Asenkron motorlar için algılayıcısız akı gözlemleyicisi ve kontrolü

Abstract

Bu tezde, asenkron motorlar için, çatırtısız kayan kipli kontrol tabanlı dayanıklı akı gözlemleyicisi geliştirilmiştir, özellikle, geniş çalışma aralığı ve ağır çalışma koşullarında hassas kontrol amaçlandığında, akı gözlemleyicisinin dayanıklılığı (robustness) çok önemlidir. Bu tezde sağlanan en önemli katkı, rotor akı gözlemleme modeline eklenen yakınsama terimleridir. Bu terimlerin eklenmesi ile gözlemleme hatalarının sıfıra yakınsayarak orada kalması sağlanmıştır. Sonuçta parametre, hız, yük gibi tüm etkilere karşı dayanıklı bir gözlemleyici elde edilmiştir. Sistem, ortak endüktans, rotor, stator direnç ve öz endüktans değişimleri, değişken yük ve bozucu moment şartlan altında incelenmiştir. Geliştirilen yöntemlerin sonuçlarının başarılı olduğu ve dayanıklı bir gözlemleyici ve kontrol sistemi elde edildiği benzeşim ve uygulama sonuçlan ile gösterilmiştir. Ayrıca hız, konum ve alam kontrol çevrimlerine de oldukça yeni geliştirilen çatırtısız kayan kipli kontrol yaklaşımı uygulanmış ve çok başarılı sonuçlar elde edilmiştir. Sonuçta dayanıklı, kararlı ve dalgalanmasız moment ve hız kontrolü sağlayabilen, yüksek cevap hızı ve hassasiyete sahip bir kontrol sistemi elde edilmiştir. Asenkron motorlar için zor sayılan sıfır hız ve civarında da, yüksek hızlarda da aynı başarımlar elde edilmiştir.

Abstract A robust flux observer and controller for induction motors is proposed based on sliding mode theory. Robustness of the flux observer is a very important issue, especially when it is aimed for use at wide working range and demanding operation conditions. in this study, the velocity, position and current controllers are also based on sliding mode. The vvhole system is analyzed under rotor, stator resistance, mutual and şelf inductance uncertainties, torque variations and external disturbances. The performance of the proposed control scheme is confirmed by simulation and experimental results. l Introduction Fully digital controlled AÇ drives are extensively used in industry. Many fıeld orientation methods are used in these drives. in these high performance induction motor (asynchronous motor) applications, parameter variations and external disturbances can be effective. Especially when it is aimed to track a certain trajectory, robust control techniques have to be used in the observer and in the velocity, position control loops. The good properties of Sliding Mode Control (SMC) in this respect are well known. The chattering problem inherent to SMC is eliminated in recently developed approaches. in this study, the design of the observer is different from methods proposed until now. The flux model is used in polar form and convergence terms are added to the rotor model. Additionally, the modifıed version of the SMC is used for chattering free control. The position, velocity and current controllers are also based on SMC. Robustness of the system is considered under dynamic load and fast reference signal, same time parameter variation and torque disturbances. 1.1 Proposed Control System in proposed control system, a flux observer is used for the calculation of the flux magnitude, angle and stator current components at rotating coordinate frame (Fig.l). The currents are controlled by the sliding mode based control system (SMC PWM). The flux reference value is selected from velocity operation point for maximal torque output. The flux and position are controlled by chattering free sliding mode algorithms in the outer loop. XV rh l*tf N) ijd 4-*-T^ ^FhKCbntjL ^.w w ^s j 5 J s*.*. SMC "^T 9 (İM tXe) A İqd PWM -: :i ^^ _ j j Bos.Gont VW ^ ~V-1^ ^ [0J^J> w q l- FUUX 1 OBSERVER l-dıat ^ Figüre l Proposed control method Superscript 'd' is used for desired value. The other symbols indicate actual values. 1.2 Chattering free sliding mode control The Variable Structure System (VSS) theory has been applied to nonlinear processes. Öne of the main features of this approach is that öne only needs to drive the error to a "switching surface", after which the system is in "sliding mode" and robust against modeling uncertainties and/or disturbances. Let us consider the plant x = A(x,f)+B(x,j).uM (1) with rank(B)=m, x ? K", u e K". in VSS control, the goal is to keep the system motion on the manifold 5 which is defîned as S=£ | sfrt) = 0} (2) The solution to achieve this goal can be calculated from the requirement that sfat)=0 is stable. The control should be chosen such that the candidate Lyapunov fonction satisfies Lyapunov stability criteria. The aim is to force the system states to the sliding surface defîned by 5=G.(xd-x) (3) Firstly, a candidate Lyapunov fünction is selected as v = /.s/2 > O and v = sr.s <0 (4) xvi it is aimed that the derivative of the Lyapunov fimction is negative definite. This can be assured if we can somehovv make sure that v = -sT.D.s<0 (5) where D is positive definite. Therefore (4) and (5) satisfy the Lyapunov conditions. From these equations s= -D.s. (6) Equating (6) to zero results in what is known as "equivalent control". in other words, the control that makes the derivative of the sliding function equal to zero is called equivalent control. Derivative of (3) G.xd-G.(A(M) + B.ueJ =0 (7) As a result, the equivalent control can be vvritten in the following form uf,=-(G.B)-'.G.(AOM)-i") (8) From derivative of (3) and using (8) 5 = (G.B).(ue,-u) (9) is obtained. The equivalent control can also be vvritten as given below u^(o = u(o + (G.B)"1.i (10) By using the definition given by (1) and (3) in (6) G.(xd-x) = G.(xd-A(x,0-B(x).u) =-D.s (11) the control is obtained as u = (G.B)"'.(G.(X" - A(X,O)+AS) (12) Using the equation (8) for the equivalent control can be vvritten as U(o = u^co + (G.B)"l.D.* (13) By looking at (13) an estimation for ueij can be made using the property that u(t) is continuous and can not change too much in a short time as given below xvii ueg(t) = U(t--n + (G.B)~\s (14) where T1 is a short delay time. This estimation is also consistent with the logic that ueq isselectedastheaverageofu. Bysubstitutingthe(14)into(13) U(/) = U(»-r) + (G.B)"1.(Z).5 + j) (15) By using Euler interpolation, we get the last form for the discrete controller (G B)~' u« = u(, - T) + [ ' '.((D.T+ l).j(o - sı, - n) (16) 2 Model of Induction Machine and Load The state equation of the induction motor viewed from the stator frame (a, ft frame) driven by voltage source inverter is given by (17-20) Rr Rr.M. Va = -~^V« -°>-Vfl + ~[^l« (17> Rr Rr.M Vp =-rVp+<».¥«+-T-ip (18) jLr Lir ^^{T^'^^-^^"} (19) <--3:{f(rr'-"-»'0-*-''*"'} (20) where subscript symbols 'ör' and '^" are used for stotionary axis elements the variables of the equations are i : Stator current u : Stator voltage y/ : Flux component û) : Angular velocity and parameters of the equations are RE :R, + Rr.M2 /L,2 Rn Rs : Rotor and stator resistance L, J.s : Rotor and stator inductance, M : Mutual inductance