### Control Systems in Python - Part 2 - Routh Hurwitz

In my last post Control Systems in Python Part 1, i described how to setup and use Python for doing some basic plotting of transfer functions. One of the biggest benefits of using sympy vs numeric packages like matlab/numpy/scipy is the fact that you can use symbolic variables. This post includes a function for computing the Routh Hurwitz table (Note: It does not work for row's of zeros).

Lets do my control systems design homework problem together :) (Warning: I have not verified if this answer is right so please correct me if it’s not!)

The Problem

The problem is DP 9.11 from Dorf & Bishop’s Modern Control Systems. ISBN 0136024580. Basically we have to design a controller to compensate for a system with a time delay.
The controller is:

And the system is:

First we approximate the exponential term with a 2nd order polynomial using pade(0.4,2) such that:

Thus the approximated system is:

Using frequency response methods, design the controller so that the overshoot of the system is P.O. <= 10%. From this we determine 0.59. When we plot the poles and zeros of the system we see that there are 3 poles in the LHP and two zeros in the RHP. The controller adds another pole at 0, so the zero of our controller should be somewhere to the left of the -5 pole on the real axis.
Thus Ki/Kp > 5. If Ki/Kp = 6. Using a Routh Hurwitz table we can see that 0<Kp<0.66 makes the system stable.

The code for this function is:

def routhHurwitz(Ts,*args):
den = Poly(Ts.as_numer_denom()[1],s).all_coeffs()
n = len(den)-1
if n < 2:
return None
m = matrices.zeros(n+1)
# Insert the first two rows
c = [den[i] for i in range(0,n+1,2)]
for i in range(0,len(c)):
m[0,i] = c[i]
c = [den[i] for i in range(1,n+1,2)]
for i in range(0,len(c)):
m[1,i] = c[i]

# Compute the rest of the entries
for i in range(2,n+1):
for j in range(1,n):
if m[i-1,j] == 0:
m[i,j-1] = m[i-2,j]
elif m[i-1,0] !=0:
m[i,j-1] = ((m[i-1,0]*m[i-2,j]-m[i-2,0]*m[i-1,j])/m[i-1,0]).together().simplify()

m = m.col_insert(0, Matrix(([s**(n-i) for i in range(0,n+1)])))
return m

When we set Kp = 0.22 we get the controller:

giving the step response of:
if the gain is reduced the %OS reduces and Ts rises.

### Kivy vs React-Native for building cross platform mobile apps

I've built three apps now using Kivy and one with React-Native, just wanted to share my thoughts on both.

Just a warning, I am strongly biased towards python and this is all based on opinion and experience and is thus worth what you pay for it. I don't claim to be an expert in either of these, just have worked with each for several months.  If something is incorrect I'd love to hear advice.

Kivy
Demo of one of the apps

Pros:
Nice to be able to run natively on the desktop WITHOUT a simulatorPython is easy to work withUse (almost) any python libraryVery easy to create custom widgetsKivy properties and data binding just work. Way nicer than React's "state" / flux / redux whatever you want to call it (stupid?). Native interfaces (pyjnius) and (pyobjc)Runs and feels pretty smooth Cons:Default widget toolkit looks like Android 4.4. Requiring you use your own widgets or a theming kit like KivyMD if styling bothers youCreating dynamic widgets declaratively is not yet s…

### Control Systems in Python - Part 1 - Bode and Step Response

I hate matlab with passion, yet sadly, nearly everyone uses it.  I'm a fan of Python and open source stuff so here's a simple article on how to do some common control systems stuff in Python.

First we need to make sure the environment is setup.
Install IPython (or you can use any other python shell, but a unicode supported shell is preferred)Install python-control (numpy, scipy)Install sympy
These should do if your on Ubuntu/debian:

sudo apt-get install python-sympy python-numpy python-scipy python-matplotlib ipython
Then you need to install python control, see How to download and install python-control
Intro to using SympyOpen ipython and run the following:

import sympy from sympy import * sympy.init_printing() s = Symbol('s')

Now we can do things like define transfer functions using the symbolic variable s.

We can expand the bottom using the .simplify() method

and we can do something more complex like...
which is really nice because it does all the multiplication for us... and it’…

### How to populate a Combo Box in GTK3 using Glade

This post will show how to use Glade to list combo box items with GTK3 since I could not find any other tutorials and it took me a while to figure it out.  No coding necessary!

Step 1:  Insert the combo box. A GtkComboBox will be created.

Step 2: Select the combo box.  In the General Properties click the ... button next to ComboBox Model and click new.  A new GtkListStore will be created and set to the combo box's model.

Step 3: With the combo box selected, open the Combo Editor by clicking the edit button from the toolbar.
Step 4; Add some columns to the combo box's liststore.  Use type: gchararry for text.  Insert any other model columns at this time as well.

Step 5: Insert data into the liststore by scrolling down in the Combo Editor and clicking the + to add a new row.  Enter the data needed for each row.

Step 6: Click the Hierarchy tab and then click add.  A new GtkCellRendererText will be created.

Step 7: Under properties and attributes, change the Text: from unset to th…