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International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012 Comparison Betwe...
International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012C. Mechanical equ...
International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012trajectory toward...
International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012 For the Lyapunov...
International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012                 ...
International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012[10] Rui Guo; Xiu...
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Comparison Between Two Different Speed Controls Of The Permanent Magnets Synchronous Machine

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This paper presents a comparison between two control strategies, field oriented control (FOC) and sliding mode control (SMC). The first study has been done on controlling the
Permanent Magnets Synchronous Machine (PMSM) by using field oriented control technique using a speed sensor to detect the rotor position of the motor. After we present the theory of sliding mode control .We can see from the simulation results that the second proposed control system (SMC), is a robust nonlinear
time optimal controller, that's will be more explained in the appendix.

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Comparison Between Two Different Speed Controls Of The Permanent Magnets Synchronous Machine

  1. 1. International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012 Comparison Between Two Different Speed Controls Of The Permanent Magnets Synchronous Machine A. Attou A. Massoum A. Meroufel ICEPS, University of Djilali Liabes ICEPS, University of Djilali Liabes ICEPS, University of Djilali Liabes Sidi Bel-Abbes, Algeria. Sidi Bel-Abbes, Algeria. Sidi Bel-Abbes, Algeria. attouamine@yahoo.fr ahmassoum@yahoo.fr ameroufel@yahoo.frAbstract—This paper presents a comparison between two control vary linearly with the q-axis current component, and thestrategies, field oriented control (FOC) and sliding mode control maximum torque per ampere is achieved which is similar to(SMC). The first study has been done on controlling the the control of a separately excited DC motor [3][5][6].Permanent Magnets Synchronous Machine (PMSM) by using Robustness as a desirable property of the automatic controlfield oriented control technique using a speed sensor to detect the systems is defined as the ability of the control system to yieldrotor position of the motor. After we present the theory of slidingmode control .We can see from the simulation results that the a specified dynamic response to its reference inputs despitesecond proposed control system (SMC), is a robust nonlinear uncertainties in the plant mathematical model and unknowntime optimal controller, thats will be more explained in the external disturbances. In its basic form, the sliding modeappendix. control (SMC) is a kind of nonlinear robust control using a systematic scheme based on a sliding mode surface andKeywords-PMSM, PI-controller, field oriented control, sliding Lyapunov stability theorem. It features disturbance rejection,mode control. strong robustness and fast response [6],[10],[13].  INTRODUCTION I. MACHINE EQUATIONS Compared with DC motors, PMSM are more difficult in Take into consideration the simplifying assumptions, thespeed control and not suitable for high dynamic performance model with two axes of the PMSM is performed by a realapplications because of their complex inherent nonlinear transformation of the three axis in a fictitious two-axis frame,dynamics and coupling of the system. So PMSM commonly which is actually based on a change of physical quantitiesrun at essentially constant speed, whereas DC motors are (voltages, fields, and currents), it leads to relationspreferred for variable-speed drives. The situation has changed independent of the angle θ and reduced-order equations of thedramatically with the advent of field-oriented control (FOC) machine. The transformation best known by electricians isor vector control theory and the advances in power electronics that of Park.and modern microcomputers[6],[11],[12]. The Field Oriented Control (FOC), also called Vector A. Electrical equationscontrol, the goal of this method is to perform real-time control  Vd  RsId  dφd - pωr φq of torque variations demand, to control the rotor mechanical  speed and to regulate phase currents in order to avoid current    dt  dφd  pωr φd (1)spikes during transient phases. It is possible to set up a Vq  RsIq   coordinate system to decompose the vectors into how much    dtelectromagnetic field is generated and how much torque is φd  Ld Id  φ f generated. This coordinate system is generally called d-q   reference coordinate system (Park transformation). The vector  (2)control technique is employed in order to obtain high torque     φq  Lq Iqcapability of the PMSM drive through the decoupling controlof d-q axes stator currents in the rotor reference frame. For a B. Electromagnetic equationPMSM, the Permanent Magnets provides the flux linkage. Bykeeping d-axis current equals to 0, the PMSM torque may Tem  p[ (Ld - Lq )I d  Iq  φ f  Iq ] (3)
  2. 2. International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012C. Mechanical equation III. FIELD ORIENTED CONTROL (FOC) The induction machine is a nonlinear model and it is dr coupled; FOC strategies transform machine three-phase J  f  r  Tem  Td (4) variables into two-phase axes in order to obtain the same dt decoupling between flux and torque that exists naturally in dc machines. That is to say maintain the flow of reaction induced Consider the voltages ( Vd, Vq ) and the excitation flux in the quadratic rotor flux produced by the excitation system.φ f as control vector, the stator currents ( Id, Iq ) as state The presented control strategy is based on a rotor field oriented control (RFOC) and the stator three phase current isvector. From (1), (2), we can write the system of equations as transformed into dq components of a rotating reference frame.follows [3],[8] : In this case, the d component of stator current controls the d [ X ]  [A][X] +[B][U] (5) magnetic state of the machine (cf. equation (2)), while the q dt component is in charge of generating the electromagnetic     torque (cf. equation (3)) [3][5].  1    0 0         Rs p r Lq     Ld   V    d  According to (1), Vd and Vq are coupled, to decouple d  Id     Ld Ld   Id    0 1 0  Vq  dt  Iq   p r Ld       (6) the system, we will introduce the compensation terms ed et eq.   Rs   Iq   Lq  φ     Lq Lq    0 0 p  r   f  The voltages Vd, Vq depends only I d (respectively for) I q .     Lq  Figure 1 shows the decoupling system with compensationWhere: terms: [A ] : State matrix [X ] : State vector (where [X]  [ Id Iq ]T ) [B ] : Input matrix [U] : Control vector (where [U]  [ Vd Vq φ f ]T ) II. MODELLING OF VOLTAGE SOURCE INVERTER The voltage inverter can convert the DC power to the AC(DC / AC). An AC electric power conversion based on Fig. 1 decoupling systemtechnique Pulse Width Modulation PWM inverter is verypopular in these days. This technique is used to control the ed   r. Lq Iq  magnitude and frequency of the AC output voltages of an Where:   (8) eq   r .(Ld Id φ f )  inverter. This technique is widely used in industrial   applications such as variable-speed electric drives and hasbeen the focus of research interests in power electronics Since the Controllers are sized classics from theapplications for many years [14]. The connection matrix isgiven by (7). parameters of the machine. So if they vary over a wide range of operation, performance deteriorated, then it is best to see VaN   2 - 1 - 1  Sa  VbN   E   1 2 - 1  Sb  (7) other tuning techniques. Where controllers are known for their   6    robustness. VcN     1 - 1 2   Sc     IV. SLIDING MODE CONTROL (SMC) The inverter controlled by the technique PWM generated Slide-mode control is one of variable structure controlby a carrier which is triangular. It is used for generating a strategies (VSC). The essential difference between VSC andsignal which controls the switches, the PWM control signal the common control strategies is the variable structure ofdelivers a square-wave, it is generated by the intersection of control-led system, namely, a kind of switch characteristic oftwo signals, the reference signal, which is generally sinusoidal making systematic structure change continually. Thelow frequency, and the carrier signal high frequency which is switching of the variable structure control is done according togenerally triangular shaped hence the name triangular- state variables, used to create a "variety" or "surface" so-sinusoidal [4]. called slip. The sliding mode control is to reduce the state
  3. 3. International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012trajectory toward the sliding surface and make it evolve on it  x  f ( x,t ) g( x,t )U (13)with a certain dynamic to the point of balance. When the state is maintained on this surface, the system issaid in sliding mode. Thus, as long as the sliding conditions Where f and g are n- dimensional continuous functionsare provided as indicated below, the dynamics of the system in x, u and t. x is an n- dimensional column vector .remains insensitive to variations of process parameters, to ( x   ) and ( u   ). n mmodeling errors [2],[3],[7]. The objective of the sliding mode control is:  Synthesize a surface, such that all trajectories of When we are in the sliding mode, the trajectory remains on the system follow a desired behavior tracking, the switching surface. This can be expressed by [2],[4],[9] : regulation and stability.   Determine a control law which is capable of S( x,t )  0 et S( x,t )  0 (14) attracting all trajectories of state to the sliding surface and keep them on this surface. The behavior of systems with discontinuities can beformally described by the equation: x( t )  f (x, t, U)  (9) Where: x : Is a vector of dimension n, x  n . t : Time. Fig. 2 sliding mode in the intersection U : control input of a dynamical system, u   . m f : The function describing the system evolution over The design of sliding mode control requires mainly the three following stages [2][3]: time.  and f A. The choice of desired surface  So we seek that the two functions f converge We take the form of general equation given by J.J.Slotinetowards the surface of commutation S and which have the to determine the sliding surface given by:characteristic to slip on it. We say that the surface is attractive [15] . S ( x)  (  x )r 1e( x ) (15) t  x( t ) f ( x,t ,U ) f ( x,t ) if S( x,t )0     f ( x,t ) if S( x,t )0 (10)    Where:   e( x ) : Error vector; e( x)  x ref  x . The vector f is in a direction towards S0mathematically, this represented as [1],[15] :  x : Vector of slopes of the S.  lim S  0 et  lim S  0 r : Relative degree, equal to the number of times he (11) derives the output for the command to appear. s  0 s  0 B. Convergence condition. The Lyapunov function is a scalar function positive for the Hence, the condition of attractiveness to obtain the sliding state variables of the system, the control law is to decrease thismode: function, provided it makes the surface attractive and  S(x).S(x)  0 invariant. En defining the Lyapunov function by: (12) 1 2 V ( x)  S ( x) (16) The function is used, generally, to ensure stability of 2nonlinear systems. It is defined, like its derivative as follows:[2],[7],[15]:
  4. 4. International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012 For the Lyapunov function decreases, it is sufficient to ensurethat its derivative is negative. This is verified by the followingequation:   V ( x)  0  S ( x)S ( x)  0 (17)This can be expressed by the following equation :  lim S  0 et  lim S  0 (18) s  0 s  0C. The insurance of the conditions of convergence In sliding mode, the goal is to force the dynamics of thesystem to correspond with the sliding surface S(X) by means Fig. 4 field oriented control of PMSM with classical control (PI).of a command defined by the following equation: The variation of the reference speed is Wr = 100 (rad / s) to u(t )  ueq (t )  uN (19) Wr = -100 (rad /s) at t = 0.6 (s), followed by an external load torque disturbance is Td=8 (Nm) at a period [0.2s] between t = 0.2 (s) and t = 0.4 (s). In which: For the sliding mode control, we will replace the PIU: is called control magnitude; Ueq :is called the equivalent controllers with sliding mode controllers (SMC), Figure (5)components which is used when the system states are in the shows the results obtained with the strategy of three surfaces:sliding mode; Un: is called the switching control which drivesthe system states toward the sliding mode, the simplestequation is in the form of relay: un  ksgnS(x) ;k 0 (20)k: high can cause the ‘chattering ‘ phenomenon. When the switching surface is reached, (14) we can write: U  Ueq avec u N  0. (21) VI. SIMULATION RESULTS To validate the structure of the sliding mode control, we Fig. 5 Results of simulation by sliding-modemade simulations using MATLAB / Simulink. VII. ROBUSTNESS TESTING To highlight the importance of the technique of sliding mode control, we will test the robustness of our machine. Fig. 3 Schematic of the overall simulation MSAP is supplied with the voltage variable frequency andamplitude by an inverter PWM voltage, the driving circuit ispowered by a constant voltage source. Fig. 6 Results of simulation of the adjustment by sliding-mode during For the first order, we will implement PI type controller. variation parametric
  5. 5. International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012 VIII. INTERPRETATION Rs : Stator resistance Different simulations allow us to see that: Ld : Inductance of direct axis Disturbance rejections are good and a weak response time Lq : Inductance of quadratic axisfor traditional controller PI. This control strategy provided a φ f : Field fluxstable system with a practically null static error and adecoupling excel for the technique suggested by maintaining p : Number of pole pairsId to zero. The sliding mode control provided a more stable J : Inertia momentumsystem with satisfactory performance compared to traditional f : The damping coefficientcontrol as well as loadless system or during the load variation F : Frequencyand also as the disturbance rejection. The results of robustness MACHINE PARAMETERStesting shows that the SMC is well known to be insensitive to R 0.6Ω;Ld 1.4mH;Lq  2.8mH;φ f 0.12wb P  4; ;inner parameters variations and outer disturbance, so the J 1.1103kgm2; f 1.4103 Nm/rds 1;F  50HZ. controller works well with robustness in a large extent whichdoes not exist in the first control. So the better dynamic REFERENCESperformance of the controller can be ensured by SMC. [1] SOSSE ALAOUI Mohammed Chakib, "Control and sliding mode Table I sums up the comparison of both control strategies observer of a pumping system and a manipulator," Ph.D. Thesis,by characteristics following: University Sidi Mohamed Ben Abdellah, Fez, Morocco, 2009 [2] MASSOUM Ahmed, "Contribution to the Order Singularly Disturbed a control FOC SMC Permanent Magnet Synchronous Machine: Variable Structure Controlcharacteristics (VSC), Neuro-Fuzzy Control", Ph.D. thesis, University of Djilali Liabes, SBA, Algeria, 2007.Complexity Medium high [3] ATTOU Amine, "control by Sliding mode of a synchronous machine with a permanent magnet," memory master, University of Djilali Liabes, SBA,Dynamic response Good Very good Algeria, 2011.Disturbance Fast Very fast [4] Sid Ahmed El Mahdi ARDJOUN, Mohamed ABID, Abdel Ghanirejection AISSAOUI, Abedelatif NACERI, "A robust fuzzy sliding mode control applied to the double fed induction machine," INTERNATIONALrobustness No yes JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING, Issue 4, Volume 5, 2011.Waveform quality Harmonic content at More harmonic higher frequencies content at higher [5] M. Aguirre ; Calleja, C. ; Lopez-de-Heredia, A. ; Poza, J. ; Aranburu, frequencies A. ; Nieva, T. , "FOC and DTC comparison in PMSM for railway tractionControl Setting up Linear application,"Power Electronics and Applications IEEE, 2011. Non Linear controllers controllers [6] Harib, K.H.; Khousa, E.A., Ismail, A, " Field Oriented Motion Control of a 3- Phase Permanent Magnet Synchronous Motor,"IEEE; Electric Power Table I: Controls Comparison and Energy Conversion Systems (EPECS) 2011. VI. CONCLUSION [7] ADJOUDJ Mohamed, ABID Mohamed, AISSAOUI Abdelghani, In this paper two different control strategies have been RAMDANI Youcef, BOUNOUA Houria, "Sliding mode control of acompared by the presentation of the theoretical part and the double-fed asynchronous machines mounted in a wind," Journal "Naturepart simulation in order to determinate the main advantage and Technology", January 2010 .and drawbacks of each control . So in conclusion, the theory of sliding model control is [8] LAHOUEL Dalila, "nonlinear adaptive control of a synchronous machinewell known to be insensitive to inner parameter variations and with permanent magnets," memory magister, University of Batna,outer disturbance. So the controller works well with Algeria, 2009.robustness in a large extent, but this robustness is limited bysetting a disadvantage which is the existence of a discon- [9] Xiuli Yu,Shimin Wei and Lei Guo, " Cascade Sliding Mode Control fortinuous control law that produces the effect of "chattering". Bicycle Robot," IEEE CONFERENCE PUBLICATIONS , Volume: 1,Page(s): 62 – 66, Publication Year 2010. NOMENCLATURE
  6. 6. International Conference on Electromechanical Engineering (ICEE2012) Skikda, Algeria, 20-22 November 2012[10] Rui Guo; Xiuping Wang, Junyou Zhao; Wenbo Yu, " Fuzzy Sliding [13] Vittek, J., Bris, P., Stulrajter, M., Makys, P., Comnac, V., Cernat, M. " Mode Direct Torque Control for PMSM,"Fuzzy Systems and Knowledge Chattering Free Sliding Mode Control Law for the Drive employing Discovery (FSKD), 2011 Eighth International Conference,IEEE 2011 PMSM Position Control,"Optimization of Electrical and Electronic Equipment, 2008. OPTIM 2008. 11th International Conference ,IEEE[11] Zhou Hu; Yang Jianguo, ―A Robust Current-Loop Controller for 2008. PMSMs’ Field Oriented Control Scheme," Computer Modeling and Simulation, 2010. ICCMS 10. Second International Conference,IEEE [14] A.W. Leedy and R.M. Nelms, "Harmonic Analysis of a Three-Level 2010. Sinusoidal," ndustrial Electronics, 2006 IEEE International Symposium on, vol. 2, 2007.[12] Li Yuan, He Feng-you, Gu Shan-mao, " Study on Sliding Mode Speed Control with RBF Network Approach for PMSM Drives,"IEEE [15] B.BANDYOPADHYAY and S.JANARDHANAN, "Discrete-Time International Conference Control and Automation; 2009. Sliding Mode Control," Electronic Journal «Technical Acoustics»,2006.

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