Sincap kafesli asenkron makinalarda modern kontrol yöntemlerinin uygulanması

Abstract

ÖZET Tezde sincap kafesli asenkron makinaya, modern kontrol yöntemleri uygulanmış, sistemin optimum ve adapti-f kontrol kurallarına göre davranışı incelenmiştir. Bunun için öncelikle maki nanın d- q eksenindeki modeli ele alınıp normalize edilerek daha kullanışlı hale getiril miştir. Böylece giriş geriliminin sadece genlik ve -fre kans bilgilerinden yararlanan skal ar kontrol yöntemle rine göre daha avantajlı olan vektörel kontrol yöntemi uygulanmıştır. Kontrol işareti olan gerilimin, genliği, fazı ve -frekansı bir vektör biçiminde gözönüne alınarak makinanın hem geçici hem de sürekli rejimine ilişkin bir matematiksel model verilmiştir. Bu modelde yer alan denklemler, lineer olmadığından bir takım düzenlemeler le lineerleştirilmiş ve seçilen bir optimal kontrol ku ralına göre davranışı, simülasyon ve pratik uygulama ile istenilen sonuçlar al ınmıştır. Oldukça basit bir yapıda elde edilen optimal kontrol algoritması pratik uygulamada C ve Assembler dilleri kullanılarak mikro bilgisayar ile gerçekleştirilmiştir. Gerçekleştirilen optimal kontrol algoritması, si stem parametrelerinde çok aşırı olmamak koşulu ile oluşabilecek değişimlerde de amaç ölçütünde istenen davranışı sağlamıştır. Fakat sistem parametrelerinde oluşabilecek değişimlerin bir- arada oluşması veya parametre ölçümlerinde yapılacak hataların, sistemi, amaç ölçütünde istenen davranıştan uzaklaştırması durumunda ise, sisteme adapti-f kontrol kuralları uygulanmıştır. Optimal kontrolün yanısıra Model re-ferans adapti-f kontrol kuralları ile parametreler daha önceden ölçülen ve değişmeyen bir modele uyumlu hale geldiği simülasyon sonuçları ile doğrulanmıştır. Pratik kontrol da kullanılan mevcut mikrobilgisayar sisteminin yavaş olması nedeni ile geliştirilen adapti-f kontrol algoritmasına ilişkin pratik sonuçlar elde edilememiştir-. Ayrıca kontrol sisteminin cevapları, sonuç bölümünde klasik bir kontrol türü olan PI kontrolör cevapları ile karşılaştırılmış ve gerek aşım ve gerekse yerleşme za manı açısından büyük bir üstünlük sağladığı gösterilmiş tir. Kİ

SUMMARY The Application of Modern Control Methods in Squirrel Cage Induction Machines The most commonly used machine in electrical drives is the squirrel cage induction machine. Its better reliability, low maintenance costs and cheaper price are the main reasons why it is preferred in many applications. However, its application was limited by the complexity of its control which arises because o-f the variable- -frequency supply, ac signals processing and complex dynamics of the machine where only stator terminals are available for control. The recent developments in power electronics have solved the variable- frequency supply problem by adequate fre quency converters. On the other hand, the implementa tion of microprocessor in the digital control circuits has intoduced a wide scope of possibilities to overcome the complex dynamics of the machine and ac signal pro cessing. Many models have been proposed to analyse and develope control algorithms for the induction machine. In gene ral, a model must cover the transient and steady states of the machine. Besides that, it must also be a simple model, as the aim is to obtain an applicable control method. This is the main reason why a model adequate to vector control is considered in this work. A general analysis has been achived by using this model where the three hidden variables amplitude, frequency and phase in an ac signal can be taken seperateley into conside ration. As the rotor field- oriented vector model is used, a more simple structure is obtained for the con trol algorithm. In this work, the input signal stator voltage is defined according to the rotor flux. A coor dinate transformation is necessary between the real and vector control variables. Therefore the unit vectors cos8` and sin6« are needed in the algorithm. There are essentially two general methods to obtain these unit vectors. One of them is the direct mrethod, and the ot her is indirect method. In the direct vector control method, the rotor flux is measured directly by Hall ef fect sensors and the unit vectors are calculeted accor- dind to the results. However, in the direct method the se vectors are obtained by speed feedback and produced rotor frequency. This method is preferred in many app lications as it is not necessary to use special cons tructions with Hall effect sensors. Thus the induction machine can be handled like a seperately excited dc machine when the rotor flux can be kept constant. HllIn the control scheme to be discussed here, the -flux is kept at its required constant value by overexcitation, so that the proposed model of the machine in the d-q coordinates becomes very similar to the simple model o-f a seperately excited dc machine. In the development o-f the model it is aimed to apply the modern control met hods like optimal and adaptive control to the induction machine. The proposed model can be given by the -follo wing equations» dt t- `/ n -C» 0 'V n 0 'mo 0 -c. m/ On the other hand, the optimal control o-f the machine is considered as a minimum time problem in the work. The -following performance index causes the actual speed to get the reference value in minimum time without overriding the chosen physical constraints: « =- -s» (n (t* )-NR) +-.»at '%. Vmo~ Tr-n- fD.dt The integral term in this equation corresponds to the transient state with physical limitations and the other term is -for the last value o-f the speed. The state equ ations and the performance index establish the Hamilto- nian -functions o-f which solutions give the following optimal control laws: V`C= fr-M + n - kss.lr-c, f` » f,_ + n V»eS - C<«» ~ C-y.fm.fr- + ki (§rdR_§rd) The necessary voltage amplitude and frequency input! for the drive unit &re obtained by the control variab les v. and f» as followss v`M = Y vmei + vm` f»R - f« + Tf < arctg ) dt V`a x 1 1 awhere Cx, Cs», C3, CU, Ce=, C ^, Cv are machine parameters and Tm is a constant. kj(grejR-rd) and -ka.fr-^ equations are used -for the overexcitation to keep the -flux con stant. SrdR is a required reference value o-f the -flux, 5,-ei and frq are the obtained -flux components and kt, k& are constants. limited the and assemb- the software The simulation results according to these control laws have been very satisfactory. Afterwards an algorithm has been developed to realise the control scheme in practice. By the implementation o-f a microcomputer in the drive unit, very close pratical results are obtai ned. However, the speed o-f the computer has theoritical performance in practice. Both C ler languages are used in mixed version -for to realise the algorithm in the real time control. The square root and arctg functions are solved by a mathe matical coprocessor in the hardware. A F'WM variable fre quency converter is used as the main drive unit which consist of an uncontrolled rectifier and voltage - fed type inverter. The pratical measurements are achived on a 3 phase, 3kW, 50 Hs squirrel cage induction machine. The mechanical load has been a separetely excited dc generator with a resistive load. It is shown that the variations of the system parame ters can be compensated in some limits by the calcula tion of the flux and load torque values from the real current and speed feedbacks. These variations are cau sed by disturbances like saturation, skin effect and torque of inertia. The measurement errors can also ef fect the optimal trajectory in practice. Therefore, the control scheme is also adapted by the adaptive control methods. As it is difficult to apply adaptive control in the nonlinear systems, the model is simplified and linearised. In this model, the fluxes are considered as variables, in order to obtain a more useful mathemati cal structure: dt -a. O 3l3 0 0 -an O a i3 Ssı 0 -833 Ö O et^t O `âgg dn dt KmX> <T. X.Xr- `. ' S »eı. £r-d 2»ö`Sr-ei' AK XIVThe nonlinear terms -f»?»*,, -f»§»ej, -fı-Sr-c,, -fr-Sr-ei in this model are in voltage dimensions. By the substitutions U.d «= V»d +*.¥.?, Ur* - *r-5r-«, Urq ^ ~ `fr-fir-d The input signals can be de-fined in such a way that the model becomes linear as -follows: There is only one nonlinear term left in the speed equ ation, but the applied model reference adaptive control algorithm does not contain this equation. The simple structure o-f the adaptive control system is shown in the -following -figure OPTIMAL CONTROL ALGORITHM 1 Ku MODEL ?O^- PLANT KP X C,m 5^ *P ? ?Figure ]l üp= - Kp, (e,t).^p+ K`(e,t).L[ is the control vector applied to the system. The criti cal point is de-f inatio^ji o-f suitable Ku and Kp matri ces. A scalar Liapunov function which contains the sta te and parameter errors, has been chosen -for this desti nation and stability conditions are taken into conside ration. By- using this conditions, KM and fÇ` matrices are obtained in proportional - integral -form xvLı.D.e.y_T.M.d£ + LsB.D.e.^T.jİ O K` Lı.D.e.uT.N.d6' + La.D. e.uT. N O where L*, L ı, Lz, La, M. and _N are positive simmetrical coefficient matrices which do not effect the stability, but simplify the control scheme, e. is the generalised error de-fined as The control signal of the machine can be given as V«»el»» - Ujscjp,.. f a»p > £ a»c*ti V»qp - Uncııa **? TsptSsqh where the Tip vector is UB = Undp UBdp f`mp is a speed dependent variable in these equations. The nonlinear speed equation where the proposed adapti ve control methods can not be implied, is considered as an error -function and applied to system. fep - Til ?+. K3. (nm - n) Here, kas is a coefficient, nm is the speed of the model and n is the speed o-f the motor, f` is calculated by the optimal control algorithm. Thus, the input signals to the drive unit are obtained by the -following equati ons: / -2 »p - -J v`dp - 2 V_a T» Rp V.cp - imf3 + TN.arctg(-- > Vedd HV1The simulation results have shown that the algorithm is very satisfactory. Especially the speed error which is added as an error -function to the -frequency equation, has remained in very low limits. Because o-f the limited speed o-f the microcomputer, only the optimal control algorithm is realised in practice. The microcomputer which has been used -for the implemen tation o-f the control algorithm and the evaluation of the -feedback signals, consist of a microprocessor, me mory elements, I/O ports, mathematical coprocessor, AD/DA converters and timers. The analog current feed back signals &re filtered by special circuits before they are converted into digital signals. A digital ro tary encoder is used for speed feedback of which output pulses are evaluated by the counters. The output sig nals &re obtained via DA converters, as the converter unit used requires analog inputs. Host of the mathema tical operations are accomplished by the coprocessor in the hardware. The frequency converter unit has two ana log control inputs for f` and f«,/v`. Therefore, the calculated vm value has been converted to the required f`/v` ratio in the microcomputer. Besides that, the control signals have been applied to the converter via some delay circuits which could not be deleted because of some hardware problems. The quantisation, rounding and truncation errors of ADC, DAC and microcomputer ha ve also caused some small deviations between the theo- ritical and practical results. In the last chapter, a control strategy with classical PI controllers has also been discussed to compare the results of the modern control algorithms. The speed and flux feedbacks have been established for this classical control method using also the vector control model of the machine. Therefore, the coordinate tranf ormation has also been necessary in this application. The simu lation results have shown that the performance of the system is lower as compared with the optimal control results. Though the parameter of the PI controllers are optimized, the overshoot and settling time have been worse in comparison with the modern control response. «Vll