## Control System & PID controller

Control systems, as it is being taught on many universities in the world, regulates the behavior of a system using feedback. Systems may be mechanical, electrical, biological, economical or any other domain. Feedback as in many aspects of life is crucial. A target value for an essential variable of the system, the process value , is set. The target value is also referred as setpoint or reference value, whereas the process value is referred as measurement value. The control system calculates the difference between the setpoint and the process value, called the error of the control system.

From this point we will focus mainly on the structure, design and implementation of the linear feedback controller. The figure below shows the structure of the control system with a linear feedback controller. We neglect any possible source of disturbance.

The linear feedback controller is often the combination a controller and multiple filters. The controller of the control system computes a control value which is applied to the process and tries to regulate the error to zero. A filter also often referred as compensator, is tries to improve the characteristics and performance.

The most famous feedback controller is the Proportional–Integral–Derivative (PID) controller is defined by (1). Based on the error it calculates a correction to be applied to the process based on proportional, integral, and derivative terms, respectively. Heuristically, the terms of a PID controller can be interpreted as corresponding to time: the proportional term depends on the present error, the integral term on the accumulation of past errors, and the derivative term is a prediction of future error, based on current rate of change.

(1)

Herein, and for which and denote the frequency at which the derivative and integral action start to become active. In addition denotes the proportional gain of the controller. An ideal derivative is not causal (2) – its output depends on future inputs see – therefore, the PID controller is often combined with either a first or a second order low-pass filter (3). This makes the PID controller causal, depending only on past and current inputs but not future inputs.

(2)

(3)

Below you see an interactive bode diagram of a PID controller combined with a second order low-pass filter with some typical values. You clearly see the integrator action up to 10 [Hz], followed by the proportional gain action from 10 to 25 [Hz]. The derivative term is visible from 25 to 300 [Hz] and eventually the low-pass filter from 300 [Hz] and further.

## Pocket Leaflet First Aid (Dutch)

In 2017 I participated with the “Nijmeegse vierdaagse” also called the The Four Days Marches. This is a walking event where people (~43.000 people) walk four consecutive days a distance between 30 to 50 kilometers a day, depending on age and gender.

During this event I had to go numerous of times to the First Aid, provided by the Dutch Red Cross, for my blisters on my feet. The organization was really impressive. As follows I decided the join the Red Cross in the Netherlands as a First Aid volunteer.

At our branch of the Red Cross, so called “LiBoZa” cards where shared. “LiBoZa” is short for “Linker Boven Zak”, which translates to “Left Side Upper Pocket”. It is a small leaflet which fits in the pocket of your blouse. This type of leaflet shows all kind of useful details about a certain topic summarized. These are used to;

• For one as to remember the most important content. As a trained individual you are supposed to know all the content. However, in the beginning when I had little to no experience I found these leaflets very useful to check upon.
• Discussion, nowadays I use the leaflet more as a conversation starter

Since I liked providing aid to people I also joined the emergency response officers at my company. At that moment I decided to produce my own leaflets. For two reasons; i) optimizing the content of the leaflet. Online there are various leaflets and all of them have different content, ii) I wanted to add leaflets about safety and fire related topics.

So without further I want to share my produced leaflets with you. Three notes;

1. I am not a (medical/fire/safety) professional, I just got the content from the internet from multiple sources and tried to combine the best out of all of them, so in no way I will be held responsible. In case you need help always request help from a professional.
2. Furthermore, the leaflet is in Dutch. So I apologies if you are English. I do want to create a translation someday, but at this moment it is only in Dutch.
3. If you are interested in the source documents, you can always contact me.

Before I go to bed, on a raining day or when I am alone, I like to read. From Fantasy Books to Magazines. However, after finishing university I started reading more self-help and professional books. Since then I have read numerous books. As such, I want to share the list below with you which I believe is worth reading when you are interested in professional development.

• Getting Things Done by David Allen

Should need no introduction. It is the book on productivity and effectiveness in your daily work. It rests on the idea of moving planned tasks and projects out of the mind by recording them externally and then breaking them into actionable work items. This allows attention to be focused on taking action on tasks, instead of recalling them.

• Strenghts Finder by Marcus Buckingham & Donald O. Clifton

A self-help book about finding your own talents which result in an individual’s tendency to develop certain skills more easily and excel in certain fields in a sustainable way while failing or not being able to sustain success or high levels of effectiveness in other fields. However, note that each talent also has pitfalls.

• One Minut Manager by Ken Blanchard & Spencer Johnson

A very short book about three techniques of an effective manager: one-minute goals, one-minute praisings and one-minute reprimands.

• I don’t have to make everything all better by Gary B. Lundberg & Joy S. Lundberg

A book about effective communication with your partner, children, friends, parents, colleagues and anyone else. The book addresses an all too common dilemma that arises when others expect you to solve their problems for them. The book is refreshingly straightforward and inspiring using entertaining.

• Our Iceberg is Melting by John Kotter & Holger Rathgeber

A must read about change management. It tells the story of a colony of penguins facing a dilemma. But contained within the story and the characters is a powerful message about the fear of change and how to motivate people to face the future and take action.

• The 7 Habits of Highly Effective People by Stephen R. Covey

Like Getting’s Things Done and the One-Minute-Manager, the 7 Habits of Highly Effective People is a self-help book about effectiveness. As the title says it explains 7 habits how one self can be more effective in both personal as professional life. It is a bestselling book and a must read for everyone who wants to work in becoming more effective.

• The Emotional DNA by Pierre Capel

The book to understand emotions and where they come from. Feelings namely do not exist, they emerge. When we talk about our feelings, we know exactly what we are talking about. But if we want to know how they emerge, where they come from and what they do to us, then we are not so sure. For many people, feelings are like a fog that floats through our body. But is that true? Feelings are linked to a rock-solid biochemistry, that has an enormous impact on our functioning.

• The Art of War by Sun Tzu

Twenty-Five Hundred years ago, Sun Tzu wrote this classic book of military strategy based on Chinese warfare and military thought. Since that time, all levels of military have used the teaching on Sun Tzu to warfare and civilization have adapted these teachings for use in politics, business and everyday life. The Art of War is a book which should be used to gain advantage of opponents in the boardroom and battlefield alike. The Art of War is still a recommended read for military officers in training.

• How to win friends and influence people by Dale Carnegie

The bestselling book of Dale Carnegie’s about proper day-to-day communication. Its advice has remained constant and applicable across the years for a reason. It’s simple and his techniques make perfect sense. Definitely a must-read.

## Birthday Calendar

Since recently I did not yet had a birthday calendar in my apartment. This was because I namely dislike the very ordinary “toilet kind” of birthday calendars, see below on the left. More than a year ago I stumbled upon a very original birthday calendar on Pinterest. Immediately I became spontaneous, it has a very nice look, it is original with its clothespins and easy to maintain as well as built.

A while ago I finally gave myself the time to replicate the idea. Using the clothespins I determined what the minimum size of the wooden plank had to be, 125 [cm] in length and 25 [cm] in width. At first I tried to find an old plank of a pallet. Those often have that old look which I wanted to go for. Unfortunately none of them did met the requirements w.r.t. the size. So in the end I just bought a plank from a hardware store and sawn it to the correct dimensions.

To do the writing of the header “birthday”, the months and the names of the people I bought a white and black acrylic marker called “DECO painter matt” of the brand Marabu. To make sure that the letters on the wood of the word “birthday” would be consistent, I made a small mold out of paper. The months I just drawn out of hand, same for the names and days on the clothespins.

In the example on Pinterest the clothespins are colored. This can be achieved by coloring the clothespins with paint or by buying colored clothespins. You can find the latter by searching on children toys. I did not color them and searched for old and worn clothespins. If you do not have those you can buy new ones and put them in the watery garden and wait a week or two.

## “Down” time games

When having a training, introduction or travel with a large group there might be moments in which everyone is a bit bored or might be waiting for something or someone. For these moments you can use so called “down” time games (in Dutch dodemoment spelletjes). These are small simple games which you can do with your group. In this blog I explain a couple of down time games for you.

## Floating

You will need four chairs arranged in a square (close together). Four people sit on the chairs. Proceeding clockwise, they recline onto their neighbors’ laps (keeping their feet on the ground). The chairs are pushed out from under the sitting/reclining people, leaving a floating group. How long can they keep it up? When there are no chairs available, you can use four people to play the part of the chair by standing on their hands and feet. In the video below you see it in action.

## The Human Knot

One person will move out of the group and shuts his eyes. The group will stand in a circle next to each other and holds hands. After this points hands should stay connected at all times. Following everyone will move crisscross, above or underneath each other to form a human knot. The person who was placed out of the group then has the task to untie the “knot”.

## The Land of No Idea

Far, far away lays the Land of No Idea. They do have people there, but no children; they have membranes, but no skin; they have no vehicles, though they do have cars and scooters. They have computers, but no modems, monitors, or keyboards. Some words do exist while others do not. The answer lies in the name of the game; The Land of No Idea. The catch is in pronunciation of the word “idea”. The correct sentence would be; The Land of no “id”. So all words with either an “i” or “d” do not exist.

## Black magic

All the players sit in a circle, and there are once again two game leaders (A and B). B leaves the room or space briefly. A asks someone from the circle to choose a nearby object, which B will have to guess. B is now called back. A begins to point out different nearby objects. For example: “Is it these trousers?” -“No”- “Is it that watch?” – “No”- and so on. B will continue to answer “No” to A’s questions, until A mentions the correct object – the one that the players previously agreed on. B will now answer “Yes”. How is that possible? How does it work? The clue is in the title – black magic. A will mention all kinds of objects that are not black. After mentioning several objects, A will mention one that is completely black. The next object that A mentions is the one that has been agreed on with the group. In other words, the game leaders know which object it will be beforehand: it is always the object that comes after the black object.

## Who am I

Everyone takes a small piece of paper and writes down a name of a person that everyone knows, taking care not to show it to the person next to them. It could be someone famous or a personal acquaintance, or a fictional character, for example. You then attach the note onto the forehead of the person next to you using sticky tape. When everyone has a name on their forehead the game can begin. Taking turns, everyone asks yes/no questions about themselves, for example, “am I a woman?”, which the group then answers with “yes” or “no”. If the answer to the question is yes, the same person can ask another question; if it is no, the turn passes to the next person. The winner is the first person to work out who he or she is – the rest of the group can continue playing if they wish.

## Black Stories

The game leader tells how a person died. The group then has to guess how the person has died and may only ask questions which can be answered with yes or no. Online you can find numerous amount of riddles or apps.

• A guy is lying dead in a phone booth; the handset is off the hook, and there is glass lying on the ground outside the booth.

Solution: He called his wife to tell her how big the fish was that he had caught. The wife asks, “How big was it?” The man stretches out both arms to indicate the length (“THIS big!”), ramming both arms through the glass. In doing so, he cut his wrists and died.

• A man is lying dead in the forest, wearing his swimming trunks.

Solution: The man had been swimming in a lake/ocean. A firefighting aircraft scooped him up and dumped him in a burning forest. The man died from the fall.

• A man has hanged himself from the roof of a warehouse four meters high (he is hanging two meters above the ground). The warehouse is in the desert, and there is no ladder or similar object to be found. How did he do it?

Solution: He was standing on a block of ice two meters high. The ice melted and evaporated.

• A man went out on the street, saw a hotel, and knew that he was bankrupt.

Solution: He was playing Monopoly.

• A sailor goes into a restaurant, eats an albatross sandwich, and then falls over dead.

Solution: He had been shipwrecked a while ago. There had been nothing to eat on the uninhabited island. Several of his companions had died of hunger. He and his buddy were also ravenous. His buddy made two “albatross sandwiches,” which they quickly devoured. It now appears that the delicacy had not been albatross at all, but one of their former shipmates. This was too much for the man.

• A man lives on the twelfth floor of an apartment building. In the morning, he takes the elevator to the ground floor to go to work. When he returns in the evening, he takes the elevator to the sixth floor and takes the stairs to the twelfth. When it’s raining, however, he takes the elevator to the twelfth floor. Why?

Solution: The man is a midget and can reach the button for the sixth floor, but no higher … unless he has an umbrella with him.

• A man is sitting in the non-smoking section of the Swiss railways. He grabs his gun and shoots himself through the head. If he had been sitting in a smoking compartment, this would not have happened. Why not?

Solution: The man had been blind for years and was just returning from having surgery on his eyes. The surgeon had said that he could not yet remove the bandage from his eyes. Once in the train, however, he couldn’t wait, and he removed his bandage. At that precise moment, the train entered a tunnel and the compartment was shrouded in darkness. The man thinks that the operation had failed and that he will never be able to see, and so he shoots himself in the head. If there had been a smoker in the compartment, he would have seen the red tip of the burning cigarette.

• The smallest man in the circus discovers sawdust under doormat: he now knows that he is growing!

Solution: As a midget, the smallest man in the circus earns his money with his stature. He does not notice that he is growing. To disguise this, his girlfriend regularly saws thin chips off the chair legs. She sweeps the sawdust under the doormat.

• Romeo and Juliet are lying dead on the bed, and the window is closed.

Solution: Romeo is a cat, and Juliet is a fish. Romeo choked to death while eating Juliet.

## Vikings

The group is in a circle. At the beginning one Viking is appointed. The two people sitting on the left and right of the Viking are the rowers. The rest is the sea. The Viking starts holding his hands like two horns to his head (like a viking helmet). Following he makes a growling Viking sound; aarrrrghh, raaaaaarrrrrrrw, et cetera. At the same time the rowers make a rowing movement (to the correct side) and say; row, row, row, row, et cetera. The people appointed as sea imitate waves with their hands and constantly say; woesh, woesh, woesh, et cetera. At a random point in time the Viking appoints a new Viking who adopts the new role and as such there will also be new rowers and a new sea.

## Implementation of a filters

The discrete-time transfer function is often obtained from its counterpart, the continuous-time transfer function via discretization. A discrete-time transfer function has the following form:

(1)

Herein, is the input and is the output of the system, and are the degree of the numerator and denominator, respectively. Where , meaning we are dealing with a proper transfer function. While (1) is valid for any order it is not recommended to directly use transfer functions of high order. These can namely introduce numerical problems very quickly. Rather factorize the numerator and denominator of (1) into a cascade of first and second order polynomials.

Now let us look at the simple discrete-time transfer function of order two:

This function is non-causal, because it depends on future inputs. Therefor, both the numerator and denominator are multiplied by reciprocal of the highest order of occuring in the denominator, in this case , to make the system causal. Hence, we obtain:

Followingly, using the linearity and time-shifting properties of the -transform, i.e., and , we obtain the difference equation. Remark that the shift operator is defined as , the forward shift operation and , the backward shift (delay) operator. As a result we obtain,

(2)

Rewriting (2) gives us:

This last equation is the difference equation which we can easily implement on our digital platform. Numerous methods exists on how to implement a filter. Four of these methods are closely related to each other. These are:

• Direct form I
• Direct form II
• Transposed direct form I
• Transposed direct form II

## Direct form I

The direct form I is an FIR filter followed by an IIR filter. That is to say, it implements followed by

(3)

In an algorithm you can implement it as:

yk = b0 * xn + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2x2 = x1x1 = xny2 = y1y1 = yn

Where, x1, y1, x2 and y2 are the four state variables.

## Direct form II

The direct form I is an IIR filter followed by an FIR filter. Which implements followed by .

(4)

In an algorithm you can implement it as:

s0 =      xn - a1 * s1 - a2 * s2yn = b0 * s0 + b1 * s1 + b2 * s2s2 =      s1s1 =      s0

Where, s0, s1, s2 are the three state variables.

## Direct form I transposed

Both direct forms can be converted to an equivalent transposed form via:

• Reverse direction of each interconnection
• Reverse direction of each multiplier
• Change junctions to adders and vice-versa
• Interchange the input and output signals

(5)

In an algorithm you can implement it as:

vn = xn + s2yn =      s4 + b0 * vns4 =      s3 + b1 * vns3 =           b2 * vns2 =      s1 - a1 * vns1 =         - a2 * vn

Note that this form is very inefficient. You can easily shift the delays to the center, obtaining the direct form II.

## Direct form II transposed

(6)

In an algorithm you can implement it as:

yn = s2 + b0 * xns2 = s1 + b1 * xn - a1 * yns1 =      b2 * xn - a2 * yn

## Symbol to represent Emergency Response Team (ERT) Bedrijfshulpverlening (BHV)

Emergency response officers (ERT), or in Dutch Bedrijfshulpverlening (BHV), within companies are trained in providing both first aid and limiting and combating (small) fires. All to limit the consequences of accidents. Various icons are used to resemble these organisations. One symbol which I have seen quiet often is the combination of first aid and a fire symbol.

However, since there was not yet a vector format available, I created one. Using the established first aid and fire sign from ISO 7010.

On the left the fire symbol with the red color. On the right half of the first aid cross with the green color. The red and green color form a gradient in the middle.

## Filters in Control Systems

In this blog I want to elaborate on the various types of filters that are being used in Control Systems. These filters are often used in combination with a PI, PD or PID controller to obtain a robust controller. The filters which we will discuss are:

• Low-Pass filter
• High-Pass filter
• Notch filter

Using these four filters we can create other filter types, such as a Band-Stop or Band-Pass filter. The behavior of each filter can be captured by a transfer function in the continuous-time using the Laplace domain of either first and/or second order. We use the transfer functions to describes the filter and as such the relation between the input and the output . Throughout this blog we will write the equations in the form of their angular frequency in [rad/s], also known as radian frequency. However, we will specify filters using their frequency in [Hz]. Using the radial frequency notation results in a more visual compact formula. Additionally, it is also possible to specify the filters in form of their time constant in [s]. The following relation holds between the angular frequency, frequency and time constant.

Many forms are used within literature, one book will use angular frequencies, the other will use time-constants. Finally, for second order filters, the only filter with possibly complex poles or zeros, can be written in various ways. We will specify second order filters in terms of the damping of the corresponding frequency. It is also possible to describe these formulas using the Quality factor . Whereas describes how oscillations decay in a system after a disturbance,  describes how underdamped the system is. The following relation holds between and

## Low-pass filter

A low-pass filter is used to pass signals with a frequency lower than a certain cut-off frequency . Below the formulas for both the first- and second-order low-pass filter is given.

Herein, denotes the gain, denotes the low-pass cut-off frequency and denotes the damping. Whereas the first-order supresses with 20 [dB/dec], the second-order supresses with 40 [dB/dec]. Low frequent the filter gain is .

## High-pass filter

The complement of a low-pass filter is a high-pass filter. This filter is used to pass signals with a frequency higher than a certain cut-off frequency . Below the formulas for both the first- and second-order high-pass filter is given.

Herein, denotes the gain, denotes the high-pass cut-off frequency and denotes the damping. Likewise as the low-pass filter the first-order supresses frequencies with 20 [dB/dec] and the second-order with 40 [dB/dec].

A lead-lag filter, also known as a lead-lag compensator, is often mainly used for phase compensation rather then magnitude. Below the formula for a lead or lag filter is shown.

Herein, and denote the frequency of the pole and zero, respectively. The filter functions as a lead filter if   and otherwise as a lag filter. The filter has its maximum or minimum phase at . Finally, at the filter has a gain of or in case of a lead or lag filter, respectively. Naturally, the filter can be cascaded with itself by which a the filter can be a lead and lag filter simultaneously.

## Notch filter

A notch filter is often used to filter undesired resonance peaks. Below the formula for a notch filter is shown.

Herein, and denote the frequency of the pole and zero, respectively. Likewise, and denote the damping of the pole and zero and is as usual the gain. When the notch will target one specific frequency. The gain at that frequency is given by . When the notch filter is also referred as a skewed notch and the difference between gain at low and high frequencies is given by .

## Getting things done

A while ago I read the book Getting Things Done (GTD) written by David Allan. In my own personal workflow I was already applying GTD. However, after reading the book I further refined my personal workflow. My fellow colleagues were interested and also in need of GTD. Therefore, I made a short presentation about my own personal workflow, with tips & tricks. Feel free to use the presentation for your own benefits.

## 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.

# 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.