Digital Control Systems 1.02

In the previous blog we introduced the various types of signals present in a digital control system and highlighted the pros and cons. In this blog we take a a closer look at the digital control system.

A digital control system, can only cope with digital signals. That is because it is inherently discrete in time and space. This is caused by the processors clock rate and due to the finite word length of a digital system. For instance, a 32 [bit] computer which runs at 4 [GHz] has a time resolution of 0.25 [ns] and the value of an unsigned integer can only range from 0 to 232 − 1.

Figure 1. Digital control system in its most elementary form. Continuous-time signals are in solid and discrete-time signals are dashed.

Figure 1 shows the digital control system in its most elementary form. Herein \mathcal{S} is the sampler. The sampler converts the analog output signal of the plant y(t) at time t \in \mathbb{R} to a digital measurement signal y[k] at discrete-time k \in \mathbb{N}. As mentioned in the previous blog, the digital signal is obtained by sampling and quantization of the analog signal. In final, \mathcal{H} denotes the recronstructor, also known as a digital-analog convertor (DAC), it converts the digital control signal u[k] provided by the controller to an analog control signal u(t).

Sampler

Figure 2 shows that the sampler exists out of two devices namely; i) a sample and hold (SH) device and ii) a analog-digtal convertor (ADC).

Figure 2. The sampler and its sub systems.

The SH device knows two different states. The first state is called the track state at which the analog input signal is tracked by the SH device. The track state is also refereed to as sample state. However because of the ambiguous meaning of the word sample we will use the track, which is also commonly used in literature. The second state is called the hold state at which the analog input signal is being kept constant for a short period of time. The hold state is activated when the hold command is given. During the hold state the ADC is able to process and digitize the signal. The hold command can be triggered by any logic device. While there are many more aspects and subtleties to be considered with a SH device this gives a summarized overview of its functionality.

Figure 3. The track and hold of a SH. Dashed red shows the original signal, solid blue shows the SH signal.

Various different strategies exists at what time instance t_k the hold command is triggered. These are called sampling strategies.

  1. Periodic sampling; the sampling instances t_k are equally spaced, that is to say t_k = kh with k \in \mathbb{N} and h, given in [s], being the sampling period. See also Figure 2(a). The sampling period h is often also denoted as the sampling rate or sampling frequency f_s, given in [Hz]. It is related to the sampling period by h = \frac{1}{f_s}.
  2. Multi-order sampling; a pattern of sampling instances \{t_k\} are repeated periodically, as a result t_{k+r} = t_k. See Figure 2(b).
  3. Event-based sampling; the sampling instances t_k are generated based on a event in the system. For instance, when a certain measurement threshold has been crossed. See Figure 2(c) in which the signal is sampled at every \pm0.4x \pm 0.2 value.
  4. Random sampling; the sampling time instances t_k are chosen at random, see Figure 2(d).
Figure 2. Visualization of different sampling techniques. Red line resembles the original analog signal, blue the sampled signal. Matlab code.

Periodic sampling is the most common in industry. That is because of several reason; i) most deterministic behavior, ii) extensively been researched, iii) easiest to model and iv) easiest to obtain key performance indicators, for instance, in time- and frequency domain. Finally, proofing stability for the other sampling strategies is much harder then for periodic sampling.

In the next blog, we will go deeper in the mathematics behind sampling.

All State of Trance episodes on Spotify

I am a staunch fan of A State of Trance of Armin van Buuren. Therefor, I made a list of all the State of Trance episodes available on spotify.

  1. https://open.spotify.com/album/65rxkH0MLVAUfvGJU2HPk4
  2. https://open.spotify.com/album/5jtGUCgpoqvSNZH8WcQf8F
  3. https://open.spotify.com/album/2RLKYKweji0JBAi2OtxOCt
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  724. https://open.spotify.com/album/5V3VhcwL5wc1qHEFtu7BUs
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  726. https://open.spotify.com/album/2v8SoYkc5wJSqFkE5Pbr8e
  727. https://open.spotify.com/album/6m9yMEqiE6uEhrRp68se0S
  728. https://open.spotify.com/album/5SD8Rdozct3RBCBmSPs89G
  729. https://open.spotify.com/album/1kWvX0tJWZQMV4ztvMmTO3
  730. https://open.spotify.com/album/7KjeWZkKmfPT0IbuGEAwHg
  731. https://open.spotify.com/album/5Mdgx8Sl0o1Z5S4yvxsk4s
  732. https://open.spotify.com/album/7z2wFRjEMx3e6TqNKa3MNd
  733. https://open.spotify.com/album/4fdm0qDYsL7ohg1KLrXqRM
  734. https://open.spotify.com/album/60N6qFFa42aKwD0AOkKgrl
  735. https://open.spotify.com/album/3ZHRUxp205uZ6h4Bxk8eRD
  736. https://open.spotify.com/album/72KQ0UvGyOg1drmEoETwsY
  737. https://open.spotify.com/album/6QzVbxXzPNEW1qQfR2y1nh
  738. https://open.spotify.com/album/1JsvK0bBbLQ3a3RUmqvhh5
  739. https://open.spotify.com/album/4YYekPlejBy5X5wotcDTLm
  740. https://open.spotify.com/album/67VfXNm7j2hVZAuNfzusND
  741. https://open.spotify.com/album/7gx0LHSSKb1zvhDsR1qlXj
  742. https://open.spotify.com/album/7wsjDzKqwlwxDJMNCr0GBc
  743. https://open.spotify.com/album/0Msj6QLuO1z7nEyzvN6Irb
  744. https://open.spotify.com/album/7JJm8HwliCfxne8IMG31l9
  745. https://open.spotify.com/album/1Z1GtIgbbzZdP8YRtBSMFQ
  746. Not available
  747. https://open.spotify.com/album/0HO5wjGn159W9tymooKuwS
  748. https://open.spotify.com/album/3vjKvq5sTB7M2o9t6lQWFW
  749. https://open.spotify.com/album/1Fe70vQ7EXYjynE7lGe5a8
  750. https://open.spotify.com/album/0mzW1Ok0eKZA1712LmEjwD
  751. https://open.spotify.com/album/2FOHuwfARdoSXytzbAuzky
  752. https://open.spotify.com/album/0O9bl7Kf2pnKZIE2UggXBU
  753. https://open.spotify.com/album/6fChr0wDnGVlbZo86pwBpL
  754. https://open.spotify.com/album/6rVtiDj4a6NTzA6cBhqzHr
  755. https://open.spotify.com/album/39e7F6yj5AkQBcMBgqx0xn
  756. https://open.spotify.com/album/4zPuW0rjBqWdW8WAOQea2C
  757. https://open.spotify.com/album/53LKezwD1gPUkbrjctewfn
  758. https://open.spotify.com/album/0jCSFZ33BJ4tIpZFSunGUS
  759. https://open.spotify.com/album/5WQawhjdyFldRPPfXzZlXB
  760. https://open.spotify.com/album/44FmS1arWXSF8msTTNLs1F
  761. https://open.spotify.com/album/6nbjor30rBuJkMDxVphr8t
  762. https://open.spotify.com/album/1j1cGp0SbDBXhDD4z9DNDE
  763. https://open.spotify.com/album/7nC8BaG7nZlVTA1oMD3d8i
  764. https://open.spotify.com/album/7It5yDcYuAwuharaGBulbp
  765. https://open.spotify.com/album/2Ab3m1wIJ7Og24AQcXqpDr
  766. https://open.spotify.com/album/1bx0cWK0nT7sszYa9y6o0X
  767. https://open.spotify.com/album/2G6fE5GqRvZAqKE7wJfuui
  768. https://open.spotify.com/album/1n8icO3BwuLa30R491S6PN
  769. https://open.spotify.com/album/3NMUXjLgqWGO6UP8L9GrbX
  770. https://open.spotify.com/album/1cSfHWplybRbrz3fQwJrlu
  771. https://open.spotify.com/album/2q478NAobUtiFplZk3irAf
  772. https://open.spotify.com/album/4GEZUQe63QHMUbVRm2qVIQ
  773. https://open.spotify.com/album/3BPKRLsFLCLsTsPNUc2HRV
  774. https://open.spotify.com/album/1s9YLn6PR4KuUOp8Vs4Xkf
  775. https://open.spotify.com/album/335jfcqrdWbZVwDfkqT0lU
  776. https://open.spotify.com/album/7ixugpsgmcFCjKfeUDL8ro
  777. https://open.spotify.com/album/1vWciNuhHcR1YuH4xXe4l4
  778. https://open.spotify.com/album/2D1GpZF8RqGlKSklBbgj6w
  779. https://open.spotify.com/album/483mk4BHBg2ma9iFzUz3M5
  780. https://open.spotify.com/album/4Th7mnq2a7uf5k2S9z7EQ1
  781. https://open.spotify.com/album/7lL2bQQPCDse2q8i3dMUjx
  782. https://open.spotify.com/album/7HhEcdNmiStc70DT0qzVxY
  783. https://open.spotify.com/album/4EjvvPim1wcnlNhNZjaP9k
  784. https://open.spotify.com/album/5aSra0kDmy7LlHe59nLcJh
  785. https://open.spotify.com/album/4vptJxkxzrfP1tXlc8m121
  786. https://open.spotify.com/album/61jYmljQv0lmucbuKEiHzC
  787. https://open.spotify.com/album/4RTghptkwIbIq160pe3jZM
  788. https://open.spotify.com/album/76TidMxZbTVogBOoM0ulA8
  789. https://open.spotify.com/album/2ac6XqWYgPrL0jYjtJHUb8
  790. https://open.spotify.com/album/4YA82is6EknJnoJSklUx4v
  791. https://open.spotify.com/album/2QweMWdHvDYUCozExzBHmM
  792. https://open.spotify.com/album/3OJP8vSzNpEw7HVzi2rTOi
  793. https://open.spotify.com/album/0aIAiBK8UkUpA6eYb1mUdW
  794. https://open.spotify.com/album/2WbGX8vWla3GiQ5PThmJZF
  795. https://open.spotify.com/album/3cw0ijH8cLdIKrCoAh1Lul
  796. Not available
  797. https://open.spotify.com/album/57bfCFzrv7MgiUhpe9oVo8
  798. https://open.spotify.com/album/1g2NpgmdW9ZJEtnYo4AAEa
  799. https://open.spotify.com/album/1WmnnvWIyZ1ESt5BQpGZ6T
  800. https://open.spotify.com/album/5bcr898rqwVdJTZta6SFo0
  801. https://open.spotify.com/album/2XsBduMp5RdZOTsWMqKJtv
  802. https://open.spotify.com/album/3ci4Yh7hNhAecGf4UqfEl8
  803. https://open.spotify.com/album/2QalqDoSKRt8Xo1RW8Xj3V
  804. https://open.spotify.com/album/1ZNocPzhsKlUjBwgWWZWuq
  805. https://open.spotify.com/album/4NR9t5I0TVUi1Yc3pLYHsx
  806. https://open.spotify.com/album/6oYSflckfXRUmL1MHnkOAQ
  807. https://open.spotify.com/album/655Ly71N60JXaE4A3bkXQt
  808. https://open.spotify.com/album/0FDRIgmEv6n2sERggnDQzy
  809. https://open.spotify.com/album/6179RIIF3vXkAaMqB1N3YV
  810. https://open.spotify.com/album/5PUYJ30eHIvzquoEaYhl8V
  811. https://open.spotify.com/album/4fOnrjQFQ2asr2asX2940u
  812. https://open.spotify.com/album/0qgsuBeCvrhEfJRboNRPxE
  813. https://open.spotify.com/album/4J0g0v4rAINnkvem7e5Fcu
  814. https://open.spotify.com/album/73rRnHjmwZbj9vFoD0tcGZ
  815. https://open.spotify.com/album/1fjWSIa9zzBMmO8OlPSW8m

Digital Control Systems 1.01

Digital control systems never did get enough attention during my Master System & Control in my opinion. In the various courses which I was taught, continuous-time control systems were always examined, but almost never digital control systems. For most courses this is also perfectly fine. However, you would expect that there would be also a more in-depth course about digital control systems into the curriculum. Especially, since almost all control systems are a digital control system.

I remember a course in which each group had to program a robot to convey pizza’s from one cabinet to another. A group mentioned, during their presentation, that they used a PID controller to control the various axis of the robot. I knew all the groups had designed their control algorithms in the continuous-time domain, therefore I asked; i) what discretization method(s) they had used, ii) if they had check the stability and iii) if they had checked the robustness (phase, gain and modulus margin) of their digital control system with respect to the continuous-time domain controller. Unfortunately none of my questions were answered. This disappointed me and was an acknowledgement of my opinion that not enough attention was given to digital control systems. Since this was one of the last courses given before one started their internship and graduation.

For the above reason, I will do a couple of blogs about digital control systems. I will try to focus on a single topic each blog and keep it clear and easy to understand; “If you can’t explain it simply, you don’t understand it well enough.”. In this first blog I will briefly go into the pros and cons of digital control systems and its analog counterpart. Followed by the introduction of the various type of signals that are present in a digital control system.

Pros and cons of digital control systems

Below is a list of pros and cons for both digital as well as analog control systems. Remark that there might be many more and that some pros or cons are subject to opinion, experience or interpretation.

Analog control Digital control
Pros
  • Robust; do not (often) break down
  • Continuous processing; no inherent bandwidth limits
  • Hard to modify; time-consuming, hardware needs to be rebuilt
  • Flexible; ability to create complicated controllers, easy to modify and fast to develop, less susceptible to aging and environmental variations
  • Robust; performance or safety can be monitored, errors can be dealt with appropriately
  • Diagnostics; on-the-fly testing, parameters can be adjusted, measurement signals can be stored
  • Low cost
Cons
  • Slow development; difficult to develop accurate designs due to tolerances in components
  • Complex: difficult to create complicated controllers, also hard to modify, testing alternatives is difficult, hard to build in intelligence, difficult to do multi-input-multi-output control
  • Disruptive noise
  • High cost
  • Discrete; signal might be inaccurate due to finite word length, time delays in control loop, discrete controller, stability might be an issue
  • Complex; complicated controllers, difficult to obtain a high bandwidth

While analog control systems have considerable disadvantages the flexibility of digital control systems stands-out. The latter made sure that companies adopted digital over their counterpart because it opened multiply doors. For instance, the rapid development of a complex controllers which incorporated optimization algorithms to maximize performance and profit. All created at the tenth of the costs for the same analog control system.

Types of signals in a digital control systems

The main disadvantage of digital control systems is found in the fact that one has to deal with discrete variables instead of continuous ones. Consequently, let us define the different types of signals. A Continuous-time signal is a signal for which every point in the time domain, this can be infinitely, an amplitude is defined. Similarly, a discrete-time signal is a signal for which only a sequence of points in time an amplitude is defined. Note that these points in time do necessarily have to be equidistant. In case it is, the signal has an associated periodic interval. Likewise to the domain, signals may also be continuous or discrete with respect to their range, i.e., amplitude.

Summarized; in general signals can either be continuous or discrete with respect to their domain or range. Herein, the domain is in general time, in case of control systems and the range can be anything; Voltage, Amperes, Newtons, meter per second, et cetera. Figure 1 shows the four possible combinations.

Figure 1. The four possible combinations of signal types.
Figure 1. The four possible combinations of signal types. Matlab code.

In Figure 1(a) an analog signal is displayed, which is both continuous in time and amplitude. Figure 1(b) shows a sampled signal; continuous in amplitude and discrete in time; Figure 1(c) the quantized signal, discrete in amplitude and continuous in time. Finally Figure 1(d), the digital signal. This signal is both discrete in time and amplitude. Remark: the exact definition of a quantized signal and sampled signal are often ambiguous. Often it is implicitly assumed that a quantized signal is also sampled, e.g., discrete in time. Likewise, the sampled signal is sometimes in explicitly assumed to be quantized as well. Lastly, the digital signal can be obtained by sampling and quantization of the analog signal.

We have read about the pros and con, and defined the different signal types present in a digital control system. Conclusively, I want you to point to the books in the references below, these are the best literature references in this field. I also use them as a reference for these blogs, and will try to point or refer to a chapter or section from the book when addressing a certain topic. In the next blog we will focus on the different system components of a digital control system.

References

[1] Levine, William S., ed. “The Control Handbook: Control System Fundamentals”. CRC press, 2010.
[2] Åström, Karl J., and Björn Wittenmark. “Computer-controlled systems: theory and design”. Courier Corporation, 2013.
[3] Franklin, Gene F., et al. “Feedback control of dynamic systems”. Vol. 3. Reading, MA: Addison-Wesley, 1994.
[4] Wittenmark, Björn, Karl Johan Åström, and Karl-Erik Årzén. “Computer control: An overview”. IFAC Professional Brief, 2002.
[5] Ogata, K. “Discrete-Time Control Systems”. Pearson Education, 1995.

Maintaining an overview of your financial expenses

At some point one you will want to keep track of your expenses to gain insight where you can save money. There are many websites and programs which offer insight into your expenses, for instance, YouNeedABudget, MoneyDashboard, GNUCash. However, for following three main reasons I decided to simply create my own expenses spreadsheet using Microsoft Excel.

  1. The programs often have a learning curve and you have to adapt to their way of working.
  2. I wanted to use a tool of which I can be almost certain that it will still exist in +20 years.
  3. Sometimes you will find yourself in the spot in which you want to have insight into some details. But, unfortunately these are not (directly) provided by the tool. Therefor I wanted to be able to program myself to gain insight. However, this still should be fairly simple to do.

Now let me tell you what my spreadsheet provides. Since I wanted to categorize my expenses I created one sheet with categories and subcategories. To keep track of all the transactions, a table was created in which all main transactions details are logged. The table has the following fields: bank account, type of account (saving or payment?), date, type  (income or expense?), amount, currency, kind (variabel or fixed?), category, subcategory and remarks. While there is a currency field, it is not used yet. The with main reason for this is because fortunately I do not have to deal with money different currency types. To gain insight into the data from the table, three pivot tables and charts were created. Using the pivot tables and charts, which are semi-interactive, one is able to, for instance, zoom-in in a particular category or time stamp. To finalize, I created a kind of dashboard in which all income and expenses data is summarized per month. First details are displayed about my balance of my payment and savings account. Followed by all the expenses details, sorted by category. Using the outline group functionality one is able to open the category and list the subcategories for that month. For each category and subcategory I show its portion (in percentage) with respect to all expenses, the median per month and the average per month. Using conditional formatting this data is also visualized to give a overview, such that you are able to identify the ratios and relationships quickly. sparklines are being used to show the trend of the expenses through out the year. Concluding, the dashboard sheet makes sure that all the data and details are visible at one glance but still manages to dive into details.

You can download an example with dummy data of the Excel sheet over here: Financien (example)

Codenames

Codenames is played between two teams, red and blue on a set of twenty-five codenames. Each team consists of a single spymaster who knows the secret identity behind each codename, with the remaining players as field operatives who will contact the codenames. On each turn of the game, the spymaster provides a clue to their field operatives. The field operatives will then attempt to contact at least one of their aligned agents based on the codenames clued. The first team to activate all of their agents wins the game!

Codenames is an interesting game since it can be adapted to a variaty of themes. For instance, it can be themed to Harry Potter. As such it is also a very good game to be played with children. Therefor, I created an excel file (Update 2017-04-30: I updated and added two additional word lists to the file; i) the official word list and ii) an extensive noun word list. Download here) from the original game which includes all the necessary items for the basic game:

  • Codenames (two categories, general and Harry Potter)
  • Map cards
  • Identity cards

You can print these on sheets of paper and cut them out. Now follows a set of detailed instructions for playing the game.

Identity cards
Identity cards
Codenames.
Selection of the codenames.
Map cards.
Selection of the map cards.

Setup

Players are divided into two teams, Red and Blue. Each team consists of one spymaster, with the remaining players as field operatives. All players observe a set of twenty-five words, representing codenames for agents aligned with each team. While field operatives do not observe the identities of each of the codenames, the spymasters each get to see the identity of all codenames on the map card.

There are four different agent identities: red agent, blue agent, bystander, and assassin. One of the teams will have nine of their-colored agents in the set of codenames, while the other team will have eight agents. The team with nine agents will take the starting turn in the game. Among the eight codenames not aligned with either team, there are seven Bystanders and one Assassin. Effects for contacting these agents are described in the following section.

Game flow

On a team’s turn, their spymaster must start by providing their field operatives with a clue for the identities for their own agents. A clue consists of a single word and a number. The word should be related to the codenames that are aligned with the acting spymaster’s team, while the number represents how many codenames are related to the clue word. Further guidelines, including two special number rules, follow in the section below.

Once a clue has been given, the field operatives are free to discuss which codename(s) should be contacted. When the field operatives have decided on a guess, they may register their guess by touching the codename. The host or spymaster will reveal the identity of the codename by putting an identity card (Red Agent, Blue Agent, Bystander or Assasin) on top of it.

If the revealed agent is of the same team as the operatives, then they may continue making guesses. A maximum number of guesses may be made equal to the number given in the spymaster’s clue, plus one. Alternatively, the field operatives may pass to end their turn, so long as they have made at least one guess already on their turn. If the revealed agent is not of the same team, then the turn ends. In the special case that the assassin was revealed, then the team that performed the reveal immediately loses the game.

Spymaster Clue Guidelines

Spymaster clues consist of a single word and a number, with the following guidelines:

  • Words must be related to the meaning of the codenames being clued.
  • The number following the word cannot be used as a clue itself.
  • Clues may not include codenames or related forms of codenames. For compound codenames, this includes the constituent words that comprise the compound word. Once a codename has been guessed, it can be used in clues.

Overall, be reasonable about rules; spymasters may consult with their opposing spymaster and the host for the validity of a clue. If an invalid clue is provided, then the turn immediately ends and the opposing spymaster may declare an agent of their own color before making their own clue.

Spymasters have two special options for numbers associated with their clue words. First, spymasters may declare zero (0) as their clue, suggesting that none of the codenames are related to their declared word. In the case that zero is declared, the field operatives do not have a limit to the number of guesses that they may make before passing. The second special option is to declare “unlimited” as their clue, suggesting at least one codename is related to the declared word. As with zero, the number of guesses that may be made by field operatives before passing is unlimited.

(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:

  • Name of the task
  • 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 (\text{min}), the most likely (\text{mode}) and the maximum (\text{max}). The probability density function (PDF) is given by

    \begin{equation*} f(x) = \frac{1}{B(\alpha_1,\alpha_2)}\frac{(x - \text{min})^{\alpha_1 - 1} (\text{max} - x)^{\alpha_2 - 1}}{(\text{max} - \text{min})^{\alpha_1 + \alpha_2 - 1}} \end{equation*}

where

    \begin{equation*} \alpha_1 = 6 \left( \frac{\mu - \text{min}}{\text{max} - \text{min}} \right), \quad \alpha_2 = 6 \left( \frac{\text{max} - \mu}{\text{max} - \text{min}} \right), \quad \end{equation*}

with

    \begin{equation*} \mu = \frac{\text{min} + 4\text{mode} + \text{max}}{6} \end{equation*}

being the mean.

An additional shape parameter \gamma 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 \alpha_1 and \alpha_2. These are namely defined as:

    \begin{equation*} \alpha_1 = 1 + \gamma \left( \frac{\mu - \text{min}}{\text{max} - \text{min}} \right), \quad \alpha_2 = 1 + \gamma \left( \frac{\text{max} - \mu}{\text{max} - \text{min}} \right), \quad \end{equation*}

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:

  1. Six things to do before writing your manuscript
  2. 11 steps to structuring a science paper editors will take seriously
  3. Writing the first draft of your science paper — some dos and don’ts

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