In [1]:

    

from state_feedback import*
init_printing(use_latex=True) #For good look equations


    

    




Symbols loaded

In [2]:

    

bx = [[0],[v1*tan(x3)]]
bx = fillM(bx)
bx


    

    
Out[2]:





$$\left[\begin{matrix}0\\\operatorname{v_{1}}{\left (t \right )} \tan{\left (\operatorname{x_{3}}{\left (t \right )} \right )}\end{matrix}\right]$$

In [3]:

    

Dx = [[cos(x3), 0],[0, z1/cos(x3)**2]]
Dx = fillM(Dx)
Dx


    

    
Out[3]:





$$\left[\begin{matrix}\cos{\left (\operatorname{x_{3}}{\left (t \right )} \right )} & 0\\0 & \frac{\operatorname{z_{1}}{\left (t \right )}}{\cos^{2}{\left (\operatorname{x_{3}}{\left (t \right )} \right )}}\end{matrix}\right]$$

In [4]:

    

V = [[z1],[v2]]
V = fillM(V)
V


    

    
Out[4]:





$$\left[\begin{matrix}\operatorname{z_{1}}{\left (t \right )}\\\operatorname{v_{2}}{\left (t \right )}\end{matrix}\right]$$

In [5]:

    

sfeed(Dx, bx, V)


    

    
Out[5]:





$$\left[\begin{matrix}\frac{\operatorname{z_{1}}{\left (t \right )}}{\cos{\left (\operatorname{x_{3}}{\left (t \right )} \right )}}\\\frac{\cos^{2}{\left (\operatorname{x_{3}}{\left (t \right )} \right )}}{\operatorname{z_{1}}{\left (t \right )}} \left(\operatorname{v_{1}}{\left (t \right )} \tan{\left (\operatorname{x_{3}}{\left (t \right )} \right )} + \operatorname{v_{2}}{\left (t \right )}\right)\end{matrix}\right]$$

In [15]:

    

f = sin(x3)*u1
f


    

    
Out[15]:





$$\operatorname{u_{1}}{\left (t \right )} \sin{\left (\operatorname{x_{3}}{\left (t \right )} \right )}$$

In [16]:

    

fd = tdiff(f)
fd


    

    
Out[16]:





$$\dot{u}_{1}{\left (t \right )} \sin{\left (\operatorname{x_{3}}{\left (t \right )} \right )} + \dot{x}_{3}{\left (t \right )} \operatorname{u_{1}}{\left (t \right )} \cos{\left (\operatorname{x_{3}}{\left (t \right )} \right )}$$

In [17]:

    

u1s = y1d/cos(x3)
u1s


    

    
Out[17]:





$$\frac{\dot{y}_{1 }{\left (t \right )}}{\cos{\left (\operatorname{x_{3}}{\left (t \right )} \right )}}$$

In [18]:

    

fd = fd.subs(u1, u1s)
fd


    

    
Out[18]:





$$\dot{u}_{1}{\left (t \right )} \sin{\left (\operatorname{x_{3}}{\left (t \right )} \right )} + \dot{x}_{3}{\left (t \right )} \dot{y}_{1 }{\left (t \right )}$$

In [ ]:

    

from nlcontrol import*
from tools import*