### Control Systems in Python - Part 3 - Root Locus Plots

In this post we can see how to make root locus plots in python. This requires the setup from part 1.

The problem is from Dorf's modern control systems AP 10.1. A three-axis pick-and-place application requires the precise movement of a robotic arm in three-dimensional space. The overshoot for a step input should be less than 13%.
a) Let Gc(s) = K, and determine the gain K that satisfies the requirement. Determine the resulting settling time (with a 2% criterion). First we compute the Routh Hurwitz table to determine the valid
range of K.

We see 0<K<20 so If we let K = 2, then the step response becomes:
which shows the settling time is 8.68 seconds and overshoot is less than 13%.

b) Use a lead network and reduce the settling time to less than 3 seconds. Since we are dealing with time response parameters the root-locus method will be used.

The new controller is:

the overshoot and settling time criteria lead to a damping ratio of 0.545 or more and the real part of the dominant poles must be to the left of -1.33 respectively.

If we choose our dominant poles to be at s1 = -2 +- 2j they fall in the correct region on the root locus and should get the desired response. The angle of the system L(s) at s1 is Ls 63.4o.  So letting m=0,
∠Gc(s1) =180 - 63.4 = 116.6o
the controller must add this amount. If we pick our zero to be at ½ , then using the relationship:
∠( s1+ z ) -∠(s1+p)  = 106.26o
we find p = 6.34 and K = 34.19.  This leads to the step response of:
from which we can see the settling time has been reduced but not enough to meet the specifications. Let's move it closer to the system pole at -1.

Reiterating through the root locus design procedure, if we move our zero out to z=¾ and recalculate p=5.86 and K=32.9, the response now is:
which shows another good improvement in the settling time but the zero still needs moved closer to the pole at -1.

Lastly let’s set our z=0.9, then p=5.63 and K=32.5. The root locus is computed using:def rootLocus(Ts,*args,**kwargs):    num = Poly(Ts.as_numer_denom()[0],s).all_coeffs()    den = Poly(Ts.as_numer_denom()[1],s).all_coeffs()    tf = matlab.tf(map(float,num),map(float,den))    r,k = matlab.rlocus(tf,*args,**kwargs)    plt.title("Root Locus")    #plt.plot(k,r)    plt.grid()    plt.show()and the output is:resulting in the final controller of:who's step response is:which shows the controller has reduced the overshoot and settling time to within the specifications (the settling time is less than 3 seconds).

### 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…