(1+sin t)(1+cos t)=5/4


ada pertanyaan dari kenalan di FB & sekalian saya simpan disini untuk dokumentasi ….

Jika diketahui (1+sin t)(1+cos t)=5/4
Berapa kah nilai (1-sin t)(1-cos t) ?

menarik juga untuk dicoba dan setelah berkali-kali mencoba selama bbrp jam saya menyerah ….:)

akhirnya browsing juga dan berikut jawabannya ..












ini linknya.

Perinncian jawaban pertama …

(1 + sin t) (1 + cos t) = 5/4

1 + sin t + cos t + sin t cost = 5/4

1 + (sin t + cos t) +1/2 ((sin t + cos t) ^2 – 1 ) = 5/4

1 + y + ½ ( y^2 – 1) = 5/4

4 + 4y + 2 y^2 – 2 = 5

2 y^2 + 4 y – 3 = 0

y1,2 = (-4 ± sqrt (16 + 24) ) /4 = -1 ± ½  sqrt (10)

lanjut … ke 5/4 – 2y (penjelasan di atas) 

5/4 – 2 y = 5/4 – 2 (-1 ± ½  sqrt (10)) = 13/4 ± sqrt (10)

Nah ternyata yang bertanya juga sudah ada jawaban lain …

(1+sin t)(1+cos t) = 5/4
==> 1 +cos t + sin t + sin t * cos t = 5/4
==> cos t + sin t = 5/4 – 1 – sin t * cos t
==> cos t + sin t = 1/4 – sin t * cos t ….. ( pers 1 )
==> ( cos t + sin t )^2 = (1/4 – sin t * cos t)^2
==> 1 + 2 (sin t * cos t) = 1/16 – 2/4 * (sin t * cos t ) + ( sin t * cos t )^2
===> 16(sin t * cos t)^2 – 40(sin t * cos t) – 15 = 0
===> sin t * cos t = [40±√(40^2-4*16*(-15))]/(2*16)
===> sin t * cos t = [5±2√10]/4 ….. ( pers 2 )
pindah ke soal
(1-sin t)(1-cos t)
= 1 – cos t – sin t + sin t * cos t
= 1 – (cos t + sin t) + sin t * cos t
= 1-(1/4 – sin t * cos t) + sin t * cos t ….. dari pers 1. ( cos t + sin t = 1/4 – sin t * cos t )

= 3/4 + 2 sin t * cos t
= 3/4 + 2 [5±2√10]/4 ….. dari pers 2. ( sin t * cos t = [5±2√10]/4 )

= [13±4√10]/4

soal mencari sudut


dah lama nggak posting artikel matematika.

ada pertanyaan dari group Facebook OSN Matematika.

sekalian saya tulis di blog ini buat dokumentasi …

Berikut pertanyaannya ..

pertanyaan cari sudut


jawabannya: X = 70 derajat.

Caranya sbb:

Cara Pertama

Kita gambar segi tiga siku2 bantu seperti gambar di bawah.


dengan asumsi garis hitam di samping kiri dan kanan itu sejajar dan tegak lurus.

Setelah itu persegi sudut dalamnya kan 90 derajat. Dan garis lurus itu jumlah sudutnya 180 derajat.

Mulai dari kiri ke kanan dan akhirnya dapat jawabannya.


Nah berikut Cara kedua


ini pakai rumus ( n-2 ) x 180 derajat dimana n adalah jumlah sisi suatu bangun ….bangunnya tercipta kalau kita buat garis horizontal di bawahnya.. sehingga tercipta bangun segi 9 … jadi nanti total sudutnya 7 x 180 …

dimana sudut dibawahnya pasti berjumlah 180 derajat .. karena sejajar pasti jumlah 180 ….

setelah itu tinggal hitung nilai X sebagai sisanya yaitu 70….

Nah ada yang posting cara lain .. sehingga terbentuk segi lima.
Jumlah sudut segi lima pakai rumus di atas (5 – 2) x 180 = 540.

Cara 3

Semoga bermanfaat …

perbedaan FGS dan ESD System

lanjutan dari artikel sebelumnya.
Buat tambah pengetahuan sekalian di sharing.

saya copas dari web emersonprocessxperts.com, penjelasan mengenai perbedaan Fire & Gas System (FGS) dengan Emergency Shutdown (ESD) System.

cukup detail penjelasannya.

Here’s Mike’s post:

At Emerson Exchange last year, Rafael Lachmann presented on the topic of Fire & Gas System (FGS) solutions with DeltaV SIS. In his presentation, he provided a basic overview of FGS concepts and then he described how DeltaV SIS could be used for FGS applications. He described how emergency shutdown (ESD) systems are different from FGS, how onshore FGS differs from offshore FGS applications, and how DeltaV SIS can be used for FGS applications.

For an ESD, a process upset will result in a process shutdown. ESD systems are preventative layers of protection, meaning that they act to prevent a hazardous event like a chemical release, fire, or explosion from occurring. A FGS is a mitigating layer of protection, because the purpose is to reduce the consequence severity of such an event when it occurs. When a combustible gas, a toxic gas, smoke, flame, or heat is detected, then the FGS will respond by annunciating audible and visual alarms and initiate a water deluge, fire suppression system, or a process shutdown. In the event of a gas leak, the FGS can act to prevent it from becoming a fire or explosion by isolating the leak and ignition sources. In the Deepwater Horizon Accident Investigation Report that was issued by BP in September 2010, this was listed as one of the 8 barriers that were breached.

The fire and gas system did not prevent hydrocarbon ignition. Hydrocarbons migrated beyond areas on Deepwater Horizon that were electrically classified to areas where the potential for ignition was higher. The heating, ventilation and air conditioning system probably transferred a gas-rich mixture into the engine rooms, causing at least one engine to overspeed, creating a potential source of ignition.

A typical ESD safety instrumented function (SIF) is typically quite simple when compared to what is implemented for a FGS. A FGS SIF can be very complex and highly distributed, with 1ooN or 2ooN voting from a large number of detector devices located throughout a unit, process, and plant area. In some cases, a FGS event can initiate a site-wide emergency shutdown.

Another important difference is that an ESD is typically designed as normally energized (de-energize-to-trip) so that it is fail-safe. This way, if there is loss of power or connectivity between system components then the SIS will respond by tripping. This results in higher safety integrity, but it can result in increased spurious trips of the process. For FGS, a spurious trip can have dangerous results. For example, initiating a water deluge system inside a building can cause damage to equipment and can be hazardous to personnel. Chemical fire suppression can be dangerous to personnel, and false alarms degrade the willingness to respond by plant personnel. For this reason, it is common to design a FGS as normally de-energized (NDE).

In a NDE design, the loop must be energized in order to initiate a trip of the FGS. This means that failures such as loss of power or connectivity between components are covert failures unless there is adequate diagnostics to detect the failures. In a NDE design, line monitoring is essential to detect open and short circuit failures in wiring between logic solver I/O and field devices.

The major differences between offshore and onshore FGS design result from the difficulty to evacuate and limited offsite emergency response assistance when an offshore incident occurs. Rafael’s discussion on how onshore FGS differs from offshore FGS will soon be covered in another blog post.

link detailnya bisa di klik disini

Ditulis dalam FGS, SIS. Tag: , . 1 Comment »

pemisahan F&G System dengan SIS

ada topik menarik dari diskusi group SIL di linkedin sehubungan dengan pemisahan Fire & Gas (F&G) System dengan Safety Instrumented System (SIS).

Dulu waktu project Arthit APP (Arthit Process Platform) saya perhatikan F&G System digabung dengan SIS.
Kalau ditempat saya kerja sekarang sih dipisah antara F&G System dengan Emergency Shutdown System.

Dari diskusi di bawah saya setuju dengan yang dipisah.

Berikut cuplikannya.



SIS used as F&G system.

Can a SIS be used as a F&G system? Can we integrate both in the same system? You know that when is required by Hazop study thast some F&G detectors shall have process action (close valves, stop pumps), normally we put that detectors into the SIS PLC.
And for mitigation action (when it is required energized to trip)? Supplier (as Emerson) already have devices to used in DElta V SIS for that purpose. With today’s technology, many companies utilize an integrated approach and interfaced the FGS with the ESD system to initiate plant shutdown if hazardous events occur. Any standard that not permitt the F&G and shut down in the same system?


Tanggapan para anggota:

Lawrence Blackmore
– I assume we are talking about IEC61511? The more you put in the SIS that contains your SIF’s the more complex it becomes to meet the requirements for operational management of the SIS. Using typical offshore production numbers for…

Ricardo Cordeiro
– What I am trying to araise is: Dont have a seprate F&G system, and implemented into the SIS (same logic solver). There are some vendor talking abou this FGS-SIS integration. So prevention layer with mitigation layer in the same safey…

Ricardo A. Vittoni
– Ricardo, you are right. Although ESD and F&G are both SIS per IEC 61511, you should not run both on the same logic solver.
We can argue two days about pros and cons, but just think about this:

You will need separate I/O cards for ESD…

Paul Gruhn,
– This has been asked a number of times before. The systems are usually separated to ease management of change, simplify the designs, minimize common cause, etc. Many will use the same logic solver technology/type, but still have two separate systems.

Koorosh Moghadam
– Although the idea does not violate any standard, it shall not be taken into practice based on Ricardo and Paul’s comments. However in small scale packages like rotary machines where F&G signals are not noticeable, there is intention of implementing both signals in an individual SIS.

Ricardo Cordeiro
– I think a big concern is when we do a plant shutdown for revamping whatever and the SIS goes to off line, but the F&G system shall be on line even in that cases, because there are works on going and the Fire or gas needs to be detected all the time.

Laxmikant Jahagirdar
– The sensors connected to F& G system are prone to failures & require frequent maintenance. Integration in SIS will add further degradation of SIS other than the reasons mentioned above.

John Thomas
– See kenexis.com. They have some great tutorials on F&G and process safety. Check out their youtube site.

Aria Putra Maulana
– The F&G system provides mitigation for operations when dealing with a loss of containment and fire event. Therefore it is important to ensure the availability of the system through any potential scenario up to abandonment of the facility (up to the highest shutdown hierarchy level). So, we use the same high integrity hardware platform as SIS for F&G for the reasons of ensuring this high availability requirement. You’re right that F&G adopts NDE (equipped with line monitoring) and SIS adopts NE for their final device circuit therefore we should not combine them in one common logic solver as they have different requirement for the fault reaction configuration, i.e. one is non-safety related and the other is safety related (i.e. shutdown the controller on any uncontrollable fault is detected such as short or open circuit of the output loops, cross wiring between output loops, any failure of the suppression diodes in the output module, etc.

Aria Putra Maulana
– So, imagine if we put SIS and F&G in a common logic solver, when there is presence of fire and it causes output circuit fault and SIS DO module failure, it will shutdown the common controller regardless the DO module redundancy and will leave all NDE F&G outputs remain de-energized e.g. power isolation will not be isolated (or circuit breakers will remain close), deluge valves will remain close and cannot be opened, firewater pump will not be able for remote start, etc. thus the system will fail to give protection against the hazard arise.

Ricardo Cordeiro,
– FGS in the same Logic Solver but differnet cards, Emerson has this apllication intregated FGS-SIS (NE to NDE)…

Ricardo Cordeiro,

Ricardo Cordeiro,

Ricardo Cordeiro,
– Fire and gas systems may be implemented in the SIS logic solver according to IEC 61511/ISA 84.00.01-2004, which requires that the user ensure that the non-SIS functions do not impact the functionality and/or integrity of the SIS.


… selengkapnya bisa di klik link ini.


Ditulis dalam FGS, SIS. Tag: , . 2 Comments »

DCS versus PLC in the modern plant

diambil dari Automation.com

artikel ini kurang lebih masih sama dengan postingan artikel DCS vs PLC bbrp tahun lalu.



DCS versus PLC in the modern plant

By Mark Proctor, Managing Director, EU Automation

The difference between distributed control systems (DCSs) and programmable logic controllers (PLCs) can be boiled down to a simple football metaphor. Your DCS is your captain. The first name on the team sheet, your DCS is dependable, hardworking and controls the whole outfit. Your PLC is more like a utility player – he’s nippy and doesn’t mind where he plays, but don’t expect him to be as reliable as your captain. This article will provide an analysis of DCSs and PLCs in the modern plant.

Traditionally, a DCS system was expensive, large, complex to implement and only seen as a control solution for continuous or complex batch process industries.

On the other hand, PLCs evolved from solid state relays and, as opposed to DCS, were used where process restarts were not a major concern, but processing speed was important.

The best way to think about DCS and PLC is like this: in the majority of cases, a PLC controls a machine and a DCS controls a plant.

A DCS is used when the value of the products manufactured is high, the production is continuous and failures in the system result in damage to process equipment – for example, if a glass kiln dropped below a certain temperature. This is because a DCS normally has built-in redundancy, ensuring a higher level of system insurance. All upgrades are made online while the system runs continuously.

Conversely, PLCs are often used when the value of the product is relatively low and production needs to be flexible. Systems can be shut down for maintenance, troubleshooting or upgrades without damage to equipment or significant downtime costs.

Diagnostics in a PLC system will alert an engineer when something is broken. Whereas in a DCS, asset management software provides alerts of what might break before it does, so a fitting substitution can be made. This kind of predictive analysis is particularly important for obsolete part replacement and avoiding costly downtime.

As a utility player, PLCs are highly customisable. They have standard libraries and routines built in, but also have the capability to be specially programmed using custom code from scratch. On the other hand, engineers expect a DCS to offer an out-of-the-box control system with features such as – historian, sophisticated alarms and logic from pre-existing function blocks. Like a good captain, the highest priority of a DCS is to deliver reliability and availability. DCS designs often trade high levels of functionality for repeatability and dependability.

The speed of logic execution is another key differentiator between DCS and PLC. PLCs are designed to meet the needs of applications that require scan rates of ten milliseconds or less. This allows them to accurately control motors and drives running at high speeds.

However, DCSs do not need to be this quick because they control systems rather than individual devices. A DCS’s regulatory control loops generally scan in the 100 to 500 millisecond range.

For all their differences, PLC and DCS are becoming more alike. DCS was originally developed for analogue control. However, the latest generations of PLCs are increasingly capable of delivering simple to complex proportional integral derivative (PID) control.

In addition, today’s DCS hardware is not as expensive as it was a couple of decades ago and is less difficult to implement. It is also no longer as cumbersome either – modern DCS hardware resembles a PLC in size. This is why DCS is now used in smaller applications, whereby it is not spread across the whole plant, but rather a complex subsection that needs reliable control. For example, take the server halls of data centres: these types of control systems are often seen as hybrids of both DCS and PLC.

Modern industrial applications are demanding the reliability of a DCS system but the flexibility of a PLC. This change has brought about a certain level of technological convergence between PLCs and DCSs that defies traditional ideas of the two. In essence, some industrial plants are now employing more than one captain to ensure critical systems are well managed. Game on.


… berikut linknya.


Ditulis dalam DCS, PLC-HMI. Tag: , . Leave a Comment »

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