Otomatik ayarlanan oransal -integral- türevsel (P.I.D) kontrolün incelenmesi ve gerçeklenmesi
A Study and a Experimental set-up of autotuning PID controllers
- Tez No: 39099
- Danışmanlar: DOÇ.DR. İBRAHİM EKSİN
- Tez Türü: Yüksek Lisans
- Konular: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol, Computer Engineering and Computer Science and Control
- Anahtar Kelimeler: PID denetleme, İntegraller, PID control, Integrals
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu çalışmada otomatik olarak ayarlanabilen oransal ( proportional )-Tümlevsel( integral )-Türevsel( derivative) (FID) kontrolörün incelenmesi ve pcl812 Simulatörü ile bası sistemlere uygulaması tanıtılmaktadır. Kendiliğinden ayarlanabilen PID kontrolörün gerçek lemesinin ilk aşamasında süreç tanıtılmaktaktadır. Bu tanıtım iki yöntemle yapılmaktadır. Birincisi birim ba samak, diğeri ise ardışıl hesaplama yöntemidir. ikinci aşamada FID kontrolörün "katsayıları Zeigler-Mchols yön temlerinden olan reaksiyon eğrisi yöntemi veya röle yön temi kullanılarak belirlenir. Belirlenen bu değerler Zeigler-Nichols'un öngördüğü katsayılara çarpılarak opti mum FID kontrolörü elde edilir ve sözkonusu süreç için uygulanır. FID kontolörün katsayılarını belirlemede kullanılan Zeigler-Nichols yöntemleri, bu katsayıları transfer fonk siyonu elde edilebilen lineer sistemler için ve %25 bağıl sönüm kriterine göre veren yöntemler olarak kısaca ifade edilebilir.
Özet (Çeviri)
SUMMARY A STUDY AHD AM EXPERIMENTAL SET-DP OF AUTOTONIKG PID CONTROLLERS The introduction of PID controllers with auto tuning capabilities has made it possible to speed up plant commissioning and also to facilitate control optimisation through regular re tuning. However, with so many brands of autotuning PID controllers availiable on the market- that claim general applications, the end-user may be missled easily into thinking that they all similiar in performance and that they are universally applicable. It is therfore useful to provide the end-users with information on the relative capabilities and possible limitations of these autotuning PID controllers. PID controllers have several important functions-' They provide feedback, they have the ability to eliminate steady-state offsets through the integral action, they can anticipate the through the derivative action, and they can cope with actuator saturation. Much good control practise is engineered into them. PID control lers are also sufficient for many control problems particularly where are being process dynamics and modest control engineering's toolbox. A large cadre of instru ment and process are familiar with the operation of PID controllers. There is also a well-established practise of installing, tuning and using them. Although PID controllers are common and well-known they often poorly tuned. Evidence for this can be found in the control rooms of any industry. The derivative action is frequently switched off for the simple reason that is diffucult to tune properly. It is no coincidence that the derivative action can be switched off in most of the controllers that provide this function. In this study, the PID controllers, the process dy namics, the design of PID controllers and the autotuning visubjects are discussed respectively. The FID controllers ie by far the most common control algorithm. Most feed back loops are controlled by this algorithm or minor variation of it. The PID algorithm can be approached from many different angles. It can be viewed as a device that can be operated with a few rules of thumb, but it can also be approached analytically. The simple feedback system with error feedback is shown in figure 1. Figure 1 : The Simple Feedback System With Error Feedback The simple algorithm of PID has the following form:.[ u(t)= R. e<t) + de(t) e(s).ds + Ta. HS \ \f t -I d t J (l) Where u is the control variable and e is the control error (e=r-y), which is the difference between set point r and measured value y. The control variable is this a sum of three terms; the P-term {which is proportional to the error), The I -term (which is propor-tional to the integral of the error), and the D-term (which is propor tional to derivative of the error). The controller parameters are proportional gain K, integral time Ti, and derivative time Td. The digital implementation of PID controller can be designed as U(z) TU+1) (3-1) E(2) Z(2+l) T.a (2) viiBefore computing the eofficients of PID controllers, the process dynamics must be defined. In other words, one method of tuning a control les is to first determine a model for the process dynamics and than calculate the the controller parameter using some methods. In this work, transient response methods and parameter estimation models are presented. In the experimental set-up, the set up response and recursive computation methods are used for de terming the model of the process. The former is a consient way to characterise process dynamics because of its simple physical interpration. Many tuning methods are based on it. A formal mathematical model can also be obtained from the step response. The latter is a simple method for estimating the parameters of the discrete time model presented below. A(q).y(kh)=A(q).U(kh) (3) where A(q) and B(q) are poly n ima Is; A(q)=qn+al.qn-l+... +an B(q)=bl.qn-l+b2.qn-2+...+bn the corresponding transfer function is B( a ) bl. qn- l+b2. qn-2+... + bıcı (4) H(a)=- A ( a ) qn+a 1. qn- 1+ *.. +an (5) After defining the model of the process, the para meters of a PID controllers can be determined. There are many methods to do this. Some of them are the Zeiger-Nichols step response method and Zeigler-Nichols frequency response methods, which are used in this work. These methods are based on limited process knowledge. To explain how these can be obtain, one has to be consired the autotuning block diagram at first. Block diagram of experimental set-up is shown in figure 2. A simple process model can be obtained from open- loop transient response experiment. A unit step input is applied. viii“I I Design T^~.) r* Estimation * ıRef _ e Regulator.”{D" Computer ?*» D/A u Process A/D J Y Figure 2: Block Diagram Of The Experimental Set-up at the process input, arid the response is measured. There are only one or two parameters that must be a priori: The amplitude and the direction of a pulse or the amplitude of a step, For determing the parameters of PID, the Zeigler-Nichols step response method used. The intersection between tangent and coordinate axes give two parameters a and L, & model of the process to be controlled was derived from this parameters. Zeigler and Nichols have given PID parameters directly as function of a and L. The other method based on frequency response is relay method. It can also be used to determine the process dynamics and autotuners which are determine the prosses dynamics and the parameters of PID automatically. In traditional frequency response methods, the transfer function of a process is determined by measuring the steady-state response to a sinusoidal system. A difficulty with this method is that appropriate frequencies of the input signal must be specified. The idea was simply to introduce a nonlinear feedback of the ixrelay type so that there would be a limit cycle oscillation- With an ideal relay the method gives on input signal to the process whose is close to the crossover frequently of the open- loop system. A block diagram of an autotuner based on the relay methods is shown in figure 3. Kef. XiL Frocess -1 Figure 3: A Block Diagram Of An Autotuner Based On The Relay Method Notice that there is a switch that selects either relay feedback or ordinary PID feedback. When it is desired to tune system, the FID function is disconnected and the system is connected to relay control. The system then start to oscillate. The period and the amplitude of the oscillation are determined when steady-state oscillation is obtained. This gives the ultimate period and the ultimate gain. The parameters of a PID controller can then be determined from this values, e.g, using the Zeiger-Hichols frequency response method. The PID controller is then automatically switched in again, and the control is executed with the new PID parameters. x
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