The estimation of PID controller parameters of vector controlled induction motor using Ziegler-Nichols method

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1 Journal of Engineering Research an Applie Science Available at Volume 4(1), June 2015, pp ISSN The estimation of PID controller parameters of vector controlle inuction motor using Ziegler-Nichols metho E. Başer 1,a, Y. Altun 1 1 Duzce University, Computer Engineering, Duzce, Turkey. Accepte 25 May 2015 Abstract Inuction motors (IM) are commonly use in inustrial applications ue to their superiorities such as low cost, less maintenance requirements, high effiency an high power ensity in comparison with other electric motors such as c motors. There are many stuies in the literature on IM control. The best known spee control metho of the IM is scalar control metho (SCM) because of its easy to unerstan an implement. The another control metho which is known as vector control metho is the fiel oriente control metho (FOC). Although FOC is more sophisticate than SCM, it is higher performance on control in general. In this stuy, the mathematical moel of IM has use on simulation an FOC metho has implemente on it. Then for spee control of IM Ziegler-Nichols metho is use.matlab/simulink software has use to simulate system. Keywors: Inuction motor; vectrol control; ziegler-nichols metho;simulink 1. Introuction The use of inuction motors is wiesprea in inustry ue to their simple structure an simple maintenance compare to other electric rives such as c motors. With the evelopment on the power electronic technology an control theories by using many control algorithms such as vector control an irect torque control the performance of IM has become more superior [1]. There are many control methos on IM such as SCM an FOC. FOC metho has superiorities than SCM ue to high performance on control [2]. PID a Corresponing author; Phone: , ekrembaser@uzce.eu.tr controllers can use to control spee of IM. Although PID controllers have simple structure, many control loops use toay are PID controllers []. There are a lot of stuies about esigning PID parameters [4-10]. The most useful metho to etermine PID controller parameters is Ziegler - Nichols metho [4]. In literature there are many stuies to improve PID controller parameters which has esigne by using Ziegler-Nichols metho. In this stuy it has trie to control spee of three phase inuction motor on Matlab/Simulink software. Spee results has shown on figures. 2. Material an Methos Firstly, to implement FOC to inuction motor mathematical moel of inuction motor has investigate from its equivalent circuit. The equivalent circuit of IM has shown on Figure-1. Equialevent circuit shown on q axis.from this equialevent circuit this equations has generate. v s = R s i s w λ sq + L i ls t s + L (i m t s + i r ) (1.1) v sq = R s i sq w λ s + L i ls t sq + L (i m t sq + i rq ) (1.2) v r = R r i r w A λ rq + L i lr t r + L (i m t s + i r ) (1.) V rq = R r i rq w A λ r + L i lr t rq + L (i m t sq + i rq ) (1.4) EElectromagnetic torque; T em = p 2 λ ri rq = p 2 λ r( Lm Lr i sq) (1.5) p is the pole number Rotor axis wining; Baser et al / The estimation of PID controller parameters of vector controlle inuction motor using Ziegler-Nichols metho

2 Journal of Engineering Research an Applie Science Volume 4(1), June 2015, pp λ t r + λ r = L m i τ r τ s (1.6) r τ r is calle rotor time constant. Stator Fluxes is written in a vector form [λ s ] = [ v s t λ sq v ] R s [ i s sq i ] w [ 0 sq Mechanical rotor of spee; ] Mrotate [ λ s λ sq ] (1.7) t w mech = T em T L J eq (1.8) Synchronous spee; w syn (t) = w m (t) + w slip (t) (1.9) θ Angel; t θ Br (t) = 0 + w syn (τ). τ 0 abc-q transform; [ q ] = 2 [cosθ cosθ 2 π sinθ sinθ 2 π (1.10) cosθ 4 π sinθ 4 π ] (1.11) q- abc transform; a cosθ sinθ [ b] = 2 [ cosθ + 4 π sinθ + 4 π ] [ c cosθ + 2 π sinθ + 2 π q ] (1.12) Figure 1. Equivalent circuit of IM on q axes. Simulink moel of IM has generate from this equations[11] on Matlab/Simulink software as shown Figure-2. Figure 1. IM moel block. Baser et al / The estimation of PID controller parameters of vector controlle inuction motor using Ziegler-Nichols metho 279

3 Journal of Engineering Research an Applie Science Volume 4(1), June 2015, pp The parameters an nameplates of IM which has simulate here are liste below. Power : HP/2.4 kw Voltage : 460 V Frequency : 60 Hz Phase: : Tüm Yüklemeeki Çektiği Akım:4A Tam Yüklemeeki Hızı : 1750 Rpm Verimliliği : %88.5 R_s : 1.77Ω R_r : 1.4Ω X_ls : 5.25Ω X_lr : 4.57Ω X_m : 19Ω J_eq : 0.025kg.m^2 Accoring to fiel oriente control theory, a reference mechanical spee has given initially to system. Then by PI controlling with which measure from motor. current has obtaine. has given 0 initially. an voltages has calculate by controlling reference currents. For controlling three phase inuction motor this an voltages has transforme from q axis to abc axis. voltage has given to inuction motor an motor has riven with this three phase voltages. In Figure- a classic vector control block scheme has shown. Simulink impelentation of this control metho also has shown Figure-4. Figure 2 Vector control block scheme. Ziegler-Nichols metho is a technique that tries to fin parameters by trial an error. System is riven by using only P controller initially an slowly increase Figure Vector controlle IM simulation. until persistent oscilation is reache. At this point value is marke as an the perio between two oscilation is enote as. In Figure-5 IMs mechanical Baser et al / The estimation of PID controller parameters of vector controlle inuction motor using Ziegler-Nichols metho 280

4 Journal of Engineering Research an Applie Science Volume 4(1), June 2015, pp spee which is reache oscilation by slowly increasing value has shown. At this point an values has T = 0,025 0,017 = 0,08 K p = 26 Then, PID controller parameters has calculate accoring to Ziegler-Nichols parameter calculation metho as shown Table-1. foune like below. K p = 0.6K p = = 15.6 K i = T 2 = = K = T 8 = = Figure 4 Oscilation state. Table 1. Ziegler-Nichols metho PID parameters calculation Controller Type K K K P Controller 0.5K p 0 PI Controller 0.45K p T /1.2 0 PID Controller 0.6K p T /2 T /8 p i. Results Calculate K p, Ki, K parameters has use spee control loop of this vector control block of simulation moel an the spee graphic of IM has obtaine as Figure-6. At the 0.1 time point the loa torque has affecte to IM an has trie to change IM mechanical spee. In this figures it is shown that spee of IM has controlle by using Ziegler-Nichols metho. Figure 5 Mechanical spee graph. 4. Conclusion In this stuy, spee control of the inuction motor has been trie to simulate by using Ziegler-Nichols metho on Matlab/Simulink software. Ziegler Nichols metho has been successful on esigning parameters an controlling IM spee. Baser et al / The estimation of PID controller parameters of vector controlle inuction motor using Ziegler-Nichols metho 281

5 Journal of Engineering Research an Applie Science Volume 4(1), June 2015, pp Acknowlegement This stuy was supporte by Duzce University Scientific Research Projects Coorinatorship. Project No: References [1] Wang, X., Yang, Y., & Liu, W. (2011, June). "Simulation of vector controlle ajustable spee System of inuction motor base on Simulink. In Computer Science an Service System (CSSS), 2011 International Conference on (pp ). IEEE. [2] Krein, P. T., Disilvestro, F., Kanellakopoulos, I., & Locker, J. (199, June). Comparative analysis of scalar an vector control methos for inuction motors. In Power Electronics Specialists Conference, 199. PESC'9 Recor., 24th Annual IEEE (pp ). IEEE. [] Åström, K. J., & Hägglun, T. (2001). The future of PID control. Control engineering practice, 9(11), [4] Bhattacharyya, S. P., Datta, A., & Ho, M. T. (2000). Structure an synthesis of PID controllers. [5] Ackermann, J., & Kaesbauer, D. (2001, September). Design of robust PID controllers. In European control conference (pp ). [6] Shafiei, Z., & Shenton, A. T. (1997). Frequencyomain esign of PID controllers for stable an unstable systems with time elay. Automatica,(12), [7] Zaeh, L. A. (1965). Fuzzy sets. Information an control, 8(), 8-5. [8] Zaeh, L. (1984). Making computers think like people: the termfuzzy thinking is pejorative when applie to humans, but fuzzy logic is an asset to machines in applications from expert systems to process control. Spectrum, IEEE, 21(8), [9] Lee, C. C. (1990). Fuzzy logic in control systems: fuzzy logic controller. II.Systems, Man an Cybernetics, IEEE Transactions on, 20(2), [10] O'Dwyer, A. (2000). A summary of PI an PID controller tuning rules for processes with time elay. Part 2: PID controller tuning rules. [11] Mohan, N. (2001). Avance electric rives analysis, moeling an control using Simulink. Minneapolis, MN: Minnesota Power Electronics Research & Euca-tion. Baser et al / The estimation of PID controller parameters of vector controlle inuction motor using Ziegler-Nichols metho 282