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Comparative study between the rotor flux oriented control and non‐linear backstepping control of a five‐phase induction motor drive – an experimental validation

2016; Institution of Engineering and Technology; Volume: 9; Issue: 13 Linguagem: Inglês

10.1049/iet-pel.2015.0726

1755-4543

Hamdi Echeikh, Ramzi Trabelsi, Atif Iqbal, Nicola Bianchi, Mohamed Faouzi Mimouni,

Electric Motor Design and Analysis

IET Power ElectronicsVolume 9, Issue 13 p. 2510-2521 Research ArticlesFree Access Comparative study between the rotor flux oriented control and non-linear backstepping control of a five-phase induction motor drive – an experimental validation Hamdi Echeikh, Hamdi Echeikh National Engineering School, University of Monastir, Ibn Eljazzar City, 5019 Monastir, TunisiaSearch for more papers by this authorRamzi Trabelsi, Ramzi Trabelsi High Institute of Applied Sciences and Technology, University of Sousse, Ibn Khaldoun City, 4003 Sousse, TunisiaSearch for more papers by this authorAtif Iqbal, Corresponding Author Atif Iqbal atif.iqbal@qu.edu.qa Department of Electrical Engineering, Qatar University, Doha, 23874 QatarSearch for more papers by this authorNicola Bianchi, Nicola Bianchi Industrial Engineering Department University Degli Studi di Padova, Padova, ItalySearch for more papers by this authorMohamed Faouzi Mimouni, Mohamed Faouzi Mimouni Department of Electrical Engineer, National School of Engineers of Monastir, ENIM, Ibn El Jazzar, ENIM, Monastir, TunisiaSearch for more papers by this author Hamdi Echeikh, Hamdi Echeikh National Engineering School, University of Monastir, Ibn Eljazzar City, 5019 Monastir, TunisiaSearch for more papers by this authorRamzi Trabelsi, Ramzi Trabelsi High Institute of Applied Sciences and Technology, University of Sousse, Ibn Khaldoun City, 4003 Sousse, TunisiaSearch for more papers by this authorAtif Iqbal, Corresponding Author Atif Iqbal atif.iqbal@qu.edu.qa Department of Electrical Engineering, Qatar University, Doha, 23874 QatarSearch for more papers by this authorNicola Bianchi, Nicola Bianchi Industrial Engineering Department University Degli Studi di Padova, Padova, ItalySearch for more papers by this authorMohamed Faouzi Mimouni, Mohamed Faouzi Mimouni Department of Electrical Engineer, National School of Engineers of Monastir, ENIM, Ibn El Jazzar, ENIM, Monastir, TunisiaSearch for more papers by this author First published: 01 October 2016 https://doi.org/10.1049/iet-pel.2015.0726Citations: 11AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Multiphase variable speed electric drives are employed in applications where the reduction in the total power per phase and the highest level of overall system reliability is required. Most of the literature on five-phase induction motor (IM) drive deals with field oriented control, direct torque control, and other non-linear control such as backstepping method. This study deals with the theoretical concept and experimental implementation of indirect rotor flux oriented control (IRFOC) and backstepping control (BSC) of a five-phase IM drive. A comprehensive comparison is done between the most popular IRFOC and non-linear BSC. Backstepping control offers high performance in both steady state and transient operations even in the presence of parameters variations. However, this strategy (BSC) allows the synthesis of the speed and the flux control for a five-phase IM, nevertheless this strategy is asymptotically stable in the context of Lyapunov. The comparison is done using experimental approach. The two control approaches are compared in different terms such as their stability proprieties, achievable dynamic performances, online computational effort, the possibilities of controller design and the complexity of their implementation. Nomenclatures Rs stator resistance (in ohms) Ls stator inductance (in henry) Rr rotor resistance (in ohms) Lr rotor inductance (in henry) Lls stator leakage inductance (in henry) Llr rotor leakage inductance (in henry) M magnetizing inductance (in henry) TL, Te load torque, electromagnetic torque (in newton metres) p pole pair number V1, V2 candidate functions of Lyapunov ωr rotor angular (in radian per second) i, v current, voltage (in ampere) λr flux (in weber) Kpv, Kiv PI parameters k1, k2, k3, k4, k5, k6 backstepping controller parameters Superscript α1, β1 stator component in the frame α1 − β1 α2, β2 stator component in the frame α2 − β2 d, q stator component in the frame d − q x, y stator component in the frame x − y Subscript (c) reference value 1 Introduction Recently, multiphase motor drive has become a serious alternative over their three-phase counterparts in certain applications where high reliability is needed due to numerous advantages offered by multiphase motors [1, 2]. The basis of interest due to high number of freedoms in electrical quantities, greater redundancy for better control, better power distribution per phase and management under fault conditions [3-6]. The main potential application areas for multiphase motor drives are the hybrid electric vehicles, battery powered electric vehicles, ship propulsion and electric aircraft. These applications during the last couple of years have rapidly emerged. Finally, utilisation of multiphase motor drive in hybrid electric vehicles and electric vehicle applications enables reduction of the required semiconductor switch current rating [7]. In ordinary vehicles with combustion engines and integrated starter /alternator are considered the particular interesting application of multiphase motor. The idea of multiphase motor enables replacement of two electric drives motor with a single motor with an aim of numerous good features. Another important aspect of multiphase motor drives that can develop torque using not only the fundamental, but also using higher harmonics of the air gap [8]. Indeed, multiphase induction motor (IM) is increasingly discussed and still the subject of several research projects [9-22]. Those references treated the subject of multiphase motor and discussed, first the advantages and shortcoming of using these kind of motors, second present the general concept to modelling of multiphase motors and finally the ideas to control the multiphase motors, precisely five-phase IM. Many control techniques concerning multiphase motor have been proposed in the literature such as direct torque control (DTC). Zheng et al. [23] developed a novel direct torque control which based on new switching table and Lu and Corzine [24] presented a DTC by using a space vector modulation strategy with optimal switching sequence and harmonics elimination. Tatte and Aware [25] have shown a reduction in the torque ripple due to hysteresis comparator for the direct torque control of five-phase IM. Wang and Yang [26] introduced direct torque control technique with duty cycle optimisation and Khaldi et al. [27] develop a new DTC strategy based on power measurement for speed computation. Parsa and Toliyat [28] use the DTC control for five permanent magnet motor drives to achieve fast torque response and low ripple in the torque and flux stator. Based on adaptive input–output feedback linearisation Tabrizchi et al. [29] developed direct torque control of five-phase PMSM and Raj et al. [30] improves the performances of DTC due to lower switching frequency. To overcome those limits of DTC an interesting alternative to FOC has been required. The indirect rotor flux oriented control (IRFOC) proposed by Blaschke is considered one of the powerful methods for high performance control of motor drive and has been accepted by industries for three-phase IM drive. Many researches in the literature present the proposed method for five-phase IM drive such as Salehifar et al. [31] employed five-phase indirect rotor flux oriented control using SPWM technique by replacing the arbitrary modulation index with controlled one. Iqbal et al. [32] presents a novelty in the development of five-phase IM which used the rotor flux oriented control with active front end converter. Xu et al. [33] developed an application of rotor field oriented control with the combination of third harmonic currents with fundamental in order to achieve high performances and to generate rectangular air-gap. Jones et al. [34] developed and present an experimental validation of the indirect rotor flux oriented control of five-phase motor drive by using a synchronous control scheme for the principle of multiphase motor drive. The flux and torque producing currents are decoupled and controlled by independent manner, allowing rise dynamics of the motor. The proposed indirect flux oriented control is to distinguish between the control of a three-phase and the five-phase motor. Eventually, regardless of the phase number the torque production requires only two currents components. The voltage source inverter VSI is controlled using a space vector pulse-width modulation (SVPWM) [35, 36]. Nevertheless, this method offers a better insight into the proprieties of multiphase drives and inverters. The SVPWM can be developed by using different strategies, first two active vectors and second four active vectors [37]. The five-phase motor model is transformed into a decoupled equations system in two orthogonal reference frames. It can be seen that d − q axis reference frame currents are responsible for contribution towards flux and torque production, indeed the x − y components do not. This allows the RFOC principle of five-phase IM which based on maintains entirely zero, the q-axis component of rotor flux. In the other part the rotor flux linkage is maintained in the d-axis component. This principle allows reducing the electromagnetic torque equation with the similar form as dc motor. Thus the rotor flux and the electromagnetic torque can be controlled separately by controlling the stator d and q currents components. In addition, many modified nonlinear state feedback schemes have been proposed in the literature such as the multi-scalar model control (MMC), sliding mode control (SMC) and the backstepping control (BSC) [38-44]. Moreover, the backstepping control offers numerous advantages such as, achievement of high precision; ensure good stability of the system and good transient performance. The DTC control in case of five-phase IM drive with sinusoidally distributed winding uses only the largest vectors from the look-up table that causes very poor performance manifested in large stator current harmonics of low order. To overcome this limit use of non-linear backstepping control is suggested in a five-phase motor drive. BSC gives high performance, fast tracking, and acceptable torque ripple in addition to high dynamics and excellent stability proprieties. The BSC technique has high performance in both transient and steady state regimes. The basic idea of the backstepping control is to render the equivalent closed-loop system to stable subsystems with order equal one which are put in cascade by the Lyapunov theory, which gives them the qualities of strength and global asymptotic stability. In other words, it is a multi-step method, at each stage; a virtual command is generated to ensure the convergence of the system to its equilibrium state. This can be reached from Lyapunov functions that ensure the stability step by step of each synthesis step [45]. Backstepping control is also successfully applied to five-phase IM [46] and six-phase IM [47]. However, only simulation results were presented in [46]. The non-linear backstepping control is also recently applied to grid integrated inverter [48]. The backstepping control technique provides a systematic method to perform controller design for the multiphase machines which is a non-linear system. The objective of this technique is to calculate, in several stages, a command which guarantees the overall stability of system. Unlike most other methods, backstepping has no constraint of non-linearity, which highlight the advantages of using BSC over the others approaches notably for multiphase machines. This paper proposes the indirect rotor flux oriented control strategy and non-linear control Backstepping follow by experimental results and comparison study to show the effectiveness and satisfactory performance of the proposed method. The rest of this paper is organised as follows, Section 2 presents the model of five-phase IM, Section 3 developed the IRFOC strategy, Section 4 presents the BSC approach, Section 5 develops the experimental results and comparison between the two approaches, conclusion outline in Section 6. 2 Five-phase IM The symmetrical five-phase motor is considered one of the commonly used multiphase machines. In the literature, two different constructions can be found of five-phase motor, the first type uses sinusoidal air gap MMF, and this type requires only sinusoidal voltages where the low harmonics are unsuitable in the motor input voltages. The second type, the air-gap MMF can be generated by using low order harmonics with this one can be benefit to enhance the torque production particularly by the third harmonic injection. In this brief discussion on modelling of five-phase induction, several assumptions of general theory of electrical machine drives are considered such as, the special displacement between two consecutive phases 2π/5, the rotor windings have the same proprieties, the air gap is constant, sinusoidal distribution in the field and the magnetic circuit is linear. The voltage source inverter have 28 = 32 possible switching states which divide on two, 30 actives and two zero [18]. Each switching state can be characterised by the vector Where Si ∈ {0, 1}, when Si = 1 indicates that the upper power switch is off while the inverse is true when Si = 0. (1)Using Concordia transformation for five-phase system, the five-phase motor can be described into two orthogonal planes α1 − β1 and α2 − β2. Where v = 2π/5. (2)The harmonics of the order 10n ± 1 with integer map into α1 − β1 plane while in the plane α2 − β2 the harmonics of order 10n ± 3 are mapped (Table 1). Table 1. Harmonic mapping for space vectors in a five-phase VSI Plane Five-phase system α1 − β1 ) α2 − β2 ) zero sequence ) The rotational transformation used to simplify the motor model is given by (3), this transformation allows to transform the variables of the five-phase IM into rotating reference frame which give two planes d − q and x − y. (3)The five-phase model can be deducted by application of the two transformations, the rotational transformation which conserve invariant and the decoupling matrix by choosing the rotor flux and stator components as state variables, the five-phase IM model in the stationary reference frame can be expressed by the following equations (4) (5) (6) (7) (8) (9) (10) (11)Here, is and vs denotes the stator currents and voltages, λr and λs denotes the rotor and stator flux and ωr denotes the electrical speed for the five-phase IM. The electromagnetic torque of five-phase IM gives by (12)The mechanical equation of the five-phase motor presented as follows (13)where Te and TL are the electromagnetic and load torques, Ω is the mechanical speed and ωr = pΩ is the electric speed. 3 Indirect rotor flux oriented control of a five-phase IM 3.1 Rotor flux oriented control strategy The aim of the indirect rotor flux oriented control is to obtain the control of five-phase IM drive similar to dc motor with separate excitation where there is a natural decoupling between the flux and the electromagnetic torque. Taking into account the flux orientation according to the d-axis (14)The decoupled torque and the rotor flux can be controlled independently, by controlling the d and q components of stator current. The IRFOC is the most used because it eliminates the influence of stator and rotor leakage reactances and yield better results than the methods based on the orientation of the stator flux. By imposing the equation of the machine in reference related to the rotating frame using Laplace transformation one obtains (15) (16)ωs denotes the synchronous speed and ωsl denotes the slip speed. Two methods of vector control are available, direct and indirect methods. In this type of control the angle θs used for direct and inverse transformation is calculated using the following expression (17)Fig. 2 shows the block of control of a five-phase IM controlled by the rotor flux orientation. The main components of this type of control are the speed control loop, those currents isd, isq, isx and isy calculation block of θs and the direct and inverse transformations. The speed is regulated through a proportional-integral (PI) anti-windup controller, the output of the speed controller is the electromagnetic torque reference or the reference current , it is limited to take into account the characteristics of IGBT inverter and the motor over load. is compared to the measurable value through a PI controller to obtain the reference voltage . In parallel with this loop, there is a control loop of isd current, the reference current is calculated from the imposed flux. The and are maintained zero because both are not responsible for the creation of the torque. 3.2 Decoupling The vector control used in this part is the indirect rotor flux oriented control. Compared with the scheme introduced in the previous section and shown in Fig. 1, it is interesting to add in terms of decoupling in order to make the d and q axes completely independent. This decoupling allows especially to write the equations of the motor and the control in a simple manner and thus to calculate the coefficients of the controllers. Then one can represent the five-phase motor by the following block diagram. Fig. 1Open in figure viewerPowerPoint Decoupling system for five-phase IM Fig. 2Open in figure viewerPowerPoint Indirect rotor flux oriented control scheme of five-phase IM The terms ωsσLsisq and ωsσLsisd correspond to the terms of coupling between the d–q axis. One solution is to add equal voltages but of opposite sign to the output of the currents controllers in order to separate the control loops d-axis and q-axis. For each of the currents loop, a PI controller is adopted typically. Where the expressions presented in Fig. 2 are gives by the following equations (18) (19) (20) 3.3 Synthesis of PI controller 3.3.1 PI-Anti windup of speed controller The block diagram of the closed-loop of the speed control is shown in Fig. 3. Fig. 3Open in figure viewerPowerPoint Structure of anti-wind up speed controller The speed loop is realised by a PI anti-windup controller whose proportional coefficient and integral coefficient are, respectively, Kpv and Kiv. The selection of the parameters of the speed controller is done in order to obtain the desired performances for the closed-loop system by imposing the damping ratio and the natural frequency ω0. The transfer function of closed-loop is given by (21)The transfer function has a second-order dynamic (22)After identifying the denominator in its canonical form, the proportion coefficient and integral coefficient of the speed controller are obtained by solving the simultaneous equations (23)In order to obtain a response without overshoot, the damping coefficient is fixed at which correspond the following relation ξ = 1. The cut off frequency is fixed at f0 = ω0/2π = 1 kHz. Thus, the parameters of speed controller are given by (24)The control loops of currents are achieved in frames. The reference currents are constants which lead the use of PI controllers that make the control efficient and simple. The parameters of the PI current controllers are chosen according to two criterions: (i) the zero of current controller cancels the pole of the dominant time constant of the process and (ii) the time constant of feedback loop is chosen lower than that of the process. The transfer function of open loop along the d–q axis current is given by (25)τs = Ls/Rs is the stator constant time. Taking into account the first rule (26)Hence the simplified transfer function of feedback loop system is given by (27)where τ0 is the time constant of feedback loop of the d–q axis current loop (28)Thus, the parameters of the d–q axis current controllers are given by (29) 3.3.2 PI controller of (x − y) axis current loop One follows the same procedure for the determination of the PI controllers parameters for x − y current components and one obtains (30) 4 Non-linear backstepping control of a five-phase IM Assuming that d-axis control the rotor flux, the five-phase IM equations given by (15) turn to be (31)The different functions fd, fq, fx, fy, fg and fω are expressed as (32)The backstepping controller mechanism for the rotor speed regulation and the rotor flux generation can be better applied to replace the traditional PI controller considered in the conventional flux oriented control strategies. The control objective is to allow on one hand, the speed control according to the reference trajectory and on the other the rotor flux stay constant. Such a tracking can be achieved through a backstepping controller algorithm by finding a direct relation between these two variables and the stator voltages vsd and vsq. In what follows, a control based on the backstepping technique for a five-phase IM is reported to achieve control with sensor. The synthesis of this control can be achieved in two successive steps. 4.1 Step 1: computation of the reference stator currents In the first step, it is necessary that the system follows the given trajectory for each output variable. To do so, a function is defined; where ωc and λc are the rotor speed and the rotor flux references, respectively. The rotor speed and the rotor flux tracking errors (e1 and e2) are defined by (33)The derivate of (33) gives (34)Accounting for (31), one can rewrite (34) as follows (35)The first Lyapunov function V1 associated with the rotor flux and speed errors is formulated as (36)Using (35), the derivate of (36) is written as follows (37)This can be rewritten as follows (38)where k1 and k2 should be positive parameters, in order to guarantee a stable tracking, which gives (39)The stator currents references then deduced as follows (40)where μ = p2M/L r J. 4.2 Step 2: computation of the reference stator voltages In this step, an approach to achieve the current references generated by the first step is proposed. Let us recall the current errors, such as (41)Accounting for (40), (41) turns to be (42)With this definition, (35) can be expressed as (43)The time derivate of (41) yields (44)Following the substitutes of (31) into (44), one can obtain (45)One can notice that (45) include the system inputs: the stator voltage. These could be found out through the definition of a new Lyapunov function based on the errors of the speed, of the rotor flux and of the stator currents, such that (46)The derivate of (46) is given by (47)By setting (45) into (47), one can obtains (48)The derivate of the complete Lyapunov function (48) could be negative definite, if the quantities between parentheses would be chosen equal to zero (49)The stator voltages then deduced as follows (50)where k3, k4, k5 and k6 are positive parameters selected to guarantee a faster dynamic of the stator current, rotor flux and rotor speed, the equation can be expressed as (51)To show boundedness all states, the dynamic (43) and (51) can be rearranged as (52)where H can be shown to be Hurwitz as a result of the matrix operation, this proves the boundedness of all the states. Indeed the real parts of eigenvalues of the matrix H are negative. A block schematic of backstepping control applied to a five-phase IM is presented in Fig. 4. Fig. 4Open in figure viewerPowerPoint Block diagram of non-linear backstepping control of a five-phase IM drive 5 Experimental validation 5.1 Test bench description The subsystem ‘Control-Command’ is composed of two parts, a part called Hardware and the other part called Software. The ‘Hardware’ part is built around a development board DS1104 R & D Controller Board, provided with its control panel (control panel CP1104). This card includes two main digital processing units (master) and secondary (slave). The first is formed by a master processor DSP floating point type ‘Power PC 603e’ of Motorola (master PPC) operating at a frequency of 250 MHz, which allows the control of analogue-to-digital converters (ADCs) and digital-to-analogue converter (DAC), the logic inputs outputs, interface incremental encoder and serial interfaces and timers. The second is composed of a DSP of fixed-point slave brand TEXAS INSTRUMENT and type TMS320F240 (20 MHz) which can generate either type of signals modulating natural or vector pulse width symmetric mode for a frequency of 1.25 Hz up to 5 MHz. The ‘Software’ part revolves essentially around two software Matlab/Simulink and Control Desk. The command developed is based on Matlab/Simulink Version 7.4. This allows easy programming of real-time application by using blocks that belong to the ‘toolbox Real Time Interface (RTI)’, which allows to configure input-output of the DS1104 card. Once validated, the algorithms are automatically compiled and downloaded into the card using dSPACE Control Desk Manager software. This second software is a graphical interface that allows, from Simulink blocks to dSPACE, control signals to control and visualise in real time the available signals in Simulink environment (control signals, images sensors output signals). The real-time implementation of any control strategy on a platform instrumented experimental dSPACE is as shown in Fig. 5. In fact, the first time one has to develop the program in the Matlab/Simulink environment. Then, once validated by simulation, this algorithm will be automatically compiled and downloaded into the card using dSPACE Control Desk Manager software. The latter was reprogrammed by software and synchronised way with its master DSP, the PowerPC floating point running the machine control program. Fig. 5Open in figure viewerPowerPoint Block diagram of the experimental platform This external synchronisation to the DS1104 card, allows, using a separate timer in the dedicated PWM, a hardware interrupt triggered by the DSP power PC. It triggers the conversion of the analogue/digital A/D. Reading the converters takes place independent of the process, during a separate interrupt to the master processor. 5.2 Experiment results The experimental results were obtained for a five-phase IM fed by a five SVPWM voltages source inverter (Vdc–voltage = 120 V) with speed equal of rated value 1000 rpm using indirect rotor flux oriented control and backstepping control. The resulting waveforms for BSC and IRFOC are shown in Figs. 6-8, side by side, speeds, torque, flux and current are recorded and presented. The experimental results obtained when the motor is driven at 1000 rpm, the tracking responses of the command rotor speed the desired rotor speed ωr, and the electromagnetic torque are presented. One start first by IRFOC which the controller designs based on PI, furthermore this method has two parameters control for each PI (speed and currents). However, in addition the BSC contains a non-linear calculation of the references based on system model. Fig. 6Open in figure viewerPowerPoint Speed and torque using IRFOC (left side) and BSC (right side) Fig. 7Open in figure viewerPowerPoint Fig. 7 (continued)Open in figure viewerPowerPoint Fig. 8Open in figure viewerPowerPoint Stator currents and using IRFOC (left side), BSC (right side) and BS speed reversal 5.3 Comparative study between IRFOC and BSC This section gives a brief comparison of the controller methods presented in this paper, this comparison depends on different criteria such as dynamic, stability proprieties, possibilities of controller design and finally the complexity of implementation and tuning. Those criteria's will be studied separately in the following paragraph. Possibilities of controller design: The IRFOC method based on PI controller, which characterised by two parameters (Kp and Ki). The determination of those parameters in closed-loop is done using pole placement technique, the achievable dynamics are restricted. In other side the BCS controller based on system model, thus an improvement of the dynamic can be achieved, moreover, the parameters of the controller in closed-loop are determinate using Hurwitz. Nevertheless, the real parts of eigenvalues of the matrix H gives previously are negative. Complexity of implementation and tuning: Due to the fact that the PI controller consists only of two control parameters contrary to the BSC method, which made the IRFOC easier to implement and to design. Thus complexity of implementation and tuning of the BSC is much higher. Stability proprieties: The stability analysis of these two methods is done by using pole compensation for IRFOC method and Lyapunov stability for BSC. It can be seen that both methods ha