Sistem kendali dapat dikatakan sebagai hubungan antara komponen yang membentuk sebuah konfigurasi sistem, yang akan menghasilkan tanggapan sistem yang diharapkan. Jadi harus ada yang dikendalikan, yang merupakan suatu sistem fisis, yang biasa disebut dengan kendalian (plant).

Masukan dan keluaran merupakan variabel atau besaran fisis. Keluaran merupakan hal yang dihasilkan oleh kendalian, artinya yang dikendalikan; sedangkan masukan adalah yang mempengaruhi kendalian, yang mengatur keluaran. Kedua dimensi masukan dan keluaran tidak harus sama.

Pada sistem kendali dikenal sistem lup terbuka (open loop system) dan sistem lup tertutup (closed loop system). Sistem kendali lup terbuka atau umpan maju (feedforward control) umumnya mempergunakan pengatur (controller) serta aktuator kendali (control actuator) yang berguna untuk memperoleh respon sistem yang baik. Sistem kendali ini keluarannya tidak diperhitungkan ulang oleh controller. Suatu keadaan apakah plant benar-benar telah mencapai target seperti yang dikehendaki masukan atau referensi, tidak dapat mempengaruhi kinerja kontroler.

Pada sistem kendali yang lain, yakni sistem kendali lup tertutup (closed loop system) memanfaatkan variabel yang sebanding dengan selisih respon yang terjadi terhadap respon yang diinginkan. Sistem seperi ini juga sering dikenal dengan sistem kendali umpan balik. Aplikasi sistem umpan balik banyak dipergunakan untuk sistem kemudi kapal laut dan pesawat terbang. Perangkat sehari-hari yang juga menerapkan sistem ini adalah penyetelan temperatur pada almari es, oven, tungku, dan pemanas air.

Ada beberapa standar input yang dinyatakan cukup mewakili dalam mendisain sebuah sistem, input tersebut dikenal dengan input satuan step, ramp dan parabola.Step Sebuah satuan step yang didefinisikan seperti :

u(t) = 0, t < 0

1, t 0

Fungsi dari satuan step ini sangatlah penting, hanya dalam sistem kontrol namun juga pada pemrogresan sinyal, analisa sistem, segala cabang dari pelajaran keteknikan. Jika satuan step dijadikan input sebuah sistem, kaluaran dari sistem akan disebut dengan respon step.

RampSebuah satuan ramp yang didefinisikan seperti :

r(t) = t u(t)

Hal yang perlu dicatat bahwa fungsi satuan step merupakan turunan dari fungsi satuan ramp:

r(t) =

Definisi akan mudah dipahami dengan menguasai prinsip Transformasi Laplace

ParabolaSebuah unit input parabola hampir mirip dengan satuan ramp:

Dapat dilihat bahwa input berupa satuan parabola sama dengan integral dari fungsi ramp:

Dan definisi juga akan mudah dipahami dengan menguasai prinsip Transformasi Laplace

Steady StateWhen a unit-step function is input to a system, the steady-state value of that system is the output value at time . Since it is impractical (if not completely impossible) to wait till infinity to observe the system, approximations and mathematical calculations are used to determine the steady-state value of the system. Most system responses are asymptotic, that is that the response approaches a particular value. Systems that are asymptotic are typically obvious from viewing the graph of that response.Keadaan mantapKetika fungsi satuan step menjadi input sebuah sistem, nilai keadaan mantapnya merupakan nilai keluaran pada waktu . Kebanyakan respons sistem merupakan asimptot.Step ResponseThe step response of a system is most frequently used to analyze systems, and there is a large amount of terminology involved with step responses. When exposed to the step input, the system will initially have an undesirable output period known as the transient response. The transient response occurs because a system is approaching its final output value. The steady-state response of the system is the response after the transient response has ended.Respon step sering digunakan dalam menganalisa sebuah sistem, dan ada banyak istilah yang digunakan dalam respon step. Ketika step diinputkan, sistem akan memiliki perioda keluaran yang tak diinginkan atau disebut juga transient response. Respon ini terjadi karena sebuah sistem sedang mendekati nilai keluaran akhirnya. Respon dalam keadaan mantap sebuah sistem merupakan respon yang terjadi setelah respon transient berakhirThe amount of time it takes for the system output to reach the desired value (before the transient response has ended, typically) is known as the rise time. The amount of time it takes for the transient response to end and the steady-state response to begin is known as the settling time.Waktu yang diperlukan untuk sistem dalam mencapai nilai yang diinginkan (biasanya sebelum respon transient berakhir) disebut dengan waktuk naik (rise time). Waktu selama berakhirnya respon transient dan mulainya respon dalam keadaan mantap disebut waktu penurunan (settling time)It is common for a systems engineer to try and improve the step response of a system. In general, it is desired for the transient response to be reduced, the rise and settling times to be shorter, and the steady-state to approach a particular desired "reference" output.Para Insinyur untuk system mencoba dan memperbaiki response sebuah system. Umumnya, perbaikan tersebut dilakukan dengan memperkecil nilai respon transient, memperpendek waktu naik (rise time) dan waktu penurunan (settling time), dan keadaan mantap mendekatik keluaran yang diinginkan.

An arbitrary step function with

A step response graph of input x(t) to a made-up system

Target ValueThe target output value is the value that our system attempts to obtain for a given input. This is not the same as the steady-state value, which is the actual value that the target does obtain. The target value is frequently referred to as the reference value, or the "reference function" of the system. In essence, this is the value that we want the system to produce. When we input a "5" into an elevator, we want the output (the final position of the elevator) to be the fifth floor. Pressing the "5" button is the reference input, and is the expected value that we want to obtain. If we press the "5" button, and the elevator goes to the third floor, then our elevator is poorly designedNilai keluaran target adalah nilai yang dicapai oleh system dengan input tertentu. ini bukanlah sama dengan nilai pada keadaan mantap, yang mana merupakan nilai sebenarnya ----. Nilai target terkadang disebut nilai referensi atau fungsi referensi dari sebuah system. Dapat dikatakan nilai ini merupakan nilai yang ingin kita harapkan di hasilkan oleh sistem. Ketika kita masukkan 5 pada elevator, kita ingin keluaran (posisi terakhir elevator) harusnya lantai kelima. Menekan tombol 5 merupakan masukan referensi dan ingin kita dapatkan. Jika tekan tombol 5 dan elevator berada pada lantai 3 maka elevator sangat buruk dalam pendesainnya.Rise TimeRise time is the amount of time that it takes for the system response to reach the target value from an initial state of zero. Many texts on the subject define the rise time as being the time it takes to rise between the initial position and 80% of the target value. This is because some systems never rise to 100% of the expected, target value, and therefore they would have an infinite rise-time. This book will specify which convention to use for each individual problem. Rise time is typically denoted tr, or trise.Waktu naik merupakan waktu yang dibutuhkan respon system untuk mencapai nilai target dari keadaan nol awal (initial state of zero). banyak referensi yang menyebutkan bahwa waktu naik itu waktu yang dibutuhkan untuk naik dari kondisi inisiasi (awal) hingga 80% dari nilai yang ditargetkan. Karena system takkan akan pernah mencapai kondisi 100% dari nilai target atau nilai yang dibutuhkan bisa sangat lama. Wwaktu naik biasanya dilambangkan dengan Rise time is not the amount of time it takes to achieve steady-state, only the amount of time it takes to reach the desired target value for the first time.

Percent OvershootUnderdamped systems frequently overshoot their target value initially. This initial surge is known as the "overshoot value". The ratio of the amount of overshoot to the target steady-state value of the system is known as the percent overshoot. Percent overshoot represents an overcompensation of the system, and can output dangerously large output signals that can damage a system. Percent overshoot is typically denoted with the term PO.Example: RefrigeratorConsider an ordinary household refrigerator. The refrigerator has cycles where it is on and when it is off. When the refrigerator is on, the coolant pump is running, and the temperature inside the refrigerator decreases. The temperature decreases to a much lower level than is required, and then the pump turns off.When the pump is off, the temperature slowly increases again as heat is absorbed into the refrigerator. When the temperature gets high enough, the pump turns back on. Because the pump cools down the refrigerator more then it needs to initially, we can say that it "overshoots" the target value by a certain specified amount.Example: RefrigeratorAnother example concerning a refrigerator concerns the electrical demand of the heat pump when it first turns on. The pump is an inductive mechanical motor, and when the motor first activates, a special counter-acting force known as "back EMF" resists the motion of the motor, and causes the pump to draw more electricity until the motor reaches its final speed. During the startup time for the pump, lights on the same electrical circuit as the refrigerator may dim slightly, as electricity is drawn away from the lamps, and into the pump. This initial draw of electricity is a good example of overshoot.Steady-State ErrorSometimes a system might never achieve the desired steady-state value, but instead will settle on an output value that is not desired. The difference between the steady-state output value to the reference input value at steady state is called the steady-state error of the system. We will use the variable ess to denote the steady-state error of the system.Kesalahan keadaan mantapTerkadang sebuah system mungkin tidak akan pernah mencapai nilai mantap yang diinginkan. Perbedaan antara keluaran keadaan mantap hingga ke nilai masukan referensi pada keadaan mantap disebut kesalahan keadaan mantap dari sebuah system. Kita menggunakan variabel ess untuk kesalahan keadaan mantap.Settling TimeAfter the initial rise time of the system, some systems will oscillate and vibrate for an amount of time before the system output settles on the final value. The amount of time it takes to reach steady state after the initial rise time is known as the settling time. Notice that damped oscillating systems may never settle completely, so we will define settling time as being the amount of time for the system to reach, and stay in, a certain acceptable range. The acceptable range for settling time is typically determined on a per-problem basis, although common values are 20%, 10%, or 5% of the target value. The settling time will be denoted as ts.

System OrderOrde sistemThe order of the system is defined by the highest degree of the linear differential equation that describes the system. In a transfer function representation, the order is the highest exponent in the transfer function. In a proper system, the system order is defined as the degree of the denominator polynomial. In a state-space equation, the system order is the number of state-variables used in the system. The order of a system will frequently be denoted with an n or N, although these variables are also used for other purposes. This book will make clear distinction on the use of these variables.Orde sebuah sistem didefinisikan oleh pangkat terbesar dari persamaan differensial linear yang digambarkan oleh sistem. Dalam sebuah fungsi alih, orde sistem didefinisikan oleh pangkat polinom denominator. Orde sebuah sistem terkadang disimbolkan dengan n atau N, tergantung penggunaannya.Proper SystemsA proper system is a system where the degree of the denominator is larger than or equal to the degree of the numerator polynomial. A strictly proper system is a system where the degree of the denominator polynomial is larger than (but never equal to) the degree of the numerator polynomial. A biproper system is a system where the degree of the denominator polynomial equals the degree of the numerator polynomial.Sebuah sistem yang proper merupakan sistem dimana pangkat denominator nya lebih besar atau sama dengan pangkat polinom numeratornya. Sebuah strictly proper system merupakan sistem dimana pangkat polinom denominatornya lebih besar dari pangkat polinom numeratornya. Sebuah biproper sistem merupakan sistem yang pangkat polinom denominatornya sama dengan dengan polinom numeraotrnya.It is important to note that only proper systems can be physically realized. In other words, a system that is not proper cannot be built. It makes no sense to spend a lot of time designing and analyzing imaginary systems.Hal yang perlu diingat bahwa hanya sistem yang proper saja yang dapat dibuat, sehingga sistem yang non proper tidak dapat diwujudkan. Jadi jangan sia-siakan banyak waktu untuk mendesain dan menganalisa sistem yang imajiner (tidak nyata/ tidak dapat diwujudkan).Find the order of this system:

The highest exponent in the denominator is s2, so the system is order 2. Also, since the denominator is a higher degree than the numerator, this system is proper.

Nilai eksponen terbesar ada pada denominator yaitu s2, jadi orde dari sistemnya adalah 2. Dan termasuk sistem proper karena pangkat denominator lebih besar dari numeratornya.in the above example, G(s) is a second-order transfer function because in the denominator one of the s variables has an exponent of 2. Second-order functions are the easiest to work with.System TypeLet's say that we have a transfer function that is in the following generalized form (known as pole-zero form):

we call the parameter M the system type. Note that increased system type number correspond to larger numbers of poles at s = 0. More poles at the origin generally have a beneficial effect on the system, but they increase the order of the system, and make it increasingly difficult to implement physically. System type will generally be denoted with a letter like N, M, or m. Because these variables are typically reused for other purposes, this book will make clear distinction when they are employed.Parameter M adalah tipe sistem, hal yang perlu dicatat bahwa bertambahnya tipe sistem Now, we will define a few terms that are commonly used when discussing system type. These new terms are Position Error, Velocity Error, and Acceleration Error. These names are throwbacks to physics terms where acceleration is the derivative of velocity, and velocity is the derivative of position. Note that none of these terms are meant to deal with movement, however.Sekarang, kita akan mendefinisikan beberapa istilah yang sering digunakan ketika membahas tipe system, yakni : kesalahan posisi, kesalahan kecepatan, kesalahan percepatan. Position ErrorKesalahan posisiThe position error, denoted by the position error constant . This is the amount of steady-state error of the system when stimulated by a unit step input. We define the position error constant as follows:Kesalahan posisi, disebut dengan konstanta kesalahan posisi . Merupakan jumlah kesalahan dalam keadaan mantap dari system ketika dimasukkan oleh satuan step. Kita mendefinisikan konstanta kesalahan posisi sebagai berikut :

Where G(s) is the transfer function of our system.Dimana G(s) merupakan fungsi alih dari system.

Velocity ErrorKesalahan kecepatanThe velocity error is the amount of steady-state error when the system is stimulated with a ramp input. We define the velocity error constant as such:Kesalahan kecepatan merupakan jumlah kesalahan dalam keadaan mantap ketika system dimasukkan satuan ramp pada system. kita mendefinisikan konstanta kesalahan kecepatan sebagai berikut :

Acceleration ErrorThe acceleration error is the amount of steady-state error when the system is stimulated with a parabolic input. We define the acceleration error constant to be:

Kesalahan percepatan merupakan jumlah kesalahan dalam keadaan mantap ketika system dimasukkan dengan masukan parabola. Kita mendefinisikan konstanta kesalahan percepatan sebagai berikut :

Now, this table will show briefly the relationship between the system type, the kind of input (step, ramp, parabolic), and the steady-state error of the system:Tabel ini merupakan hubungan antara tipe system, jenis masukan input (step,ramp dan parabola) dan kesalahan pada keadaan mantap dari system :

Phase marginFrom Wikipedia, the free encyclopediaJump to: navigation, search In electronic amplifiers, the phase margin (PM) is the difference between the phase, measured in degrees, and 180, for an amplifier's output signal (relative to its input), as a function of frequency. Typically the open-loop phase lag (relative to input) varies with frequency, progressively increasing to exceed 180, at which frequency the output signal becomes inverted, or antiphase in relation to the input. The PM as defined will be positive but decreasing at frequencies less than the frequency at which inversion sets in (at which PM = 0), and PM is negative (PM < 0) at higher frequencies. In the presence of negative feedback, a zero or negative PM at a frequency where the loop gain exceeds unity (1) guarantees instability. Thus positive PM is a "safety margin" that ensures proper (non-oscillatory) operation of the circuit. This applies to amplifier circuits as well as more generally, to active filters, under various load conditions (e.g. reactive loads). In its simplest form, involving ideal negative feedback voltage amplifiers with non-reactive feedback, the phase margin is measured at the frequency where the open-loop voltage gain of the amplifier equals the desired closed-loop DC voltage gain.[1]More generally, PM is defined as that of the amplifier and its feedback network combined (the "loop", normally opened at the amplifier input), measured at a frequency where the loop gain is unity, and prior to the closing of the loop, through tying the output of the open loop to the input source, in such a way as to subtract from it.In the above loop-gain definition, it is assumed that the amplifier input presents zero load. To make this work for non-zero-load input, the output of the feedback network needs to be loaded with an equivalent load for the purpose of determining the frequency response of the loop gain.It is also assumed that the graph of gain vs. frequency crosses unity gain with a negative slope and does so only once. This consideration matters only with reactive and active feedback networks, as may be the case with active filters.Phase margin and its important companion concept, gain margin, are measures of stability in closed-loop, dynamic-control systems. Phase margin indicates relative stability, the tendency to oscillate during its damped response to an input change such as a step function. Gain margin indicates absolute stability and the degree to which the system will oscillate, without limit, given any disturbance.The output signals of all amplifiers exhibit a time delay when compared to their input signals. This delay causes a phase difference between the amplifier's input and output signals. If there are enough stages in the amplifier, at some frequency, the output signal will lag behind the input signal by one cycle period at that frequency. In this situation, the amplifier's output signal will be in phase with its input signal though lagging behind it by 360, i.e., the output will have a phase angle of 360. This lag is of great consequence in amplifiers that use feedback. The reason: the amplifier will oscillate if the fed-back output signal is in phase with the input signal at the frequency at which its open-loop voltage gain equals its closed-loop voltage gain and the open-loop voltage gain is one or greater. The oscillation will occur because the fed-back output signal will then reinforce the input signal at that frequency.[2] In conventional operational amplifiers, the critical output phase angle is 180 because the output is fed back to the input through an inverting input which adds an additional 180.In practice, feedback amplifiers must be designed with phase margins substantially in excess of 0, even though amplifiers with phase margins of, say, 1 are theoretically stable. The reason is that many practical factors can reduce the phase margin below the theoretical minimum. A prime example is when the amplifier's output is connected to a capacitive load. Therefore, operational amplifiers are usually compensated to achieve a minimum phase margin of 45 or so. This means that at the frequency at which the open and closed loop gains meet, the phase angle is 135. The calculation is: {{{1}}} See Warwick[3] or Stout[4] for a detailed analysis of the techniques and results of compensation to insure adequate phase margins. See also the article "Pole splitting". Often amplifiers are designed to achieve a typical phase margin of 60 degrees. If the typical phase margin is around 60 degrees then the minimum phase margin will typically be greater than 45 degrees. A phase margin of 60 degrees is also a magic number because it allows for the fastest settling time when attempting to follow a voltage step input (a Butterworth design). An amplifier with lower phase margin will ring[nb 1] for longer and an amplifier with more phase margin will take a longer time to rise to the voltage step's final level.A related measure is gain margin. While phase margin comes from the phase where the loop gain equals one, the gain margin is based upon the gain where the phase equals -180 degrees.