
import control
import scipy
rcParams['figure.figsize'] = (10,5)
rcParams['font.size'] = 12


    

    




Populating the interactive namespace from numpy and matplotlib

In [11]:

    

def plot_poly_set(verts):
    # close poly for plot
    verts_closed = column_stack([verts, verts[:,0]])
    plot(verts_closed[0,:], verts_closed[1,:], '-b')
    
def add_vector_to_poly(v, poly):
    new_poly = zeros(poly.shape)
    for j in range(len(v)):
        new_poly[j,:] = poly[j,:] + v[j]
    return new_poly

def plot_traj(A= matrix([[0, 1],[-1,-1]]), x0=[0,0], d_x0=0.1, x_targ=[0,0], dt=0.1, tf=10, d_u=0.01):
    
    x0_box = d_x0*array([[-1,-1],[-1,1],[1,1],[1,-1]]).T
    x0_box = add_vector_to_poly(x0, x0_box)
    plot_poly_set(x0_box)
    x = x0_box
    Psi = matrix(scipy.linalg.expm(A*dt))
    t = arange(0, tf, dt)
    
    for i in range(len(t)):
        x_diff = add_vector_to_poly(-array(x_targ), x)
        x_diff_new = Psi*x_diff
        x = add_vector_to_poly(x_targ, x_diff_new)
        
        # input effect
        # minkowski sum for 2d
        n = x.shape[0]
        x_min = zeros(n)
        x_max = zeros(n)
        for i in range(n):
            x_min[i] = x[i,:].min()
            x_max[i] = x[i,:].max()
        verts = array([
            [x_min[0] - d_u, x_min[1] - d_u],
            [x_min[0] - d_u, x_max[1] + d_u],
            [x_max[0] + d_u, x_max[1] + d_u],
            [x_max[0] + d_u, x_min[1] - d_u],
        ]).T
        plot_poly_set(verts)


    

In [12]:

    

clf()
plot_traj(x0=[0,0], x_targ=[1,0])
plot_traj(x0=[1,0], x_targ=[0,0])
plot_traj(x0=[0,0], x_targ=[-1,0])
plot_traj(x0=[-1,0], x_targ=[0,0])
plot_traj(x0=[1,0], x_targ=[-1,0])
plot_traj(x0=[-1,0], x_targ=[1,0])
title('flow pipes')


    

    
Out[12]:





<matplotlib.text.Text at 0x72c9090>