Simulation Based Analysis of Two Different Control Strategies for PMSM

Transcription

1 International Jornal of Engineering Trends and Technology (IJETT) - Volme4Isse4- April 23 Simlation Based Analysis of Two Different Control Strategies for PMSM Lindita Dhamo #, Aida Spahi #2 # Department of Electro technic, #2 Department of Atomation, Polytechnic University of Tirana Mother Teresa Sqare,Nr.4, Albania Abstract In low power application generally permanent magnet synchronos motor (PMSM) are sed. Becase of their high performance/cost ratio, the attention toward PMSM in variable speed application, is greater. Control of torqe, rotation speed and position for for qadrants and low speed operation, with high-performance dynamic behavior, are often reqired in indstrial applications bt they are sensitive from the standpoint of the control strategies reliability. Vector control based on fieldoriented control (FOC) is one of the methods most investigated and discssed by many researcher and now it is an indstry standard. Traditional control methods based on FOC se position sensors reslt to be very expensive in electrical drive with low power. The aim of this paper is to show that sensorless control strategy based on MRAS approach can be applied sccessflly in PMSM drives with low cost. The reslts are obtained from comparison of two algorithms of vector control of PMSM: traditional FOC sing position sensor and model reference adaptive system (MRAS) approach based on sensorless vector control.based on reslts obtained, advantages and disadvantages of the proposed control strctres will be discssed. Keywords Vector Control, Field Oriented Control, Model Reference Adaptive System, PMSM. I. INTRODUCTION The variable speed drive with PMSM reqires optimal motor speed and position determination by sing a shaft position sensor to sccessflly perform the PM motor field oriented control (FOC). The aim is not to se this mechanical sensor to measre the position directly, bt employ some indirect techniqes to estimate the rotor position. There are many problems at sensorless control of AC motor particlarly at the low speed range becase at this domain there are slggish changes of signals and offsets, and inaccracies of sensors are more evidently. The main advantages of sensorless vector control are: the cost saving, smaller dimensions and weight, more reliability and noise immnity. Frther more, the compting power of digital signal controller (DSC) allows application with complicated math models and their processing in real-time. Vector control can be implemented in different configrations, and crrently is one of the most matre technologies sed in different indstrial technology. The vector control s impact of alternating crrent drives, in traditional and new technologies, motivates to work in this direction. This paper will be focs on vector control of permanent magnet synchronos motors with the principle of the field orientation control, which is realized throgh two different techniqes: with position sensor throgh FOC and withot position sensor throgh MRAS approach. The reslts obtained in the MATLAB/Simlink will refer to performance of vector control for for qadrants and low speed operation of PMSM electrical drive. II. FIELD ORIENTED CONTROL Vector control of AC machines, based on the field oriented control (FOC) principle, where the motion control loop (position, speed or torqe loop) and the magnetizing control loop (flx loop) are decopled by sing the flx phasor (vector) as reference system and splitting the crrent phasor into an active and a reactive component. This control strategy is the most compter time and effort demanding (revealed also in the costs of the system) bt ensre the best dynamic performances and energy efficiency in variable speed control []. The principle of the field oriented control (FOC) is based on an analogy to the separately excited dc motor. In this motor flx and torqe can be controlled independently. The control algorithm can be implemented sing simple reglators, e.g. PI-reglators. In PMSM independent control of flx and torqe is possible in the case of coordinate system is connected with rotor flx vector. Vector control, known as decopling or field oriented control, aim to get high dynamic performance control of flx and torqe by its ability to independently control them. The flx is controlled by the field crrent alone and is termed flx-prodcing crrent. Keeping the field crrent constant at any time instant (hence the flx constant), the torqe is controlled independently by the armatre crrent alone, that is termed torqe prodcing crrent. Controlling the field and armatre crrent magnitdes as they are DC variables, the flx and electromagnetic torqe are controlled precisely as in a separately excited DC motor drive, which has an excellent dynamic control of flx and torqe. To solve this problem, we mst find an eqivalent flx prodcing crrent and torqe prodcing crrent. The key to that, for AC drives, came in two ISSN: Page 96

2 International Jornal of Engineering Trends and Technology (IJETT) - Volme4Isse4- April 23 forms: () the machine modelling in space phasor form, which redce a three phase machine into a machine with one winding each on stator and rotor, that making it into an eqivalent DC machine, and (2) the ability of the inverter to prodce a crrent phasor with absolte control of its magnitde, freqency and phase [2]. In this paper we will apply both forms. The reslts taken from the first form are considered as theoretical and reslts of second form will be applied in a sensor less scheme based on MRAS approach. The fll scheme for sensor vector control PMSM with FOC is as in Fig. : Fig. Block diagram of the PMSM with Field Oriented Control (FOC) AC machines develop maximal torqe when the armatre crrent is perpendiclar to the flx linkage or the load angle is 9. If we flfil this condition all the time, that is, if we make a correct orientation of the field, the reslt is a considerably redction of torqe ripple and a better dynamic response, bt the rotor position is reqired. III. MODELLING OF PMSM IN (D,Q) REFERENCE FRAME A clear and comprehensive description of the synchronos machines dynamic behavior is a fndamental reqirement for their application in speed or torqe controlled drive systems. The set of motor differential eqations (Eqations,2,3) are well known. The stator voltage eqations can be expressed as follows: a b c R s i i i a b c d a b c () cos( r ) a Laa Lab Lac ia 2 where : b Lba Lbb Lbc ib PM cos( r ) 3 c Lca Lcb Lcc ic 4 cos( ) r 3 (2) Becase of the constrctive symmetry of PMSM, all phase resistances, phase and mtal indctances, and flx-linkages can be thoght as eqal or as a fnction of the rotor electrical position with a 2 displacement. The relation between mechanical and electrical qantities are described by the motion eqation as follows: d Jm r Mem sign( r ) M Where: J is total moment of inertia. m L B m M r f (3) B is the friction coefficient. m M is a Colomb friction torqe. f M is the mechanical load. L r is the rotor anglar velocity. Vector transformations makes possible to transform the three phase variable machine description to another reference frame. The choice of the reference frame can considerably simplify the complexity of the mathematical model of the PM synchronos motor. The dynamic eqations are nonlinear as some of the terms are the prodcts of two crrent variables or a crrent variable and rotor speed. For a controller design with linear control system techniqes, the nonlinear dynamic eqations cannot be directly sed. They have to be linearized arond an operating point sing pertrbation techniqes. The ideal model for pertrbation to get the linearized model is that one with steady state operating state variables as DC vales. This is possible only with the rotor reference frame model of PMSM. Frthermore, from them we can get important and sefl information for vector control algorithm that we have setp. In this paper, is sed vector transformation of math model of PMSM in the time domain to rotor reference frame or (d, q) plane, by Park-Clarke (PC) transformation, 2 2 cos cos( ) cos( ) 3 3 d a q PC sin sin( ) sin( ) b c and the above eqations, assming that the transformation dd di d d Rs id r q Rs id Ld r Lqiq (4) dq diq q Rs iq r d Rs iq Lq r Ld id r PM argment is eqal to the electrical rotor position r, are presented as (4). Where: d, q are stator voltages in rotor reference frame (d, q), i d, i q are stator crrents in rotor reference frame (d, q), R s, is stator resistance, L d, L q are stator indctances in rotor reference frame (d, q), Ψ PM is rotor flx, ω r is rotor speed[rad/s]. Electromagnetic torqe of PMSM with symmetrical winding, is: 3 M em p iq ( PM ( Lq Ld ) id ) () 2 Althogh a qadratre axis PMSM model in a stationary reference frame (α, β) is already simple, when compared to the fll three phase model, it still contains a position variant indctance matrix. Both crrents and voltages are also AC vales that make it difficlt for a control strctre. Therefore it is chosen the vector transformations in rotary reference frame (d, q). ISSN: Page 97

3 International Jornal of Engineering Trends and Technology (IJETT) - Volme4Isse4- April 23 Based on Eqation (4) and (), is bilt p the PMSM model in d, q reference frame in MATLAB/Simlink environment, as in Fig.2 : Fig. 2 Block diagram of the PMSM model in d, q reference frame The algorithm is exected in two control loops. The fast inner control loop is exected with a hndred µs period range. The slow oter control loop is exected with a period of ms range. The essential feedback signals are three-phase stator crrent and rotor speed. The inner control loop by the three phase stator crrent (abc-plane) is controlled with hysteresis controller and the oter control loop by the rotor speed is controlled with nonlinear PI controller with satration action. Nonlinear actions like hysteresis and satration are applied to compensate the strong nonlinearity of PMSM model. The command law and torqe load is bild p to realise the first scenario :torqe, speed, position control at for qadrant operation in.4s and, the second scenario is the control torqe, speed, position for low speed operation. The reference crrent i* q is obtained from PI+ sat action on absolte error of speed, while the reference crrent i* d is kept. The reference crrent i* d and i* q, together with information taken from motor block abot shaft position, at Clarke-Park block otpt, generate the reference three phase crrent i* abc. These last, smming with actal crrent measrement by crrent sensors, generate the absolte error of stator crrents in (abc) frame, and from the hysteresis controller we get the appropriate vales of stator crrent. Becase of the PMSM model is made in (d,q) frame, we have make another vector transformation Park-Clarke, and these signals are inpts for the motor. All vector transformations are made to get information for rotor position, information that we have taken from the mechanic block at the otpt of motor where is calclated the rotor speed and position. Simlations are made for a Srface Monted PMSM with these parameters: TABLE I PMSM PARAMETERS Parameters Symbol Vales Nominal Power P n W Nominal Speed ω n rpm Stator Resistance R s 2.87 Ω Indctance in d-axis L d 8 mh Indctance in q-axis L q 8 mh Magnetic Flx linkage Y PM.7 Wb Pole Nmber p 4 Inertia J. kgm² Friction coefficient B.38 Nms IV. SENSORLESS VECTOR CONTROL OF PMSM BASED ON MRAS APPROACH Qalitative position sensor is a necessary component of the drive systems with PMSM sed in indstrial applications bt the high cost and strict reqirements limit their application widely. So that it is wanted to develop the position sensorless control technology of PMSM. Eliminating the se of mechanical position sensor, can increase the reliability of the drive system. Reviewing the reslts obtained from many researchers working in this field, is clear that some techniqes are sensitive by parameters vibrations, so it is difficlt to garantee the immnity and stability of the drive system. Techniqes like High Freqency Injection are sed to detect the speed of the motor and the initial position when the freqency is low, depends on no parameter, so it s more robst. Bt this way can be sed only to motors with obviosly saliency like interior PM motor. Neral network and non-linear self-adaptive observers have sed the Extended Kalman Filter (EKF), those schemes have high precision, bt it is complicated in arithmetic which make the reglations and parameter designs more difficlt, even reqest higher perform in hardware. In this paper, model reference adaptive system (MRAS) approach has been applied to the system in order to eliminate the se of speed sensor. It se two machine models of different strctres that estimate the same state variable (rotor speed) of different set of inpt variables. The estimator, that does not inclde the qantity to be estimated, is chosen as the reference model, and the other estimator may be regarded as the adjstable model. The error between the estimated qantities obtained by the two models is proportional to the anglar displacement between the two estimated flx vectors. A PI adaptive mechanism is sed to give the estimated speed. As the error signal gets minimized by the PI, the tning signal approaches the actal speed ω of the motor. Based on MRAS principle, different researchers propose different soltions. For example, Andreesc. G.D [3] has sed voltage and crrent model to calclate stator flx, and the error between the two reslts is sed to estimate rotors speed. Thogh it is simple for application, the estimated reslt depends greatly on motor parameter accracy. In order to overcome this problem, Piippo A, in [6] and [7] have sed a combined method. The idea comes from injection method. In the proposed method a calibration signal ε, ISSN: Page 98

4 International Jornal of Engineering Trends and Technology (IJETT) - Volme4Isse4- April 23 containing estimated angle error, is sed for the calclation of stator flx sing the voltage model. The athors have proved that the proposed combination of the two methods reslts in an observer having good steady-state accracy and excellent dynamic properties over a wide speed range. Other researchers are based on model reference adaptive system that comptes instantaneos reactive power (Q ref ) and the adjstable model comptes steady-state reactive power (Q est ), Kmar P. Sai at [4]. This paper present a MRAS method based on the information taken from measrement of stator crrents. An adaptive mechanism is established sing PMSM motor itself as a reference model, as shown in (Fig.). Lipeng Wang at al in [], have sed the sliding mode variable strctre strategy instead of the conventional constant gain PI controller as the adaptive mechanism to fit with the speed estimation problem. The athors have applied a new speed-estimation adaptation law for the sliding mode scheme based on Lyapnov theory to ensre stability and fast error dynamics.the speed estimation is given by eqation (6): t ˆ k ˆ ˆ r ( ˆ ) ˆ ˆ r ( ˆ i i d i q i q i d i q i q d k p i d i q i q i d i q i q ) Ld Ld (6) Where: k p and k i, are the proportional and integral constants respectively. The simlation reslts of Lipeng Wang s paper are satisfactory for operation in first qadrant. This paper try to prove that with MRAS speed estimator, the sensorless control of PMSM will be good enogh even in For Qadrant Operation and low speed operation, withot need to retne the PI controller gains. The tracking performance of the speed estimation and the sensitivity to noise are depending on proportional and integral coefficient gains. The integral gain k i is chosen to be high for fast tracking of speed. While, a low proportional k p gain is needed to attenate high freqency signals denoted as noises, Swankawin S [8]. This method is easy for indstrial application. Based on vector control theory of PMSM and eqation (6) estimation, it is bilt p a scheme in MATLAB/Simlink software, based on model reference adaptive system. The stability of the system is garanteed by the Popov sper stability theory. It is somewhat robst to parameter inaccracy. V. SPEED ESTIMATION SCHEME BASED ON MRAS Figre.3 shows the speed estimation scheme based on model reference adaptive system from stator crrents. It ses the otpts of both models: reference model that have independent inpts from rotor s speed and the adaptive model that have dependent inpts from rotor s speed in order to generate an error signal. Fig3. Speed Estimation Scheme for Model Reference Adaptive System The adaptation mechanism ses a PI controller to garantee the convergence of the system. For the same motor and for the same scenarios (for qadrant and low speed operation) is bild p a sensor less scheme for torqe, speed and position vector control of PMSM with FOC method. In this case, the model reference adaptive system scheme is adopted to estimate the speed and position of the motor, acting as the feedback sensor like the speed and position shaft sensor. The inpt signals of speed and position estimator are the stator crrents and voltages in (d,q) reference frame, while the otpts are the rotor speed and position estimated. Overall scheme for vector control of PMSM based on Model Reference Adaptive System Approach, is as in Fig.4: * ˆ ˆ Fig. 4. Sensorless block diagram of PMSM with MRAS In traditional vector control with FOC, the reference crrent by direct d-axis is zero, i.e., i* d = and the control of three phase inverter is realized by Space vector PWM(SVPWM). The essential feedback signals are three-phase stator crrents and stator voltages. For proper operation, the presented control strctre reqires a speed feedback on the motor shaft. In the case of the presented algorithm, a sensorless algorithm is sed. The fast control loop exectes two independent crrent control loops. They are the direct and qadratre-axis crrent (i d, i q ) PI controllers. Becase of the direct-axis crrent (i d ) control the rotor magnetizing flx which is constant, i d *=. By keeping d-axis crrent to zero vale, the demagnetization is also avoided. The qadratre-axis crrent (i q ) corresponds to the motor torqe. The crrent PI controllers otpts are smmed with the corresponding d and q axis components of the decopling stator voltage. Ths, the desired space vector for the stator voltage is obtained and then applied to the motor. The fast control loop exectes all the necessary tasks to be ISSN: Page 99

5 Time [s] International Jornal of Engineering Trends and Technology (IJETT) - Volme4Isse4- April 23 able to achieve an independent control of the stator crrent components: three-phase crrent reconstrction, Clark-Park transformations, DC-bs voltage ripple elimination, Space Vector PWM (SVPWM). VI. SIMULATION RESULTS Different simlation tests have been designed and exected to obtain comparative reslts of both systems. Both schemes of Vector Control of PMSM, based on and Sensorless FOC with MRAS, are simlated in MATLAB/Simlink for two different working condition: for qadrant operation and Low speed operation, and the reslts are shown respectively in figre and 6. A. For Qadrant Operation Rotor speed[r/min] Sensorless -actal speed (estimated) Reference Speed Time[s] Absolte Speed Error[r/min] Time[s] Fig. Comparison of behaviors, torqe, position and absolte speed error of PMSM dring For Qadrant Operation in sensor FOC and sensorless control with MRAS. B. Low Speed Operation Electromagnetic Torqe[Nm ] Reference Torqe Reference Torqe C Time[s] Electromagnetic Torqe[Nm] Rotor Speed [r/min] Sensorless-actal speed Sensorless -estimated with MRAS Reference Speed Time[S] Time [s] Rotor Position[rad] Sensorless actal speed Time[S] ISSN: Page 6

6 International Jornal of Engineering Trends and Technology (IJETT) - Volme4Isse4- April 23 Absolte Speed Error[r/min] Rotor Position[rad] Sensorless actal estimated speed with MRAS Time [s] Time [S] Fig. 6 Comparison of behaviors for Speed, Torqe, Position and Absolte Speed Error of PMSM dring low speed operation in sensor FOC and sensorless control with MRAS. The aim of this paper is to compare the performances of sensor FOC and sensorless FOC based on MRAS when applied to PMSM drives and point ot the strengthness and weaknesses that can help to make a choice between them for a particlar application. Analysing both methods, we consider that it is very important to establish the conditions to have a fair comparison between them. In order to carry ot a comparative analysis of two different schemes of FOC, it was stdied the performance of both methods dring transients and steady-state operation. Regarding transients the main characteristic to be analysed is the time response to a torqe and speed step. This test is performed at different vales of load torqes and speeds. For the steady state performance, two different characteristics can be analysed regarding flx and torqe responses: the absolte error and the oscillation or ripple in the torqe and stator flx. FOUR QUADRANT OPERATION for Torqe Steady-state response for torqe TABLE II SUMMARY OF THE COMPARISON FOC-MRAS Sensor FOC. Qick.2s Qick.2s Low ripple 6% Sensorless FOC-MRAS.4s.2s High ripple 2% Steady-state response No ripple Low ripple.2% Absolte speed error.2%.2% Control tning Hysteresis band PI Gains LOW SPEED Sensor FOC Sensorless FOC-MRAS OPERATION for Torqe Qick.2s.7s Qick.2s.4s Steady-state response for torqe Higher ripple % Low ripple 2% Steady-state response No ripple No ripple Absolte speed error.2%.2% Control tning Hysteresis band PI Gains From the comparison is clearly seen that both methods for vector control of PMSM have satisfactory performances and are available for indstrial applications, bt scheme with position sensor is better. The choice will be made based on economic and technologic reqirements. For vector control scheme with position sensors, the PI controller coefficients are chosen: k p =, K i =. For sensor less vector control scheme, the PI controller coefficients of adaptation mechanism of MRAS speed estimator, are chosen: k p =2, K i =. These coefficients are available for both schenarios, for qadrant and low speed operation. VII. CONCLUSIONS In this paper, it is proposed a sensorless scheme based on MRAS for control of PMSM drive system. The reslts obtained are compared with a vector control scheme based on indirect FOC method that se the position sensor. Under different operation conditions, simlation reslts have proved that the proposed sensorless method has a good performance for the torqe, speed and position control of PMSM. The MRAS for estimating rotor position angle and speed is based on a stator crrent estimator, de to the fact that only stator crrents are directly measrable in a PMSM drive. The proposed method is simple, needs a low comptation capacity and has a high speed adaptation even at very low speeds. This method is more stable and robst becase the prodced error in the speed adaptation (by PI action) is eliminated. The obtained simlation reslts, as discssed in above paragraph, are satisfactory in terms of estimation errors, robstness and global stability of the electrical drive system for different operating conditions. Reslts obtained show that sensorless control strategy based on MRAS approach can be applied sccessflly in PMSM drives with low cost. ISSN: Page 6

7 International Jornal of Engineering Trends and Technology (IJETT) - Volme4Isse4- April 23 REFERENCES [] Biro M.T Ilian Robst control of sensorless AC Drives based on Adaptive Identification, Recent Advances in Robst Control-Theory and Aplications in Robotics and Electromechanics, Edited by Andreas Meller,ISBN [2] Krishnan R. Permanent Magnet Synchronos and Brshless DC Motor Drives, CRC Press, ISBN: [3] Andreesc.G.D Position and speed sensorless control of PMSM drives based on adaptive observer, EPE Proc [4] Kmar P.Sai, J.S.V. Siva Kmar Model Reference Adaptive Controlled Application to the Vector Controlled Permanent Magnet Synchronos Motor Drive -International Jornal Of Power System Operation and Energy Management (IJPSOEM),Volme-,Isse-, 2. [] Lipeng Wang, Hagang Zhang, Zhaobing Li,Limin Ho, Xichong Li, Research on the Sensorless Control pf SPMSM Based on AaRedced-Order Variable Strctre MRAS Observer ICIC Express Letters,Volme 4, Nmber, October 2, ISSN 88-83X [6] Piippo A, Lomi J. Adaptive Observer Combined With HF Signal Injection for Sensorless Control of PMSM Drives, IEEE International Conference on Electric Machines and Drives,-8 May 2, [7] Piippo A, Hinkkanen M, Lomi J. Analysis of an Adaptive Observer for Sensorless Control of PMSM Drives, 32ndAnnal Conference of Indstrial Electronics Society, IECON2. 6- Nov. 2, [8] Swankawin S., and Sangwongwanich S., Design strategy of an adaptive fll-order observer sensorless indction motor drives- tracking performance and stabilization IEEE Trans. on powerelectron.3 () (26) ISSN: Page 62