A Novel Position Control of PMSM Based on Active Disturbance Rejection

Transcription

1 A Novel Position Control of PMSM Base on Active Disturbance Rejection XING-HUA YANG, XI-JUN YANG, JIAN-GUO JIANG Dept of Electrical Engineering, Shanghai Jiao Tong University, 4, Shanghai, CHINA Abstract: - Consiering the unavoiable an unmeasure isturbances, parameter variations an position measure error of real motion control applications, a novel controller is evelope for the motion control of permanent-magnet synchronous motors (PMSM) First, an active isturbance rejection controller (ADRC) base on extene state observer (ESO) is employe to ensure the high performance of the entire control system The ESO estimate both the states an the isturbances so that the ADRC has a corresponing part to compensate for the isturbances An then, the inertia of system is ientifie online to improve the performance At last, consiering the case of position measure error, which is commonly in the applications that an encoer is use for position etection, an asynchronous sampling metho (ASM) is use The ASM etects the position at the moment of actual encoer pulse input, thus eliminating encoer positioning error Simulation an Experimental results are shown to verify the metho Key-Wors: - Permanent-magnet synchronous motors, Active isturbance rejection controller, Extene state observer, Asynchronous sampling metho, Inertia ientification Introuction Motion control applications can be foun in almost every sector of inustry, from factory automation an robotics to high-tech computer har-isk rives Permanent magnet synchronous motors (PMSM), which possess the characteristics of high power ensity, torque/inertia, efficiency, an inherent maintenance-free capability, have been recognize as one of the key components in motion control applications Conventionally, PID control is alreay wiely applie in the PMSM system ue to its relative simple implementation Over the years, many researchers have evelope various tuning methos for the ease of application[-5] However, the PMSM system is a nonlinear system with unavoiable an unmeasure isturbances, as well as parameter variations This makes it very ifficult for PID control algorithm to obtain a sufficiently high performance for this kin of nonlinear systems in the entire operating range Recently, with the rapi progress in microprocessors an moern control theories, many researchers have contribute their efforts towar nonlinear control algorithms, an various algorithms have been propose, eg, aaptive control[6, 7], robust control[8-], sliing moe control[, ], input-output linearization control[], back-stepping control[4, 5], an intelligent control[6, 7] These algorithms have improve the control performance of PMSM from ifferent aspects However, in real inustrial applications, PMSM systems are always confronte with ifferent isturbances, eg, friction force, unmoele ynamics an loa isturbances Conventional feeback-base control methos usually cannot react irectly an fast to reject these isturbances, although these control methos can finally suppress them through feeback regulation in a relatively slow way Since it is usually impossible to measure the isturbances irectly, one efficient way of improving system performance in such cases is to evelop an observer to estimate the isturbances The isturbances observers offer several attractive features In the absence of large moel errors, they allow inepenent tuning of isturbances rejection characteristics an comman-following characteristics[8-] Further, compare to integral action, isturbances observers allow more flexibility via the selection of the orer, relative egree, an banwith of low-pass filtering Another kin of isturbance rejection techniques is active isturbance rejection control (ADRC), which is propose by Jinqing Han[] The ADRC is esigne without an explicit mathematical moel of the plant Hence the controller is inherently robust against plant variations Generally the ADRC ISSN: Issue, Volume 9, November

2 ɵ θ[ n ] ɵ θ[ n] ɵ θ [ n+ ] ɵ θ [ n+ ] θ[ m ] θ[ m] θ [ m+ ] + angle Fig Block iagram mechanical moel of PMSM motion control system Fig Timing iagram of angular position measurement consists of three parts: Tracking Differential (TD), Extene State Observer (ESO) an Nonlinear State Error Feeback control law (NLSEF) The ESO regars the total isturbances of the system, which consists of internal ynamics an external isturbances, as a new state of the system This observer is one orer more than the usual state observer It can estimate both the states an the total isturbances Base on the ESO, a fee forwar compensation for the isturbances can be employe in the control esign Then ADRC compensates the system parameter isturbance of the moel, suppresses the isturbance outsie the system at the same time However, accuracy measurement of angular position is vital for the implementation of ESO In the real motion control applications, incremental encoers are popular for etecting angular position Since the angular position is only available at the moment of encoer pulse input, there are positioning error an etection elay between the actual angular position an that etecte by the ESO (as shown in Fig) When the system operates in the low spee range, the positioning error an etection elay will eteriorate the performance of the ESO as well as the entire control system In orer to suppress the effect of isturbances, parameter variations an measurement error of angular position on motion control system, a novel controller is evelope in this paper First, a linear ADRC base on ESO is employe to ensure the high performance of the entire control system Then, for the purpose of obtaining angular position precisely in the situation of low spee, an asynchronous sampling metho (ASM) is employe Mathematical moel of PMSM system is given in Section The principle of ESO-base linear ADRC is escribe in Section The etail implementation of ESO with asynchronous angular position sampling is iscusse in Section 4 Moel of PMSM System The block iagram mechanical moel of PMSM motion control system is shown in Fig The motion equation in the motor sie can be written as below, θm = ωm t () ω m Jn = Tm TL t () T = f ω, J () ( ) L m L θ m -the mechanical angular position ω m - the mechanical angular velocity J n -the total inertial moment of system, incluing the moment of PMSM J m an that of loa J L T M -the evelope torque T L -the isturbance torque Normally, the isturbance torque T L varies with the change of loa an working conitions It is unavoiable an immeasurable PMSM is a complex nonlinear system with multivariables an strong coupling In orer to reuce the analysis, the saturation an amping effects are neglecte A schematic of the PMSM motion control system base on vector control is shown in Fig As shown in Fig, two PI algorithms are use in the two current loops, respectively Uner the fiel-oriente vector control scheme, the torque- an flux-proucing components of the stator current are ecouple so that the inepenent torque an flux controls are possible as in c motors Usually, the -axis current reference i * is set to be i * = in orer to approximately eliminate the couplings between angular velocity an currents Assuming that the current controllers are properly esigne an the controller for -axis current loop works well, the output i satisfies i =i * = Then the -axis flux linkage is fixe an the evelope torque T m is then proportional to q-axis current i q, which is etermine by close-loop control T = K i (4) m T q K T is the torque coefficient ISSN: Issue, Volume 9, November

3 Fig Schematic iagram of the PMSM motion control system Fig4 Block iagram of the linear ADRC base on ESO ADRC for PMSM System A linear active isturbance rejection controller (ADRC) is introuce to achieve high ynamic performance in the overall operating range It is compose of two parts (shown in Fig 4): ) extene state observer (ESO), an ) linear state error feeback control law The essential part of ADRC is the extene state observer Extene State Observer The ESO is a configuration for observing the states an isturbances of the system uner control without the knowlege of the exact system parameters Unlike the full orer (N th orer) state observer, ESO utilizes N+th orer (full orer plus ) state observation to achieve state an isturbance estimation The total isturbances in PMSM system inclue external isturbances such as loa variation an internal uncertainties such as the moelling errors For the PMSM motion control system, consiering parameter variations as well as unavoiable an unmeasure isturbance torque T L, () can be rewritten as ω m = * a( t) + bi (5) q t TL K * T K T * a( t) = + ( iq iq) + b iq Jn Jn Jn represents external isturbance torque, the tracking error of the current loop of i q, an the moeling error Note that b is an estimate of K t /J n The isturbance a(t) is unmeasurable an time-variant Regar isturbance a(t) as an extene state an let a(t)/t=h, with h unknown Define x = θ m, x = ω m, x = a(t), y = θ m, u = i * q, then the state equations of PMSM system are given by x= Ax+ Bu+ Eh (6) y = Cx A =, B = b, C = [ ], E = In the PMSM motion control system, angular position can be etecte by encoer Base on the plant moel (6) an real output angular position from the plant, the linear ESO of PMSM is constructe as[] ISSN: Issue, Volume 9, November

4 ɵ z = Az + Bu + L( y y) (7) ɵ y = Cz z is an estimate of state x, L is the observer gain vector, T L = l l l (8) Assume the poles of the ESO (7) are p, p an p (p, p, p <) So the obserer gains can be calculate by l = p + p + p (9) l = p p + p p + p p () l = p p p () Define the estimation error e i =x i -z i, i=,,, an the error equation can be written as e= Aee+ E h () l A l e = A LC = l If the roots of the characteristic polynomial of A e are all in the left half plane an h is boune, the ESO (7) is boune-input boune-output stable [] In the PMSM motion control system, although the isturbance, a(t), is not measurable, it varies continuously So the erivation of the isturbance, h, is always boune The remaining issue is to properly esign the observer gain vector, L, to satisfy the performance of ESO There are many methos use to obtain L, such as the pole placement technique It is important to note that a proper selection of the gains in (7) is critical to the success of the observer The ESO must be stable firstly, or it woul cause the whole system to be unstable Seconly, the response of the ESO must be as soon as possible, so as to obtain the estimation of states an isturbances quickly The banwith shoul not be smalller than sampling frequency of angular postion It shoul be pointe out that a nonlinear ESO can also be use to estimate the isturbances[4] The avantages of nonlinear ESO are that it may obtain a better observation precision an a faster converging estimation However, it nees to tune more parameters to ensure the estimation performance ADRC Usually, a practical structure of cascae control loops for PMSM motion control system inclues a loop of position, a loop of spee an two loops of current (as shown in Fig) In this paper, we emphasize the esign of position controller an spee controller, an assume that the current controllers are properly esigne, so that the gain of current loop is set to With the linear ESO (7) properly esigne, its outputs will track the states x, x an isturbance a(t), respectively So a fee forwar compensation for the isturbance a(t) can be employe immeiately in the control esign The structure of linear ADRC base on ESO for PMSM motion control system is shown in Fig4 The controller is given by z+ u u= () b Equation () emonstrates the key iea of ADRC: the control of complex, nonlinear, time-varying, an uncertain process in (6) is reuce to a simple problem by a irect an active estimation an rejection of the generalize isturbance Ignoring the estimation error in z, that is, z = a(t), the plant is reuce to a unit gain ouble integrator, ( ) ( ( ) ) y= a t + b u= a t z + u u (4) From (4), we can see that all isturbances are compensate completely The plant (4) is easily controlle with a PD controller, * u = k θ z k z (5) ( ) p m Where θ * m, z an z are the set point of angular position, estimations of mechanical angular positon an mechanical angular velocity, respectively Note that -k z, instea of k (θ * m /t-z ), is use to avoi ifferentiation of the set point an to make the close-loop transfer function pure secon orer without a zero: k p Gcl = (6) s + k s+ k p Here, the gains can be selecte as k = ξω, an k = ω (7) c p ω c an ξ are the esire close loop natural frequency an amping ratio ξ is selecte to avoi any oscillations From the iscussion above, we can get some useful conclusions ) Since the esign of linear ADRC is base on the ESO, the performance of ADRC is largely epenent on that of ESO As the ESO is locate in the feeback channel, any estimation error woul result in the steay-states error which cannot be overcome by the controller In aition, the c ISSN: Issue, Volume 9, November

5 characteristic of robustness of the ADRC woul be lost ) In the ESO-base linear ADRC, a PD controller achieves zero steay state error without using an integrator So the ynamic response of ADRC is faster than that of traitional PID controller It is worth to note that, the PD controller in (5) can be replace with a more elaborate loop-shaping esign, if necessary ) The esign of ADRC is moel inepenent Once the ESO is set up, the performance of ADRC is quite insensitive to the moel variations an other isturbances The only parameter neee is the approximate value of b in (4), which is an estimate of K T /J n There are many methos to ientify the inertia moment of the plant In fact, by using ifferent linear gain combinations in the ESO an the feeback, one can easily fin many ifferent controllers in the same ADRC structure Regarless of which one of these control laws is chosen, the controller coefficients are not epenent on the mathematical moel of the plant, thus making ADRC largely moel inepenent These coefficients are primarily functions of the time scale, ie, how fast the plant changes That is, the controller only nees to act as fast as the plant can react, an this is implicitly represente by the choice of the sampling perio 4) The combine effects of the unknown isturbance an the internal ynamics are treate as a generalize isturbance By augmenting the observer to inclue an extra state, it is actively estimate an cancele out, thereby achieving active isturbance rejection Estimation of b As iscusse above, the performance of ESO-base linear ADRC applie in the PMSM motion control system is largely epenent on the precise an fast response of the ESO The parameter, b, an approximate value of K t /J n, is vital for the ESO However, in most applications, the real value of b can not be obtaine Since the torque coefficient K t that is relate to rotor flux is change slowly as the operating of system, it is consiere to be constant in this paper Therefore, the value of b is etermine mainly by the inertia of system, which varies when the PMSM rives ifferent loa evices that have ifferent inertias The variation of loa will egrae the performance of the ADRC, an in some extreme circumstances, the whole control system will be unstable if the approximate value of Table Parameters of the PMSM Rate power (kw) Poles Rate torque (Nm) 477 Rate phase current (A) 57 Torque coefficient 47 Rate spee (rpm) Phase resistance (Ω) 45 Phase inuctance (mh) 4 Inertia moment ( -4 kgm ) 444 b is fixe to a constant value Next, we will show this phenomenon by simulation results The parameters of the PMSM use in the simulation are shown in Table Here, in the simulation, the poles of ESO are all assigne to - Parameters of the PD controller, k p an k, are set to 987 an 64, respectively Fig5 an Fig6 show the step responses of the ADRC controller In Fig5, the value of b is fixe to K t /J m, 585, while the inertial moments of system are assigne to J m, 5J m an J m, respectively In Fig6, the inertial moment of system is fixe to 5J m, while the value of b is change From the simulation results, we can see that the performance of the ADRC controller will be iminishe if the inertia of the whole system varies largely an the controller oes not have any aaptation ability to hanle this kin of changes In fact, when the inertia of the system is increase, K t /J n becomes smaller, an b shoul become smaller accoringly However, if b is fixe to be a constant b = K t /J m, when the inertia of the system is increase, neither the control term i * qnor b changes, then the term b i * q becomes bigger an makes ω become bigger accoring to (5) At last, the performance of whole system is eteriorate To improve the control system, the b i * q term shoul corresponingly be ecrease, ie, b shoul be reuce when the inertia of the system is increase So in orer to get a higher performance rive, the inertia of the system shoul be ientifie, an b shoul be ajuste accoring to the variation of system inertia There are many methos to ientify the value of system inertia Here we use the metho introuce in [5] to ientify the loa inertia kt lim T q ( ) t k k T Jn( k) =, k =, kt lim q t k ( k ) T (8) J n = Jn + Jn (9) ISSN: Issue, Volume 9, November

6 Position/ra Position reference Jn=Jm, b=kt/jm Jn=5Jm, b=kt/jm Jn=Jm, b=kt/jm Fig5 Step responses of ADRC when the inertial memont of system increases Positon/ra Position reference Jn=5Jm, b=kt/jm Jn=5Jm, b=kt/(5jm) Jn=5Jm, b=kt/(jm) Fig6 Step responses of ADRC when inertial moment of system is fixe an b is change Position/ra 5 Position reference kp=987, k=754 kp=987, k=68 kp=9478, k= Fig8 Step responses of ADRC with ifferent PD controllers Position/ra 5 Reference PID ADRC Fig9 Comparation of ADRC controller an normal PID controller, J n =J m 5 5 Positon/ra Position/ra Position reference Jn=Jm Jn=5Jm Jn=Jm Fig7 Performance of ADRC when b is ajuste accoring to the inertial moment of system Reference PID ADRC Fig Comparation of ADRC controller an normal PID controller, J n =J m J n (k) is k-th sample increment of inertia, J n is the estimation of system inertia, an q satisfies q = λq + λωr, q( ) = () t λ >, λ is the pole of observer Once the inertial moment of system is ientifie, b is change corresponingly Fig7 shows the performance of the ADRC controller when b is ajuste accoring to the inertial moment of system We can see that, the ADRC controller works well at ifferent situations Fig8 shows step responses of ADRC with iffenent PD controllers From the simulation results, we can conclue that, once the ESO is set up, the performance of ADRC is mainly ISSN: Issue, Volume 9, November

7 epenent on k p an k, which are easily etermine by the esire close loop natural frequency an amping ratio 4 Comparation Stuy A comparation stuy between ADRC controller an normal PID controller is carrie out Two PMSM motion systems are establishe in MATLAB/ SIMULINK One is implemente with ADRC controller, an the other one is implemente with PID contoller The specifications of PMSMs use in simulation are the same as that shown in Table Current loops of the both systems are set to unit gain Other parameters of PID controller are given as follow: spee-loop proportional is 944, spee-loop integral gain is 47, an position-loop proportional gain is Parameters of ADRC controller are selecte as: k p is 987, an k is 64 A step signal is use as position reference The responses of both systems with ifferent loas are shown in Fig9 an Fig Both controllers perform well but ADRC yiels smaller error an faster response It is worthy to note that, increasing the position-loop proportional gain will inuce faster response However, an overshoot will generate, which is not allowe in some applications 4 Experimental Verification 4 Experimental System The harware schematic of experimental system is shown in Fig A surface PMSM is use in the experiment an Tabel gives the parameters of the PMSM The PMSM is riven by a three-phase current controlle PWM inverter The inverter is implemente by the Intelligent Power Moule (IPM) incluing gate rives, six-igbts an protection circuits The rotor position is measure by means of 5-pulse/revolution encoer A programable logical evice FPGA XCS5AN is use at the encoer interface to process outputs of the encoer Vector-controlle PMSM rive incorporate with the propose control scheme is experimentally implemente using TI DSP TMSF8 The new TMSF8 is the inustry s -bit control DSP with on-boar flash memory an performance up to 5 MIPS It s esigne specially for inustry control applications The structrue of whole control system in the test inclues a linear ESO, an ESO-base linear ADRC Fig Configuration of the experiment system an two current loops The current control loops are realize by two PID controller with parameters well tune Since this paper emphasizes the esign an performance of ADRC, the tuning metho of current contol loops is not iscusse Since the linear ESO mentione in Section is vital for ADRC, the metho how to implement the ESO in DSP is iscusse etailely in the following section Moreover, in orer to obtain angular position precisely in the situation of low spee, an asynchronous sampling metho (ASM) is employe 4 Implementation of ESO The ESO (7) is a full observer, which can reconstruct all the state variables In orer to illustrate how to implement the ESO, write (7) in iscrete form, ( ) [ n+ ] = [ n] + u[ n] + y[ n] ɵ y[ n] z A z B L () [ n] ɵ θ ɵ T m n ω m n a n z =, A T T / A A T A A = =, bt / lt l B L B = = bt L lt l = B = L lt l, an T is the control sampling perio, us While in practice, the state of angular position may be obtaine irectly an accurately from the encoer, so that a reuce-orer observer is suitable, in the remaining state variables ω m, a(t) are to be observe For clarity herein, z is replace by θ[n] From () a reuce-orer observer becomes z[ n+ ] = ( A L A) z[ n] () + L θ m n+ θ m n B u n + B u n ( ɵ ɵ ) ISSN: Issue, Volume 9, November

8 [ n] ω ɵ m n a[ n] T z = The minimum-orer observer for angular velocity an total isturbance requires only the current an previous sample angular position as provie by the encoer, along with the known q-axis current Using () an measure information of angular position an q-axis current, θ m [n], u[n], an estimate value of angular position base on ω m [n], a[n] can be written as ɵ ɵ m θ m θ [ n] ω b u n T n+ = n + T T / + a n Defining estimation error θ n+ θ m n+ θ n+, m ɵ m () m () can be rearrange as ɵ ɵ ω m but θm n+ = θm n+ + θm[ n] + T T / + (4) a n [ n] with (4), () can be written as z n+ = A z n L θ n+ + B u[ n] (5) m Formula () is the final form of the ESO use in this paper In real applications, actual angular position θ m [n] is etecte by counting the number of encoer pulse In the high or mile spee region, the angular position can be obtaine immeiately an accurately, so the ESO works perfectly However, in spite of the high precision encoer, a pulse interval becomes longer than the control sampling interval in a very low spee region an occasionally only one pulse income into several sampling intervals (as shown in Fig) In such case, there are positioning error an etection elay between the actual angular position an that etecte by the ESO The error an elay will eteriorate the performance of the ESO To aress this problem, a metho enote as asynchronous sampling metho (ASM) is evelope in the following section 4 Asynchronous Sampling Metho The ASM has two sampling rate for angular position In the high or mile spee region, the angular position θ m [n] is force to be synchronize with control sampling perio, T While in the low spee region, the angular position is force to be synchronize with encoer pulse interval At the moment of an encoer pulse input, the estimates z are upate by θ m Between these long sample upates, at each new short T control sampling instant, angular position θ m an angular velocity ω m are estimate, while isturbance a(n) is assume constant The process of calculation is illustrate as follow As shown in Fig, at the moment of m-th encoer pulse input, the actual angular position is θ m [m] an the estimate value is given by ( ) ɵ ɵ θ n θ n ω [ n] T [ n] T [ n] a ɵ [ n] b u[ n] = / (6) maux m m aux aux T aux [n] is the interval between the latest n-th control sampling an m-th encoer pulse It s easily obtaine by a simple harware logical evice, such as FPGA Then we can obtain the estimation error θ n = θ maux n θ m (7) maux ɵ Yiel θ maux [n] as input to (5) to improve the estimates for ω maux [n] an a aux [n] ɵ m ( ) ω n = ω n + a n + b u n T l θ n (8) maux m aux maux aɵ [ n] a ɵ [ n] l θ [ n] = (9) aux maux At the instant of control sample immeiately after the encoer pulse, the estimator uses the actual θ[m] an estimate ω raux [n] as the ol state, an upates the new estimate as ɵ θ m n+ = θm m + ω maux[ n] ( T Taux[ n] ) + ( T ) ɵ Taux n ( aaux[ n] + bu[ n] ) / ω ɵ ( )( ) m n ω maux n a aux n b u n T T aux () + = + + () 44 Experimental Results an Discussion In orer to check the performance of ADRC, a unit step position comman of 4ra is applie at t=s The inertia moment of loa is 4-4 kgm Fig shows the measure responses with ifferent k p an k It is clear that the steay state error of the tracking response is zero, although there is no integrator Forthurmore, the performance of the entire system is ecie by k p an k, an is inepenent on the moel Increasing k p an k will inuce faster tracking response But there will be an overshoot if k p an k are too large In the real applications, k p an k can be set accoring to the control sampling time an the entire inertia moment of motion system Fig shows the tracking responses of PMSM rive incorporate with ADRC an PID controller, respectively The parameters of ADRC controller an PID controller are the same as that specifie in 4 Since a PD controller is use instea of a PI controller in ADRC, the ynamic response of ADRC is faster than that of traitional PID controller Fig4 shows the results of ESO use synchronous sampling metho (SSM) an asynchronous ISSN: Issue, Volume 9, November

9 position (ra) 5 k p =987,k =68 k p =9478,k =57-5 time (s) cm k p =987,k =754 Fig Tracking responses of PMSM rive incorporate with ADRC position (ra) 5-5 time (s) cm ADRC PID Fig Tracking responses of PMSM rive incorporate with ADRC an traitional PID controller, respectively spee (rpm) 5 time (s) Fig4 Results of ESO in low spee region SSM ASM sampling metho (ASM) in the low spee region In this experiment test, a rample position comman of (πt)/5ra is applie at t=s So the spee reference is rpm The estimation errors of ESO us SSM an ASM are ±rpm an ±7rpm, respectively 5 Conclusions In the real motion applications, there are many isturbances, which make it ifficult to obtain a sufficiently high performance for PMSM motion control systems in the entire operating range Furthermore, since the angular position is etecte by counting the pulses of encoer, there are positioning error an etection elay between the actual angular position an the measure value in the low spee region To aress these issues, a novel active isturbance rejection control scheme has been propose in this paper A linear ESO is use to estimate all the isturbances, an then make the corresponing compensation in a linear ADRC The ESO-base linear ADRC is moel inepenent It achieves zero steay state error using a PD controller instea of an integrator In the linear ADRC, the combine effects of the unknown isturbance an the internal ynamics are treate as a generalize isturbance By augmenting the observer to inclue an extra state, it is actively estimate an cancele out, thereby achieving active isturbance rejection When the PMSM operates in a low spee region, an ASM is use to obtain the accuracy angular position Experimental results have shown that the propose metho achieves a goo performance in the presence of isturbances an the entire operating range References: [] P Cominos an N Munro, PID controllers: recent tuning methos an esign to specification, Control Theory an Applications, IEE Proceeings -, Vol 49, No,, pp 46-5 [] L H Keel, J I Rego, an S P Bhattacharyya, A new approach to igital PID controller esign, Automatic Control, IEEE Transactions on, Vol 48, No 4,, pp [] A Kiam Heong, G Chong, an L Yun, PID control system analysis, esign, an technology, Control Systems Technology, IEEE Transactions on, Vol, No 4, 5, pp [4] S Jianbo, Q Wenbin, M Hongyu, an W Peng-Yung, Calibration-free robotic eye-han coorination base on an auto isturbance-rejection controller, Robotics, IEEE Transactions on, Vol, No5, 4, pp [5] S Piccagli an A Visioli, Minimum-time feeforwar technique for PID control, Control ISSN: Issue, Volume 9, November

10 Theory & Applications, IET, Vol, No, 9, pp 4-5 [6] Y A R I Mohame an T K Lee, Aaptive self-tuning MTPA vector controller for IPMSM rive system, Energy Conversion, IEEE Transactions on, Vol, No, 6, pp [7] K Ying-Shieh an T Ming-Hung, FPGA-Base Spee Control IC for PMSM Drive With Aaptive Fuzzy Control, Power Electronics, IEEE Transactions on, Vol, No 6, 7, pp [8] K Seok-Kyoon, Spee an current regulation for uncertain PMSM using aaptive state feeback an backstepping control, IEEE International Symposium on Inustrial Electronics, 9, pp 75-8 [9] S Kuo-Kai, L Chiu-Keng, T Yao-Wen, an I Y Ding, A newly robust controller esign for the position control of permanent-magnet synchronous motor, Inustrial Electronics, IEEE Transactions on, Vol 49, No,, pp [] S Jianbo, M Hongyu, Q Wenbin, an X Yugeng, Task-inepenent robotic uncalibrate han-eye coorination base on the extene state observer, Systems, Man, an Cybernetics, Part B: Cybernetics, IEEE Transactions on, Vol 4, No 4, 4, pp 97-9 [] Y Lin-Ru, M Zhen-Yu, W Xiao-Hong, an Z Hao, Sliing moe control for permanentmagnet synchronous motor base on a ouble close-loop ecoupling metho, Proceeings of the Fourth International Conference on Machine Learning an Cybernetics, 5, pp9-96 [] S Jayasoma, S J Dos, an R Perryman, A FPGA implemente PMSM servo rive: practical issues, Universities Power Engineering Conference, 4, pp [] H Hahn, A Piepenbrink, an K D Leimbach, Input/output linearization control of an electro servo-hyraulic actuator, Proceeings of the Thir IEEE Conference on Control Applications, 994, pp 995- [4] J Hu, Y Xu, an J Zou, Design an Implementation of Aaptive Backstepping Spee Control for Permanent Magnet Synchronous Motor, The Sixth Worl Congress on Intelligent Control an Automation, 6, pp -6 [5] S S Wankun Zhou, Zhiqiang Gao, A Stability Stuy of the Active Disturbance Rejection Control, Applie Mathematical Sciences, Vol, No, 9, pp [6] B Porter, Issues in the esign of intelligent control systems, Control Systems Magazine, IEEE, Vol 9, No, 989, pp [7] H Hui-Min, An architecture an a methoology for intelligent control, IEEE Expert, Vol, No, 996, pp [8] J W Choi, S C Lee, an H G Kim, Inertia ientification algorithm for high-performance spee control of electric motors, Electric Power Applications, IEE Proceeings -, Vol 5, No, 6, pp [9] K Euntai an L Sungryul, Output feeback tracking control of MIMO systems using a fuzzy isturbance observer an its application to the spee control of a PM synchronous motor, Fuzzy Systems, IEEE Transactions on, Vol, No 6, 5, pp [] Y A R I Mohame, Design an Implementation of a Robust Current-Control Scheme for a PMSM Vector Drive with a Simple Aaptive Disturbance Observer, Inustrial Electronics, IEEE Transactions on, Vol 54, No 4, 7, pp [] C Young-Kiu, L Min-Jung, K Sungshin, an K Young-Chul, Design an implementation of an aaptive neural-network compensator for control systems, Inustrial Electronics, IEEE Transactions on, Vol 48, No,, pp 46-4 [] J Q Han, Auto-isturbance-rejection control an its applications, Control Desision, Vol, No, 998, pp 9- [] G Zhiqiang, Scaling an banwith -parameterization base controller tuning, Proceeings of the American Control Conference,, pp [4] G Zhiqiang, H Shaohua, an J Fangjun, A novel motion control esign approach base on active isturbance rejection, Proceeings of the 4th IEEE Conference on Decision an Control,, pp [5] I Awaya, Y Kato, I Miyake, an M Ito, New motion control with inertia ientification function using isturbance observer, Power Electronics an Motion Control, Proceeings of the 99 International Conference on Inustrial Electronics, Control, Instrumentation, an Automation, 99, pp 77-8 ISSN: Issue, Volume 9, November