Elektrohidrolik bir servo-sistemin simülasyonu
Simülation of an electrohydraulic servo system
Yazar: İLYAS İSTİF
Danışman: DOÇ. DR. KENAN KUTLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1995
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Benzetim = Simulation ; Servovalf = Servo valve

Özet:
Hidrolik sistemler, birçok endüstriyel uygulamada önemli bir yer tutmaktadır. Dünyada ve Türkiye' de otomasyon alanındaki gelişmeler, otomasyonda kullanıma elverişli olmaları nedeniyle hidrolik sistemlerin önemini vurgulamaktadır. Bu sistemlerin tasarımı, kontrolü ve test edilmesinde bilgisayar kullanımı maliyetleri büyük ölçüde düşürmektedir. Bu çalışmada, servovalf ve asimetrik silindirden oluşan elektrohidrolik bir sistemin dördüncü dereceden matemetik modeli oluşturularak simülasyonu gerçekleştirilmiştir. Bu amaçla, ilk bölümde sistemle ilgili genel bilgiler verilerek bu konuda daha önceden yapılan çalışmaların özetlerine yer verilmiştir. İkinci bölümde elektrohidrolik sistem elemanları ve sürekli rejim özellikleri incelenmiş ve nonlineer debi denklemlerinin doğrusallaştırılması anlatılmıştır. Üçüncü bölümde sistem elemanlarının modellenmesi ile sistem modeline geçiş anlatılmış, nonlineer sistem modeli ve ikinci bölümde anlatılanların ışığı altında doğrusal sistem modeli elde edilmiştir. Son bölümde, herbir model için sistemin simülasyonu gerçekleştirilmiştir. Sistemin kontrolü için PID kontrol algoritması uygulanmıştır. Optimum kontrol katsayıları, Ziegler Nichols deneysel metodları uygulanarak bulunmuş, kontrol simülasyonu 486 mikroişlemcili kişisel bilgisayarda gerçekleştirilmiştir.

Abstract:
In recent years, there have been much stricter specifications on the performance of technical systems in general and servo-hydraulics in particular. In order to be in a position to satisfy those specifications, both now and in the future, the designers of such drives must have an accurate understanding of the internal relationships that make up the system. Simulation techniques can provide valuable assistance in this area, but in the past, they have found it very difficult to take the step from the office of the pure scientist onto the desk of the practical engineer. Simulation techniques open up the way to cost-cutting in project planning, design and testing as well as providing a higher degree of security in the development of hydraulic drives. Progress in digital computing technology gave fresh impetus to the story of simulation. Most of all, it brought advantages in the area of non-linear calculation, simulation control and the further processing of results. In this thesis, language-oriented simulation of an electrohydraulic servo- system, which has an underlapped servovalve controlled asymmetric cylinder, studied. Before deriving mathematical model, typical system components used in the electrohydraulic control system and their steady-state characteristics (pressure/flow characteristics) are discussed. One of the important characteristics of the electro-hydraulic systems is the compressibility of the oil. Also bulk modulus, which is a measure of the compressibility of a fluid and is inevitably required to calculate hydraulic undamped naturel frequency in the system. The basic definition of fluid bulk modulus arises by considering the compression of a fluid initially at atmospheric pressure and volume V0 to a new value V at pressure P. The spring constant or hydraulic stiffness of the hydraulic system (which has an asymmetric cylinder) is essentially determined by the pressurized oil volume, and is calculated according to the formula: Ao C = /?e 1 A] A~>. + Arhx A2-(Limx-hK) Where J3e is the effective bulk modulus of the system. V\ and V2 is the entrapped oil volume for each side of the cylinder. Also, natural frequency of a cylinder-mass system is given by: It is immediately apparent that the natural frequency is considerably affected by the relation between piston area and stroke. The factor A/h is also called slenderness ratio. In this respect, short strokes and large areas are distinct advantage. The dimensioning of the piston areas though is also determined by a number of other factors such as size, pressure, and volumetric flow. When using the above approche, line volumes are ignored. And it is evident that in order to keep natural frequency as high as possible, the target must be to keep dead volume to a minimum, in other words short, rigid lines between the valve and cylinder. P yr ^>-ry-^Tnt?i^ R öı P a Figure 1. Closed-loop position control of a cylinder. There is a large amount of literature available on the interconnection between a servovalve and actuator, and a variety of computational techniques have been used to solve non-linear differantial equations with non-linear flow characteristics. In figure 1 consider, first the servovalve which is assumed to be symmetrically underlapped. Deriving flow equations with respect to drive current equivalent of spool movement is used, ei=*f('u+o-V(A-^)-*f('u-o-V^i-^ Q2 = kr{iu+i)-4p2-pe-kr{iü-i)-Jp^ and modifying the equations further to allow for sign of current and the correct flow directions, finally gives:Ql^Z2-kf-(iu+i)-yj\Ps-Pl\-sign(Ps-Pl)-Zrkr(iu-i)^\pl-Pe\Sign(Pl-Pe) Q2=Z2-kf (/u + /). J\p2 - Pe\ ? sign(P2 -Pe)-Zx-k(-  0 Z2 = 1 and i > iu Zl = 0 / < /u Zx = 1 for / < 0 Z] = 1 and / < -/u Z2 = 0 / > -/" Z2 = 1 For the asymmetric linear actuator, shown in figure 1, applying generalized flow continuity equation to the cylinder volumes V\ and V2 for extending and retracting cases, I- extending II- retracting Vx dPj ^ K, dA P, ât *i i - ^ d/ V-> dA V, dR and adopting a notation such that flow into side 1 and out of side 2 is termed positive and extending velocity is termed positive, then a pair of equations may be used to define both extending and retracting cases as follows: n a F2 dP2 Dynamically both volumes Vx and V2 vary with piston motion, although variations from mean volume are neglected. Therefore, for the asymmetric cylinder, there are two capacitans terms: Q " P, Cl = L Next, the generalized momentum equation for the system can be written as: P,. Ax - P2 ? A2 = FL + Bv -u+M-~ Recalling the servovalve flow equations, then gives a possible set of actuator equations as follows: Ql = kr(in+i)-J(Ps-Pl)-kr(iu-i)-Jf]=Al-u + Q2 = kr(i1l+iy^-kr(iu-i)^Pa-P2=A2-u-^---^- Using above equations, state space equations of the electrohydraulic system can be written as follows:.Xi - - X'y. _ Bv_ A A^ F± X2~~M'X2 + M'X3~M'X4~ M *3 = ç-'[Ql(X3>')-4-X2] x4 = --. [Q2 (x4,;') -A2-x2] If we do not neglect volume variation by piston motion these equation can be modified in the following form: JT] = Xi. __A o-A _A _^_ Xl~ M'*2 M'X* M'Xa M *3=-r±r'[Qi(x3>i)-Arx2] A\ 'x\ X4 - a (T CTT. [Ö2 (*4 J) -A2-x2] ^2 'V-hiiax ~x\) Linearized system equations can be written in the following form: Simulation programme is developped by Pascal programming language and states variables of the system for each model are integrated on a personal computer The outputs of the programme, is plotted on the computer by a programme written in the same language and WINMCAD software package. XllIn the simulation, classical PD control is applied to the system and control parameters are calculated by Ziegler-Nichols rules. It is found that, proportional gain kp is strongly depended on supply pressure. Higher values of the supply pressure decreases kv. Some results have been obtained from simulation of the system is shown in figure 2. 0.12 0.11 - Position (m) 0.1 - 0.09 0.08 PI (bar) 0 0.1 0.2 0.3 Time (s) 0 0.1 100 P2 (bar) 04 0.5 0.2 0.3 Time (s) 02 0.3 Time (s) 0.4 0.5 Ql*e-3 (m3/s) Control fi _ 0.2 0.3 Time (s) Figure 2. Simulation results. Simulation flow chart is shown in figure 3. (^StarP) System Model Simulation Loop Control Type Runge Kutta IV Integration t = t + h Writing States Variables on Files Figure 3. Simulation flow chart.