SymPy teaser

Here's something I did recently with sympy: figure out the Jacobian matrix of the $\dot{\tau}$ control law.



In [1]:

    
from sympy import *
init_printing()

State variables:

s: displacement
v: velocity
d: deceleration

Parameters:

b: stiffness



In [2]:

    
s, v, d, b = symbols('s, v, d, b')



In [3]:

    
state_variables = Matrix([s, v, d])
state_variables









    Out[3]:





$$\left[\begin{matrix}s\\v\\d\end{matrix}\right]$$



In [4]:

    
def tau_dot(s, v, d):
    return s * d / v**2 - 1



In [5]:

    
d_deceleration = - b * (tau_dot(s, v, d) - (-1/2))
d_deceleration









    Out[5]:





$$- b \left(\frac{d s}{v^{2}} - 0.5\right)$$



In [6]:

    
full_model = Matrix([
    - v,
    - d,
    d_deceleration
])
full_model









    Out[6]:





$$\left[\begin{matrix}- v\\- d\\- b \left(\frac{d s}{v^{2}} - 0.5\right)\end{matrix}\right]$$



In [9]:

    
jac =full_model.jacobian(state_variables)
jac









    Out[9]:





$$\left[\begin{matrix}0 & -1 & 0\\0 & 0 & -1\\- \frac{b d}{v^{2}} & \frac{2 b}{v^{3}} d s & - \frac{b s}{v^{2}}\end{matrix}\right]$$



In [ ]: