## (Modified) PERT distribution

The United States navy developed in the 1950’s a program evaluation research task (PERT). It was designed to analyze the duration of a project and the tasks within the project. Each task in the project is given the following properties:

• Predecessor, the list of tasks that have to be completed before the task can start.
• The amount of time it will take for a task to be finished.

The duration of a task is often not fixed. It can vary between a minimum and maximum. The PERT distribution was created to give a good estimate of what the probability is of the duration of a task. It uses the same three parameters as the Triangular distribution, namely, the minimum (), the most likely () and the maximum (). The probability density function (PDF) is given by

where

with

being the mean.

An additional shape parameter might be added, in which case we are dealing with the modified PERT (MPERT) distribution. The parameter influences the peakness of the distribution. The only difference with PERT is the definition of and . These are namely defined as:

I created some Matlab code which includes functions for the PDF, the (inverse) cumulative distribution function (CDF). The inverse CDF is important for when you want to generate random numbers. The code can be download from here.

Finally, below is an interactive example of the PDF of PERT (blue) and MPERT (red) distribution.

## Published articles

During and after my Master thesis I authored and co-authored three articles. Two for a scientific journals (IEEE) and one for a Dutch professional magazine (Mechatronica & Machinebouw). While it took me a lot of time writing these articles and I do think that the current publish or perfish system is completly wrong – can write a whole blog about this or maybe read this article – I am glad I took up the challenge to write them next to my thesis.

Writing a scientific article is completely different compared to writing your thesis. For your thesis you have numerous pages to explain your story for a scientific article you only have a few. As a result, you will have to be very precise in your writing and choose the words carefully. It has to be very clear, precise and short. This can be very challenging when your story touches a lot of subjects from different fields. Angel Borja wrote a three articles on writing your article and I would like to share these with you:

In addition, I found the UW-Madisons Writer’s Handbook and especially the page about Transitional Words and Phrases useful.

Finally, without further ado, the three articles I have written.

# Frequency-domain analysis of real-time and networked control systems with stochastic delays and data drops

Abstract—We present a novel frequency-domain analysis framework for a closed-loop model capturing a wide range of real-time and networked control systems with stochastic delays and packet drops. Our results allow for inferring the mean and variance of the output response to deterministic inputs, based on a new frequency response plot. We illustrate the usefulness of our results in the context of real-time control systems with input-to-output delays resulting from the use of a shared processor.

Keywords—Frequency-domain analysis, networked control systems, real-time systems, stochastic systems, data losses, delays

pdf

# The impact of deadline misses on the control performance of high-end motion control systems

Abstract—In high-end motion control systems the real-time computational platform must execute tasks from multiple control loops operating at high sampling rates. In recent years traditional special-purpose platforms have been replaced by general purpose multi-processor platforms, which introduce significant fluctuations in execution times. While considering worst-case execution times would severely reduce the sampling rates, accepting deadline misses and assuring that the control system still meets the desired specifications is challenging. In this paper, we provide a framework to model and assert the impact of deadline misses in a real-time control loop. We consider stochastic models for deadline misses and characterize the mean and the variance of closed-loop output variables based on a time-domain analysis. We illustrate the usefulness of our framework in the control of a benchmark motion control experimental setup and in the control of a wafer stage in a lithographic machine.

Keywords—Deadline misses, data losses, packet drops, performance analysis, stochastic analysis, industrial case study, hybrid systems, cyber-physical systems, real-time systems

pdf

# Smarter balancing between performance and costs in control systems

Abstract—In order to ensure the performance of control systems, the digital platforms on which they are executed are often over-dimensioned, which are unnecessary costly. State-of-the-art model based techniques make it possible to create cheaper control systems, without performance degradation.

Keywords—Deadline misses, data losses, packet drops, performance analysis, stochastic analysis, industrial case study, hybrid systems, cyber-physical systems, real-time systems

pdf

## Fantasy book frame quote

A few weeks ago I saw the following tweet by Bo Marit. I really liked how the quote and the symbol reference stand out in front of the text in the frame. Since, I liked them so much I decided to be a copy-cat. However, I added also another frame with a reference to Game of Thrones.

The font that she uses for the quote is called Darleston. It is a really elegant calligraphic font created by Youssef Habchi. For the book page text I used Garamond, a standard font on most computers. I chose this font because it has an oldish style to it. While this could easily be created in Photoshop or any other graphics editor, I simply recreated it with Microsoft Word, which is maybe even easier! I simply created a two column layout, added two textboxes for the quotes and the symbol image. You can download the word file here (note: you will need the fonts Darleston and Garamond) or a pdf file here. As an frame I would recommend a simple wooden frame as Bo Marit uses, I think it gives adds elegance and makes it look more humble. Furthermore, I would not use regular A4 paper to print this on. I searched for the same type of paper you often see used in books. Most likely you will find this type of paper in your local hobby store.

Finally, my result:

I plan the hang the Harry Potter frame near to a light switch, the Lord of the Rings frame near to the clock and the Game of Thrones frame near to the thermostat.

## GEWIS GEMOLD 2014

From 28th of May to the 1st of June GEMOLD14 takes place. GEMOLD14 is the GEWIS version of the popular Dutch television program wie is de mol?, literally translated who is the mole?. The program is about 10 candidates who have to complete several assignments with which they can earn money. However, one of the candidates is the mole, it is his solely purpose to make sure that assignments fail and the team of candidates earn as less money as possible.  At the end of each episode there is an execution, the candidates have to answer a number of questions about the identity of the mole. The candidate who answers the least amount of questions correct has to leave. Candidates can earn jokers, which turns a falsely answered question into a correct one, or free-cards with which they do not have to do the answer the questions at all and guarantees continuation to the next episode. At the end of the program there are only three candidates left, the mole and two candidates. The winner is the candidate, who is not the mole of course, who answers the most correct questions about the identity of the mole.

On the 23rd of February I got an e-mail from the GEMOLD14 committee with the message I was selected to participate as a candidate. Together with the e-mail I received a questionnaire which I immediately filled in. You can download it here, however, it is in Dutch. I also had to write a small introduction about myself for the website, which you can view here, also in Dutch. After that it was just waiting for the 28th of May.

On the 28th of May all 14 candidates gathered at GEWIS in the Metaforum at the university. Before I went to GEWIS I made a visit to the bathroom where I wrote mole on mirror with soap just as a tease for the other male candidates who might had to go to the bathroom after I went. Later we were delegated to come to balcony of the Metaforum. After a group picture with all the candidates GEMOLD14 was finally about to start. Tim the host of GEMOLD14 showed up and welcomed us. He explained some organizational matters and how jokers and free cards looked like. We handed in our mobile phones, wallets and everything else that we were not allowed to have in our possession during the weekend. Afterwards, he told us to prepare ourselves for execution! With only the questions from questionnaire  someone was already going to leave the group. Everyone was in shock, while I only had an eye for the joker and free card which Tim showed us as an example and left on a small table. With an easy pace I walked up to the table and grabbed them while everyone was gasping and watching me. Unfortunately however, one of the other organizers came up to me and told me to give them back. As polite as I am, I gave them back. Very stupid afterwards since they really lay in the open and the organizers were only to blame themselves to leave them so in the open. In the meantime the monitor was placed. Ruben, the host who did the executions, called the first name: Rik — who I think is the mole by the way — got a green screen. He was followed by Celine, Mark, Jos, Arno and Levi who all got a green screen. Then it was Wout’s turn, he was one of the finalist of GEMOLD13. Unfortunately for him he got a red screen and we were left with 13 candidates.

Wout was executed and the remaining candidates and myself gathered between the Metaforum and the Main building. Tim showed up. He asked for two volunteers who were lazy, Jos and Annebel presented themselves after which they were escorted away from the rest. Tim asked for someone who still had to recover from the shock, Mike presented himself and he was also escorted. At the end Tim needed two more volunteers who would enjoy a little walk, Ingmar and Leroy presented themselves. The rest had to fetch our bicycles and were escorted by two people from the organisation, Merel and Serge. For clearance here a list of the people:

• Two volunteers who were lazy: Jos and Annebel.
• One volunteer who still had to recover from the shock: Mike
• Two volunteers who enjoyed a walk: Ingmar and Leroy
• The rest who were gonna travel by bicycle: Wouter (me), Jorik, Celine, Wim, Levi, Rik (mole!), Patricia and Arno.

While I was waiting to be picked up by one of the organizers I started to write in my mole booklet. After a while the group reappeared and we drove back to the starting point to pick up everyone after which we drove straight to the camp location. At the camp location we had to step off from our bicycles and one by one we had to go to the gates from the encampment. Jorik went first, he however came back and told us that he did not get in. He told us that we were getting a yes or no question about if we wanted to get into the encampment for -500 mole money. In the meantime Arno did went to the gate and got in. At first I thought he told yes. Then Wim and Celine got in as well. I got to the gate and got the question which Jorik told me I would get, I clearly said no and got in. From what I learned afterwards Jorik told not clearly no but said “euh no. Inside the main building of the encampment I learned that while there was some confusion on the road, after I was left behind, we succeeded with the assignment. When every candidate was inside Tim greeted us. He told us that Ingmar and Leroy were inside the encampment in time with which we earned 500 mole money. However, Mike also made it also into the encampment with which he earned a free-card. This did however cost -1000 mole money. So actually we did fail with the assignment, since we got -500 mole money in the end. The mole had succeeded and we went to sleep.

The next morning all candidates gathered in a small room. Tim joined and explained the lie and cheat assignment. The moles of the three previous editions of GEMOLD would join us they would act as a jury. Tim would then ask each candidate two questions, one had to be answered truthfully the other with a lie. The jury would then try to guess which answer was a lie. Each candidate could earn mole money when the jury did not manage to find out which answer was a lie. When a previously candidate managed to fool the jury the next candidate could choose to call. The mole money earned by the previous candidate would then be safe. If he continued and the jury would guess correctly which answer was a lie then the previously earned mole money would be gone. The amount of mole money earned would raise by:

• 10 mole
• 30 mole
• 100 mole
• 200 mole
• 500 mole
• 1000 mole
• 1500 mole

First Ingmar and Patrice who both did not manage to fool the jury. Then other candidates told me I had to go, I resisted a bit but gave in to the pressure. Tim asked me two questions, if I had a part-time job and what my favorite book was. Since I did not quiet understand the game at that moment, I was wondering if the question which were asked stood in the questionnaire, I decided to answer the first question falsely and the second truthfully. The jury then guessed wrong. The next candidate did not decide to call and unfortunately he did not fool the jury. The 10 mole earned by me were gone. After my question, I gave the assignment some more thought and I believed that we could have lied always regardless what type of question we were asked because the questions did not actually come from the questionnaire. Hence it could never be checked if the candidate was actually lying towards the jury. After I got executed, I looked it up and indeed both questions which I was asked were not in the questionnaire. As such I think I was correct during the game and we could all just have lied towards the jury. Unfortunately everyone was to truthfully towards the jury and we only managed to obtain 100 mole. We could have earned a lot of mole money very easily. This time the mole was not clever, we were dumb.

After the next assignment, I unfortunately got executed. I wrote this blog almost immediately after I was executed. However, I did not describe the events during the last assignment, I did plan to finish it at a later stage. However, as you can see that never happened. Because the episodes are being aired now, I decided not describe these events anymore from my point of view.

# Mole booklet

## Testimonial Master’s program TU/e Systems & Control

In November 2013 I was asked by the PR of the Mechanical Engineering department of the TU/e to write a story about myself and how I perceived the master Systems & Control. It would be used as a testimonial on the TU/e website. In the end only a part of my full story was incorporated, below is the full-text which I submitted.

Hello, my name is Wouter Geelen. Currently I am following the Master Systems & Control at the Eindhoven University of Technology. First I will tell you something about why I decided for the Master System & Control, then something about how I experience the Master track and what currently keeps my life occupied.

When I was finished with my Bachelor in Mechatronics (HBO) it was clear to me that I wanted to continue studying. Choosing at which University I wanted to do my Master was a really easy choice for myself for 2 main reasons. Firstly, since I was raised in a small town in the province of Limburg and did not yet wanted to drift off to far from my roots and secondly I did two years of my Bachelor in Germany near Düsseldorf and at that time I still went regularly to Germany to visit friends. Therefor I decided that the University in Eindhoven was best the best choice. However, choosing the master was a really hard and difficult decision. After a Bachelor in Mechatronics there are several possible Masters which you can choose from. In my case there were basically two options: i) Embedded Systems or ii) Systems & Control.

During my graduation project for my Bachelor I created a double inverted pendulum (video) which would be a typical project for students from Systems & Control, but with the knowledge at that time it was a difficult problem for myself. However, I successfully completed the project. After a lot of talking with my former teachers and a graduate from Systems & Control, who helped me with my graduation project, I decided to start with the Master Embedded Systems and that I would choose several Systems & Control courses in my free electives. When you come from a University of Applied Sciences you will have to do a pre Master first, before you can actually start with the “real” Master. I did the pre Master of Embedded Systems, it had a lot of fun and interesting courses. After I finished the pre Master and had started with the real Master it started nagging me that the control courses which I wanted to do for my electives where really hard because of a knowledge gap. Furthermore, the master Embedded Systems also focused really on energy-efficient chip design which I really did not find interesting at all. I am the type of person which just wants to pick a chip from the shelve after which I work my magic on it. For those two reasons I decided to switch to Systems & Control. Luckily most of the courses of the pre Master of Systems & Control where the same as the pre Master of Embedded Systems so I finished it quickly. Furthermore, after asking the examination board of Systems & Control for permission, I could take 3 courses from Embedded Systems with me to the Systems & Control. So luckily that detour of half a year Embedded Systems was not a complete waste.

The core program of Systems & Control covers really all the basics about control engineering and the whole cycle of model based design. There are very theoretical courses but also very practical courses, which, I think is perfect for a University of Technology. You can then namely apply what you learnt in your theoretical courses in your practical courses. You also have a lot of freedom in choosing your electives: i) there are a lot of elective courses from which you can choose from and ii) if there is a course which you really like but is unfortunately not on the list then, if you have good arguments, you can ask the examination board for permission. Which I did as you have read earlier.

For a lot of courses you have to work together with another student or a group of students. Which is nice since most students in System & Control all have a different background, as well in study, as in culture. As such groups get really mixed up, which is good for learning how to work with a very diverse group of people. Also all the Professors excel in their field of expertise, they really challenge you during college. Since the TU/e is a small University you really get to know them and can almost always ask them anything if you don’t understand something. So the distance between you as a student and the Professor is really small.

Inside the master Systems & Control there are several specialization groups. At first I did choose for the Hybrid Systems group. However , during the summer they did merge with the Control Systems Technology group, which made them one of the strongest groups at the TU/e and one of the strongest in control theory worldwide. The reason why I did choose for this group is very simple. During my graduation presentation of the double inverted pendulum I was asked if I could compute the best possible transition between the two controllers. The system namely consisted out of two controllers one for bringing the pendulum in upwards position and one for stabilizing it. At that time I could not answer that question yet, but now and thanks to the help of Hybrid Systems, which combines continuous and discrete systems, I can answer that question! Which makes me feel kind of proud of myself.

Nowadays I am busy with a literature survey about several Matlab toolboxes which help in analyzing and simulation of systems in which wireless networks are involved. Wireless networks are namely increasingly more being used for control systems. To give an example where one could have used a wireless network inside a control system is my double inverted pendulum, namely at the encoder where the two pendulums meet. In that case the encoder at the connection of the two pendulums is not wired anymore. Wireless networks however bring all kind of nasty behavior with them which influences the stability of the system. Furthermore, wireless networks combined with control systems are still hard to analyze mathematically. Therefore there are still a lot of open questions to be answered around this subject.

## High quality interesting freely publicly available e-books

During my studies at the Eindhoven University of Technology some professors have been referring to freely available e-books. Some of these are mentioned here, others I just did find useful for other reasons. I tend to expand this list whenever I find an freely publicly e-book which I think is worth sharing.

# A Mathematical Introduction to Robotic Manipulation

By Richard Murray, Zexiang Li and Shankar Sastry

A Mathematical Introduction to Robotic Manipulation presents a mathematical formulation of the kinematics, dynamics, and control of robot manipulators. It uses an elegant set of mathematical tools that emphasizes the geometry of robot motion and allows a large class of robotic manipulation problems to be analyzed within a unified framework. The foundation of the book is a derivation of robot kinematics using the product of the exponentials formula. The authors explore the kinematics of open-chain manipulators and multifingered robot hands, present an analysis of the dynamics and control of robot systems, discuss the specification and control of internal forces and internal motions, and address the implications of the nonholonomic nature of rolling contact are addressed, as well. The wealth of information, numerous examples, and exercises make A Mathematical Introduction to Robotic Manipulation valuable as both a reference for robotics researchers and a text for students in advanced robotics courses.

# Mathematical Control Theory

By Eduardo Sontag

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematics Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. v Preface to the Second Edition The most significant differences between this edition and the first are as follows: Additional chapters and sections have been written, dealing with: nonlinear controllability via Lie-algebraic methods, variational and numerical approaches to nonlinear control, including a brief introduction to the Calculus of Variations and the Minimum Principle, – time-optimal control of linear systems, feedback linearization (single-input case), nonlinear optimal feedback, controllability of recurrent nets, and controllability of linear systems with bounded controls.

# Synchronization and Linearity : An Algebra for Discrete Event Systems

By François Baccelli, Guy Cohen, Geert Jan Olsder and Jean-Pierre Quadrat

This book proposes a unified mathematical treatment of a class of ‘linear’ discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the ‘max-plus algebra’. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide ‘discrete event system theory’, which is shown to parallel the classical linear system theory in several ways. This class of synchronized systems finds its main current industrial applications in the modeling, optimization and control of communications networks, computer architectures, manufacturing and transportation systems. The book should hence appeal to students and researchers in probability-statistics, applied mathematics, (industrial and electrical) engineering, operations research, as well as computer and management scientists.

# Convex Optimization

By  Stephen Boyd and Lieven Vandenberghe

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

# Linear Matrix Inequalities in System and Control Theory

By Stephen Boyd, Laurent El Ghaoui, Eric Feron, and Venkataraman Balakrishnan

In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.

# A Brief Introduction to Neural Networks

By David Kriesel

Neural networks are a bio-inspired mechanism of data processing, that enables computers to learn technically similar to a brain and even generalize once solutions to enough problem instances are tought. The manuscript “A Brief Introduction to Neural Networks” is divided into several parts, that are again split to chapters. Part I: From Biology to Formalization — Motivation, Philosophy, History and Realization of Neural Models. Part II: Supervised learning Network Paradigms. Part III: Unsupervised learning Network Paradigms. Part IV: Excursi, Appendices and Registers.

# The Feynman Lectures on Physics

By Richard Phillips Feynman, Robert Benjamin Leighton and Matthew Sands

This revised edition of Feynman’s legendary lectures includes extensive corrections Feynman and his colleagues received and Caltech approved, making this the definitive edition of The Feynman Lectures on Physics. For all readers interested in physics.

# Motion Mountain the adventure of physics

By Christoph Schiller

Motion Mountain is an entertaining and free e-book in six pdf files introducing physics – the science of motion. Explore the motion of wheels, birds, lightning, planets, light and empty space itself! Be fascinated by the beauty of nature and by the concepts of modern physics, from the principle of cosmic laziness – least action – to gauge symmetry!

## TU/E LATEX HOUSE STYLE TEMPLATE

Last month I blogged about a template I made for my thesis at the Eindhoven University of Technology. It so happens that the TU/e actually has a house style template for reports. It can not be found threw any public channels, such as the corporate identity webpage of the TU/e. You will have to connect to the network drive \\winstorage\MikTex\MiKTeX29\. Which is accessible from the TU/e network or threw a VPN connection. An example of the package output can be downloaded here. If you want to have the source please contact me.

For now I will just stick with my own template. The TU/e template namely generates some warnings and errors. Furthermore, it is also limited in its capabilities. Of course I can expand it, however, I do not feel the need to do that at this time.

## TU/e LaTeX Template

On the second of June, my birthday actually, I will start with my Master thesis at ASML Holding NV. ASML produces machines for the production of integrated circuits. Using their machines other companies, such as Intel, Apple, Samsung and many more, can create, for instance, CPUs, SoCs, DRAM or flash memory. But this blog post is not about my graduation at ASML actually. It is about my template which I created for my thesis.

The university where I study, the TU/e, does unfortunately not provide a nice template for their students to use. Joos Buijs actually created a kind of template à la TU/e style. However, as geeky as I am, I decided to create my own template. An example of how it looks can be downloaded here, the complete source can be downloaded here. It might be possible that you find a bug or you have a question about the template, if so, please contact me. To give you a heads-up, most likely you will not have the beautiful font MinionPro installed. If so, and you want to compile the source, you will need to remove line 590 (\figureversion{lining,proportional}%) from the class file (thesis.cls) and select one of the other fonts in the main file (thesis.tex).

Most features of the class will speak for themselves some might need a little explanation. The \thSupervisors command for instance can take an arbitrary number of supervisors. The input has to have the format {name} / {Affiliation}, and elements need to be separated by a comma.

\thSupervisors{%
{F.A.J. Rompa} / {Eindhoven University of Technology}, {D.S. Addiks} / {ASML Holding NV},
{J. Appelhof} / {Embedded Systems Institute}, {S.R.E. Wessel} / {Van der Lande Industries}}

The class also provides a nomenclature. Symbols are to be put in the file ./frontmatter/symbols.tex. In the file the same format is used as the \thSupervisors command accepts with an extra element, namely, {symbol} / {meaning} / {unit}. The unit can be expressed using the siunitx package. Any acronyms can be inserted in the  ./frontmatter/acronyms.tex file which has the format {acronym} / {meaning}Furthermore the class can insert a custom title page. The title page can either be a .pdf or .tex file which is set as \thTitlePageOne{pdf}{./frontmatter/titlepage.pdf}.

To create this class I used a lot of internet resources, especially the Q&A site tex.stackexchange, which is the number one spot on the internet for all  related questions. Here follows a list of all the internet resources which I consulted.

The template is ready for use but I will most likely give it an update in the coming months. I tend to make it more robust with use of the etoolbox package instead of the ifthen package.

## Hello world!

Hello world. Often referred to as being the simplest program of a programming language, which illustrates the most basic syntax. I will abuse it, like many before, as the title of my first blog. What will I be blogging about? My tag-line says: