Hidrolik sistemlerde ikili konum kontrolu ve mikroişlemci uygulaması

Abstract

ÖZET Hidrolik Konum Kontrolü sistemlerinin incelenmesin de bilgisayarların kullanılabilmesi, bu sistemlerin özelliklerinin ve kontrolünün belirlenmesine önemli katkılar getirmiştir. Bilgisayar vasıtasıyla, kullanılan akışkanın sıkıştırılabilme. etkisi gibi evvelce sistem modeline dahil edilmekten kaçınılan nonlineer etkiler de sistem modelinde gözönüne alınıp sistemin kontrolü gerçekleştirilebilmektedir. Bunun yanında, geliştirilen yeni ölçme teknikleri ve elemanları ile bilgisayarın beraber kullanılması sonucunda daha hassas ölçme ve kontrollar yapılabilmektedir. Bu çalışmada, ikili bir yön valfiyle kontrol edilen hidrolik bir konum kontrol sisteminin, akışkanın sıkıştırı- 1abilirliğide gözönüne alınarak nonlineer matematik mode li kurulmuştur. Kurulan matematik modeldeki bütün terimlerin etkisinin incelenebilmesi için ölçeklendirme yapılmış tır. Daha sonra, sistemin kontrolü için gerekli olan sistem durum ve giriş matrislerinin bulunabilmesi için ölçeklendirilmiş nonlineer model lineerleştirilmiştir. Bu arada yine sistemin kontrolunda kullanılmak amacıyla, nonlineer mate matik model, ikinci mertebeden modele indirgenmiştir. Sis temin çeşitli durumlar altında davranışlarını incelemek gayesiyle nonlineer model üzerinde bir dizi simülasyon çalış ması yapılmış ve sistemin cevap eğrileri elde edilmiştir. Sistemin kontrolü için ölçeklendirilmiş lineer modele Lineer Regülatör Problemi uygulanarak, uygun geribesleme katsayı larıyla kontrollü sistem davranışları elde edilmiş ve daha sonra bu geribesleme katsayılarından yola çıkarak ikinci mertebeden sisteme kontrol uygulanmıştır, ikinci mertebeden sistemin kontrolunda, hız geribesleme katsayısının arttırılmasıyla sistemin aşmaları giderilmiş ve ideal davranışa uygun kontrol eğrileri bulunmuştur. Bu yaklaşım, gerçekleştirilmesi çok karmaşık olan minimum zaman probleminin çözümüne bir alternatif getirmektedir. vr

S UM M AR Y -OFF POSITION CONTROL OF THE HYDRAULIC SYSTEMS AND MICROPROCESSOR APPLICATION In this study, The realization of a hydraulic po sition control system with the on-off control approach is investigated. A mathematical model is derived for an asymmetric linear actuator including the compressibility of fluid and nonlinearity of the control valve. This mathematical model is suitable to examine the basic properties of the system such as reverse flow and pressure oscillations. The mathematical model of the system is simulated on a digital computer. Because the pressure dynamics of the system is much faster than the velocity and position dynamics, the large differences in the system coefficients occur, they are removed by scaling. Thus, it is possible to observe the whole dynamic characteristics of the system. The simulation curves which are obtained and given in the thesis are in close agreement with the results of previous work related to this subject. Linear Optimal Control Methods are applied to the model to find the optimal feedback matrix for the time optical on-off control of the system. The variables in the system are weighted unequally according to their contribution to the global system performance. At the end of this work where real parameter values are used, position and velocity feedback coefficients are found, VIIthen the control is applied in the form of on-off control. With small improvements in the coefficients obtained with this approximation, a behaviour very close to the minimum time response is obtained. The first model used in this study is based on the use of a zero lapped valve. In the simulation using this model the neutral position is observed to be unstable. In addition, initial conditions are indeterminate, so an underlapped valve is used later in this study. In the model using the underlapped valve, it is observed that the instability and the uncertainty in the initial conditions of the system disappear. As a result of the leakage flow due to the underlap, it is observed that the oscillation amplitudes of the system are decreased. Besides, it is assumedthat the opening and closing of the valve solenoids are not as step functions but ramps, opening in 0.06 second and closing in 0.04 second, and this characteristic is used in the simulation. Because of the large valve size chosen during the first trial, it is observed that control in short distances is not possible. Thus, a smaller valve is chosen and the rest of the study is done with this smaller valve. The state space equations of the system using an underlapped valve are as follows: x =x 1 2 ( X 3 - O1X4 ) M * M M x3 = C-x2 + Q.(x,,ü)/A g- x. x,= - £ x2-Q2(x,,U)/A2] (L*-x ) - VIIIwhere flow rates are nonlinear functions of the state variables, for example, for U>8 Q1(x3,U)=k1{U+o) sign(Ps-xj)y(Ps-xj)sign(Ps-x?) Q2K,U)=k2(U46) sign(x4-Pt) Ax«-Pt)sign(x*-Pt) for -5<U<8 QjtXj.U^kjCU+o) sign(Ps-xJ)7(Ps-xJ)sign(Ps-xs) +MU-6) sign(x3-Pt) 7(x3-Pt)sign(xrPt) Q,(x«,U)=k2(U+6) sign(x4-Pt) /öü-P^)sign(x^) +k3(U-ö) sign{Ps-x4)7(Ps-xJ sign(Ps-xJ for U<-6 Q1(x3,U)=kjU-6) sign(x3-Pt)y(x3-Pt) sign(x3-Pt) Q2(x^U)=k3(U-6) sign(P -xj7(P -xj sign(P -xj s «' v S *' Following results have been obtained when the behaviour of system using the underlapped valve is examined in various cases: It is observed that pressures for the control input U=+1 are lower than those for U=-1, while the net pressure acting on the piston in the direction of motion is larger for U=+1. When the valve is in the neutral position, i.e. when U=0, and due to the leakage flows, very small IXamplitude oscillations are observed in position, velocity, pressures and flow rates about their initial values, and pressures increase very slowly in time. For different supply pressures, it is observed that system response amplitudes increase proportionally with the supply pressure. When the viscous damping coefficient increases, it is seen that system response amplitudes decrease. A change in load mass affects only the transient responses of the system. When both the viscous damping coefficient and the load mass are increased, damping of the system also increases. When different external forces are applied to the system, the behaviour curves shift depend ing on the direction of the external force. During studies involving cylinders of various sizes and based on the area ratio a, the oscillation frequency increases, but the amplitude decreases with decreasing a. The control problem of the system using an under- lapped valve, is handled as a linear regulator problem. Since a scaled system is used, the scaling transformations are also made in the linear regulator problem solution where needed. The feedback gain matrix obtained is applied to, the system with servovalve control, and then the same feedback gain matrix is applied to the on-off system to compare the behaviours of two systems. On the curves obtained for the on-off system, it is observed that pressures, control input and flow rates oscillate with high frequencies and with very small amplitudes, while nonosci 1 latory curves are obtained for the system with servovalve. When the fourth order system is controlled using only the first two elements of the feedback gain matrix, the pressure oscillation amplitudes increase and oscillations arise in velocity since there is no pressure feedback in this case. Meanwhile, it is observed that both the control input and flow rate are positive. given The block diagram of the on-off control system is below. Reference m KThis feedback gain matrix is then applied to the second order system. Firstly, a cascade combination of propor tional and on-off controls is used with the first element of the feedback gain matrix and it is observed that the position settles with oscillatory behaviour in approxi mately 1.14 seconds. Then, a combination of proportional plus derivative and on-off controls is applied with the first two elements of the feedback gain matrix and it is observed that the position settles with an overshoot of 5% and the steady state error of 1% in approximately 0.5 second. Then corrections in the elements of the feedback matrix are made and the velocity feedback is increased. In this case, it is seen that the position reaches the reference value with two switchings, an overshoot of 0.51 and a steady state error of 0.4%. A further increase in the velocity feedback coefficient led to a behaviour where the position reaches the reference value with one switching and a steady state error of 0.08% without overshoot. This case corresponds to the minimum time control of the system. The curves obtained for this last case are given below. 0.35 (n) h Wsoc) t lies) 0.S 1 `2 (ra&a:) So -os _ 0 e s Position X, (o) 0J5 t [sec) 0.75 Consequently, in this study, it is shown that a precision hydraulic position control system can be reali zed with the on-off control approach and the required methods for design are presented. The results obtained through simulation are satisfactory, and they establish a basis for further study. A rotational encoder is used for position and velocity measurements because of the ease of connection to the microprocessor, and analog transducers is used for pressure measurements. To measure the position, the XIoutput pulses of the encoder are counted with a counter circuit and fed to the microprocessor in parallel form. The velocity measurements can be made in two ways: The first way is to count the output pulses of the encoder with a second counter for known time intervals. The second way is to use the proper velocity measuring integrated circuits. For this reason, serial pulses at the output of the rotational encoder are fed to the PTM (Programmable Timer Module) for the 6800 microprocessor, or the CTC (Counter-Timer-Circuit) for the Z80 microprocessor, or the VIA (Versatile Interface Adapter) for the 6502 micro processor. Thus, the microprocessor can have the velocity measurement available any time it is required, when appropriately programmed. Analog pressure measurements are converted to digital form with an ADC (Analog to Digital Converter) before entering to the microprocessor. Feedback gain values, found by simulation, are loaded into the microprocessor memory. Control is determined only, according to the sign of the expression which is obtained with this feedback gains, and it is applied to the sole noids of valve through the valve driver circuit. Block diagram of the microprocessor controlled hydraulic system is given below. MICROPROCESSOR Such a system can easily be realized using a microprocessor, and can be programmed in a very simple way. The required circuits and programs are specified within this study. The cost of the system is less than that of the servovalve controlled system for the same precision level. XII