root locus

ROOT LOCUS

Pada sebuah pengendalian water tank level berdasarkan ketinggian, tentu kita pertama kali harus mengetahui transfer function dari sebuah water tank tersebut. Setelah kita tahu TF nya maka kita dapat mengontrol ketinggian air dengan cara menggunakan Controller. Controller ini digunakan untuk menyetel kondisi akhir TF sesuai dengan yang kita inginkan. Agar tercipta kestabilan dalam melakukan sistem kontrol maka kita memasang untai blok diagramnya menggunakan sistem FeedBack dan untuk steady state error analysis kita menggunakan analisis kestabilan berdasarkan rootlocusnya.

Berikut gambar untai diagramnya:

Kemudian kita menyetel kondisi controller sesuai yang kita hendaki kemudian kita cari transfer function keseluruhan blok diagram untuk steady state error analysis with root locus.

Sebelum kita membahas lebih jauhmengenai analisis kestabilan menggunakan root locus, hendaknya kita tahu dulu dari definisi root locus tersendiri:

• ROOT = akar-akar

• LOCUS = tempat kedudukan

• ROOT LOCUS

– Tempat kedudukan akar-akar persamaan karakteristik dari sebuah sistem pengendalian proses

– Digunakan untuk menentukan stabilitas sistem tersebut: selalu stabil atau ada batas kestabilannya?

Root locus merupakan suatu metode yang ampuh untuk analisis dan disain yang ditemukan oleh W.R. Evans

Root locus merupakan suatu teknik grafis yang memberikan kita deskripsi kualitatif mengenai performa suatu sistem kontrol.

Root locus dapat digunakan untuk memecahkan persoalan-persoalan kontrol untuk sistem-sistem ordo tinggi

Root locus dapat juga digunakan untuk menaksir stabilitas.

Adapun cara-cara untuk mengetahui atau mencari root locusnya sebagai berikut:

• Cara 1: Mencari akar-akar persamaan karakteristik pada tiap inkremen harga Kc (controller gain)

• Cara 2:

– Mencari harga pole dan zero

– Menentukan harga breakaway point, center of gravity, asimtot

– Mencari harga w_u (titik potong dengan sumbu imajiner, menggunakan substitusi langsung)

Dan untuk mengetahui kestabilan tersebut tentu juga kita harus mengetahui pole dan zero dari persamaan TF total dari blok diagram:

• Untuk mempermudah analisa respons suatu sistem digunakan

– Pole - Zero

• Pole :

– Nilai variabel Laplace s yang menyebabkan nilai transfer function tak hingga

– Akar persamaan dari penyebut (denominator) transfer function sistem.

• Zero :

– Nilai variabel Laplace s yang menyebabkan nilai transfer function nol

– Akar persamaan dari pembilang (numerator) transfer function sistem.

Total respon output sistem :

• Definisi kestabilan (berdasar natural response):

– Sistem stabil jika natural response mendekati nol saat waktu mendekati tak hingga

– Sistem tidak stabil jika natural response mendekati tak hingga saat waktu mendekati tak hingga

– Sistem marginally stable jika natural response tetap/konstan atau berosilasi teratur

• Definisi kestabilan (berdasar total response/BIBO):

– Sistem stabil jika setiap input yang dibatasi mengahasilkan output yang terbatas juga.

– Sistem tidak stabil jika setiap input yang dibatasi mengahasilkan output yang tidak terbatas

Nah untuk lebih jelasnya bagi agan-agan semua nie dapat dilihat di presentasi kami klik di sini.

Man in Control

As we promise to you that we’ll back sooner with update content,here it is: Man In Control engineering. The reason why we concerned with this article is the truth that nowadays student doenst recognize it’s principal,I mean someone like lyapunov,laplace,and kalman. We just use their invention,without knowing who they are,pretty sad,huh? Haha,so here it goes

1. Pierre-Simon Laplace 1749 - 1827
I know what you may thing,yeah he is THAT laplace transform guy,the one who make us suffer,the one who make us didn’t sleep for weeks,the one who we cry because of signal and system aka ISIS ^^
Aside from that,Laplace transform guy or should I call him by his name: Pierre-Simon Laplace is quite nice French, living the same era as Napoleon Bonaparte. Known for -well you name it- Laplace transform which can transform time domain into frequency domain and vice versa. His contribution toward control engineering is priceless, simplify complex calculation into simple calculation,making control engineer’s task easier.
A mathematician who firmly believed the world was entirely deterministic. Like a man with a hammer to whom everything was a nail, to Laplace the universe was nothing but a giant problem in calculus. Laplace is good? Yeah definitely not for us !!


2. Rudolph E. Kalman
Seriously,I didn’t know this man,except its Kalman filter that is used in praktikum ISIS ^^. Here is what I find from wiki:
Rudolf (Rudy) Emil Kalman, born on May 19, 1930, in Budapest, Hungary, is a Hungarian-American electrical engineer, mathematical system theorist, and college professor, who was educated in the United States, and has done most of his work there. He is currently a retired professor from three different institutes of technology and universities. He is most noted for his co-invention and development of the Kalman filter, a complicated mathematical formulation that is widely used in control systems, avionics, and outer space manned and unmanned vehicles. For this work,.
Another genious guy born in the right time,that is Rudolph E. Kalman. Graduated from MIT and Columbia university is enough to make us drooling ^^. We know this man from praktikum isis,yeah THAT kalman filter. Kalman filter is a mathematical technique widely used in the digital computers of control systems, navigation systems, avionics, and outer-space vehicles to extract a signal from a long sequence of noisy and/or incomplete technical measurements, usually those done by electronic and gyroscopic systems.
Kalman's ideas on filtering were initially met with vast skepticism, so much so that he was forced to do the first publication of his results in mechanical engineering, rather than in electrical engineering or systems engineering. Kalman had more success in presenting his ideas, however, while visiting Stanley F. Schmidt at the NASA Ames Research Center in 1960. This led to the use of Kalman filters during the Apollo program, and furthermore, in the NASA Space Shuttle, in Navy submarines, and in unmanned aerospace vehicles and weapons, such as cruise missiles.
To appreciate his contribution in control automation engineering U.S. President Barack Obama awarded Kalman with the National Medal of Science on October 7th, 2009

3.Aliaksndr Lyapunov
Hahaha,I know what you think,is it real? Yeah, his moustache are real^^
Well back to topic here is what I can get from wiki ( im sorry for CTRL C+V on wiki for aliaksandr lyapunov’s. I dunno anything about this man) :
Aleksandr Mikhailovich Lyapunov (Russian: Александр Михайлович Ляпунов; June 6 [O.S. May 25] 1857 – November 3, 1918) was a Russian mathematician, mechanician and physicist. His surname is sometimes romanized as Ljapunov, Liapunov or Ljapunow.
Lyapunov is known for his development of the stability theory of a dynamical system, as well as for his many contributions to mathematical physics and probability theory.
Lyapunov contributed to several fields, including differential equations, potential theory, dynamical systems and probability theory. His main preoccupations were the stability of equilibria and the motion of mechanical systems, the model theory for the stability of uniform turbulent liquid, and the study of particles under the influence of gravity. His work in the field of mathematical physics regarded the boundary value problem of the equation of Laplace. In the theory of potential, his work from 1897 On some questions connected with Dirichlet's problem clarified several important aspects of the theory. His work in this field is in close connection with the work of Steklov. Lyapunov developed many important approximation methods. His methods, which he developed in 1899, make it possible to define the stability of sets of ordinary differential equations. He created the modern theory of the stability of a dynamic system. In the theory of probability, he generalised the works of Chebyshev and Markov, and proved the Central Limit Theorem under more general conditions than his predecessors. The method he used for the proof found later widespread use in probability theory

Like many mathematicians, Lyapunov preferred to work alone and communicated mainly with few colleagues and close relatives. He usually worked late, four to five hours at night, sometimes the whole night. Once or twice a year he visited the theatre, or went to some concert. He had many students. He was an honorary member of many universities, an honorary member of the Academy in Rome and a corresponding member of the Academy of Sciences in Paris

I don’t know whether this article is an interesting or not,but for sure,knowing founding father (until now,I can’t get who is founding mother :D) is a common policy and working knowledge for control engineer!!

Ps: anyone noticed this blog’s name? LEER-BEHEER? Just go check it out in your african’s dictionary and you will find what that weird words mean ^^


Contributed by : Rian Fatah M,34458
Reference : wikipedia.org

1st case: water level

Hi,

This time we,kelompok kucing beranak 5 will present our task that Mr.Priyatmadi gave us yesterday. Yeah,it is our 1^st task,”How to control water level tank”. The task itself contain 2 cases. The 1^st is controlling water level tank into stable height 1 metre,so if the level reached 1 metre, the source water (ie water tap) stopped; in other word the level maintained constant 1 metre.

The 2^nd case is how if we want to control its level? Off to topic,thanks to indra we had completed this 2^nd case which way more difficult than 1^st cause of his experience in robotic design (yes,INDRA DARMAWAN BUDI teamed with his friends compete for national robotic art festival held not in july,lets pray for their victory ^^),oke back to topic, the idea for 2^nd task is simple. Just do it with microcontroller.

Oke,here it goes my group’s plan about the task given by Mr priyatmadi;

1. Maintained water level into constant 1 metre

Well,to be honest, at first we didn’t knew what should we did -_-. Then Mr priyatmadi came to our group and asked if we had completed the task or not. Hahaha,we honestly said that we hadn’t did anything yet. Then mr.priyatmadi said: “why don’t you use transducer as its core?” Voila,yeah we forgot about transducer. Basicly,transducer is a device that converts one type of energy to another. The conversion can be to/from electrical, electro-mechanical, electromagnetic, photonic, photovoltaic, or any other form of energy. While the term transducer commonly implies use as a sensor/detector, any device which converts energy can be considered a transducer.

From Instrumentation Elektronik class,we had received some transducer lesson,so we decided to use pressure transducer,that is flexiforce. The characteristic of flexi force is a transducer or we should say sensor that convert pressure or weight into resistance. The idea is simple: place flexiforce at the bottom of the tank and then connect its output with adc and then follow with some nice listing in micro (see the file,). Maybe it is easier to understand with step:

1. Collect data

Convert pressure given by water at various level into resistance using flexiforce (just put it in the bottom of the tank). The result later used to code microcontroller

2. Design listing in microcontroller

Our idea is simple,from data that we had collected before,various resistance that produced from flexi converted in adc into random number starting from 0-255. This number is our key to design micro. Simply,use 0 to describe zero level and 255 to 1 metre level.

But from indra’s experience (yeah,indra and his robot’s :p) if we just use exact number (I mean 0 for zero water and 255 for 1 metre) we couldn’t get exact 1 metre level because there were some interference produced from response time from flexiforce –adc-micro-pump. So in micro that we design we determine 0-10 to describe zero level and 250-255 to 1 metre just to make sure that interference didn’t hamper our design. (for complete syntax and program discussed in ppt)

3. -_-

Simply connect flexi force – adc – micro with pump and voila,case 2 is solved ^^

2^nd case :

Well,the 2^nd case is not much different from 1^st case,based on indra’s experience controlling the level is what we wanted,just determine what adc conversion should be made. I mean,in 1^st case we determine that zero level = 0 adc and 1 metre = 255. So if given the maximum height is 2 metre then,just make a complete conversion list of adc, the idea is simple -_-, 0 adc for zero level,255 for max level (2 metre) and from 1 – 254 for other height,such as 10 for 5 cm and 150 for 120 cm. the device that we design is not 100% automatic,for 2^nd case it require operator to turn water tap on or off,basicly,our 2^nd case device is just for reminder of height, if the height is suitable the the operator can turn the water tap off,if it’s not yet suitable just keep it on.

3^rd case:

Well,actually there isn’t 3rd case,its about development of our plan about device that we made,we added some cool feature,that is telemetry. What is telemetry? It is a technology that allows remote measurement and reporting of information. The word is derived from Greek roots tele = remote, and metron = measure. Systems that need external instructions and data to operate require the counterpart of telemetry, telecommand.

Basicly if we added telemetry and telecommand,we could remote water level tank from anywhere and we could control its level from anywhere,pretty cool huh? To allow that first we must get what called API ( application program interface). It is an application that allow communication 2 different devices. In this case we use handphone as an controller for water level tank

Interested? Download full presentation file in here ^^

DC Motor

Today,or I mean this night. Yeah I update this blog at 11 pm T.T. it was when my friend,apri setiawan call me via telephone and said that I shouldn’t forget about updating this blog. Okay,here it goes. The topic would be Motor DC with PID controller,it is 3rd task that Mr Priyatmadi order us to solve.

Well,lets start with the definition of dc motor. DC motor is an electric motor that runs on direct current. Furthermore, The DC motor utilizes this concept by changing the direction of the current flowing through the brushes into the coiled wire in the armature. A permanent magnet creates a constant magnetic field, and when current runs through the coils, a force is created that turns the armature. When the armature has turned far enough, the brushes are now in contact with the opposite ends of the coiled wire, effectively reversing the polarity of the voltage across the coil and reversing the current flow, which create a force that spins the armature further in the same direction. This process repeats as long as voltage is supplied to the motor, creating the motor rotational force

We are not here to discuss definition of DC motor,but about application of PID controller in DC motor. As we know before,Mr priyatmadi had told us before about usage of PID controller. A proportional–integral–derivative controller (PID controller) is a generic control loop feedback mechanism (controller) widely used in industrial control systems – a PID is the most commonly used feedback controller. A PID controller calculates an "error" value as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error by adjusting the process control inputs. In the absence of knowledge of the underlying process, PID controllers are the best controllers. However, for best performance, the PID parameters used in the calculation must be tuned according to the nature of the system – while the design is generic, the parameters depend on the specific system.

In our presentation mainly covered about usage of different controller,such as: PI controller;PD controller;and PID controller. Not much complex,because we just demonstrate it in matlab,and that is all,we examine what happened and making some conclusion.

For further understanding about our presentation,please download it in here.

Here are some conclusion that can be taken from our presentation:

sudoku matlab

Hi,another week another task,huh -_-
This time,we’d like to present, our group’s task about learning Matlab. As Mr Priyatmadi said,he’d like to see some presentation about matlab,not only about PID thing but also something more than it ^^
My group wanted to show everyone that matlab is not only about PID,but it also can be used to solve something funnier than PID. That is SUDOKU.
Anyone knew what Sudoku is? Well,Sudoku is a game originated from America (if im not mistaken) its purpose is to fill blank spot in its region. There are many types of Sudoku,like:2x2; 3x3,9x9,and 81x81. Our group’s idea is simple,if matlab is said could be used to solve every engineering’s task,why don’t we used it to solve Sudoku @-@
Here it goes
Solving Sudoku is one of my hobby,so when asked for matlab presentation I’d like to perform Sudoku solver (and happily my friends agree with that). There were some algorithm that commonly used in sudoku solver:
1. Scanning
We scan entirely grid 9x9,and find which row is scannable, lets say there were some row composed by number like this:
1 4 5 6 7 8 9 0 3

It is obvious that blank spot must be filled with 2

2. Quad scanning
Aside with scanning,quad scanning offer reliable and faster solving process,we scan small grid (3x3) first and then another sub grid
Here is the example:
0 3 4
1 2 5
7 0 9

Well,there are 2 possibilities, 6 and 8, which number is correct later discussed,in combining step from other 3x3 grid.

3. Recursive tracker
Let's get back to solving the hard sudokus, the ones which require an analytical/guessing approach. First, how do we distinguish such a problem from one which can be scan-solved? This may be a hard question to answer theoretically (is it the halting problem?) but in practice it's easy - if the Quad Scan / Matrix Scan combo runs its course in a loop until it produces no further improvement, and if at this point the matrix still contains blank slots indicated by 0s, we know it's time for the harder stuff.
sounds cool,isn’t it? Wait,we haven’t introduce a cooler one yet; :p
4. Brute force
Think that you are lucky enough? Then try brute force,no brain just brawn :p. and it is solved.LOL

5. Smart force ^^

Development of brute force,still guessing but row scanning and quad scanning were added. Way to go Sudoku master :p

That was the step that is used to solve Sudoku,the final one must be combining all that step into matlab program. You can download the syntax and our presentation here and here.

Here are some screenshot from the Sudoku solver program













And this is the result,voila 9x9 solved :p

Water Tank with PID

Okay,this time we still discuss about task given by Mr Priyatmadi.

This is the 2^th task,that is controlling water level with PI

For better understanding,firstly we must state what we are going to control,yeah that is water tank level. Given by Mr priyatmadi,a water tank with specification below:

Here are the transfer function

Well,preparation are complete,lets start with the main topic, combine it with PI Controller.

Well,if we change plant,we need large amount of money to change its transfer function,furthermore it’s process are irreversible,so we did some modification on PI controller to get stable output. The modificitaion on the PI controller can be seen in presentation.download it in here