## Archive for the ‘control theory’ Category

I currently work at The University of Manchester in the UK as a ‘Scientific Applications Support Specialist’. In recent years, I have noticed a steady increase in the use of open source software for both teaching and research – something that I regard as a Good Thing.

Even though Manchester has, what I believe is, a world-class site licensed software portfolio, researchers, lecturers and students often prefer open source solutions for all sorts of reasons. For example, researchers at Manchester can use MATLAB while they are associated with the University but their right to do so ceases as soon as they leave. If all of your research code is in the form of MATLAB and Simulink models, you had better hope that your next employer or school has the requisite licenses.

This summer, a few people in the Control Systems Centre of Manchester’s Electrical and Electronic Engineering department asked the question **‘Is it possible to implement all of the simple MATLAB/Simulink examples we use in a second year undergraduate introduction to Control Theory using free software?’ **In particular, they chose the programs Scilab and Xcos.

Since the aim of this course is to teach control theory principles rather than any particular software solution, it would ideally be software agnostic. Students aren’t asked to develop models, they are just asked to play with pre-packaged models in order to improve their understanding of the material.

Student intern Danail Stoychev was tasked with attempting to port all of the examples from the course and in fairly short order he determined that the answer to their question was a resounding ‘Yes’.

For example, the model below is an example of **feedback with a first order transfer function and a dela**y. First in Simulink:

and now in xcos

Part of the exercise set for the students is to define all of the relevant parameters in the workspace: b,a,k and so on. If you attempt to download and run the above, you’ll have to do that in order to make them work. You’ll also need extract and plot the results from the workspace.

It can be seen that the two models look very similar and, for these examples at least, it really doesn’t matter which piece of software the students use.

The full set of MATLAB/Simulink examples along with Danail’s Scilab/Xcos conversions can be found at http://personalpages.manchester.ac.uk/staff/William.Heath/matlab_scilab.html

I recently picked up a few control theory books from the University library to support a project I am involved with right now and was interested in the seemingly total dominance of MATLAB in this subject area. Since I’m not an expert in control systems, I’m not sure if this is because MATLAB is genuinely the best tool for the job or if it’s simply because it’s been around for a very long time and so has become entrenched. Comments from anyone who works in relevant fields would be most welcome.

On its own, MATLAB is insufficient to teach introductory control systems courses — you also need the control systems toolbox as a bare minimum but most books and courses also seem to require Simulink and the symbolic math toolbox. All of these are included in the student edition of MATLAB which is very reasonably priced.

If you are not a registered student, however, and don’t work for someone who can provide you with MATLAB it’s going to be very expensive! As far as I can tell, your only option would be to purchase commercial licenses which are very expensive (as in thousands of dollars/pounds for MATLAB and a few toolboxes).

**What else is out there?**

I have a strong interest in mathematical software and so I know that there are several products that have support for control theory. Here are some that I know of and have access to myself

- Mathematica – Its symbolic math support far exceeds that of MATLAB and it is on an equal footing numerically but its control systems support is much more recent and I don’t know of a textbook that utilizes it. One benefit of Mathematica is that it doesn’t separate functionality out into toolboxes – everything is just built in. Another benefit to tinkerers is the home edition which gives you the full product at a much lower price than commercial licenses.
- Maple – This also has very strong symbolic and numeric math support. It also comes with some Control Systems support built in. Like Mathematica, it has a home edition for non-commercial tinkering and learning.
- Labview – A graphical programming language that I’m only just starting to get used to. It has lots of users and advocates in my employers electrical and mechanical engineering departments. There is no support for symbolic computing as far as I know.
- Python – Python is a superb general purpose scripting language that’s also completely free. Numerics are taken care of by Numpy, symbolics by Sympy and there is a control theory module, the development of which is coordinated by Richard Murray of Caltech (The same Richard Murray that co-wrote the book Feedback Systems: An Introduction for Scientists and Engineers).
- Octave – Octave is a free implementation of the MATLAB .m language. It also has a free control package.
- Scilab – Scilab is a free numerical environment that also has a free control package.

I haven’t mentioned Simulink alternatives in this post since I’ve discussed them before.

**Questions**

Some questions that arise are

- Are there any other alternatives to those listed above?
- Do these alternatives have sufficient functionality to support undergraduate courses in control systems and control theory?
- What would be the best language to use if you were teaching control systems as a Massively Open Online Course (MOOC)?
- Does it matter to employers which computational language you learned your control systems in as an undergraduate?

I find that the final point is very divisive among people I discuss it with. On the one hand you have those who say ‘It’s the concepts that matter, the language you choose to implement them in is much less important’ and on the other hand you have those who say ‘It’s gotta be MATLAB, my father used MATLAB and his grandfather before him. Industry uses MATLAB, I only know MATLAB, we must teach MATLAB.’