Research Article ADRC and Feedforward Hybrid Control System of PMSM

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1 Matheatical Probles in Engineering Volue 3, Article ID 879, pages Research Article ADRC and Feedforward Hybrid Control Syste of PMSM Song Wang School of Mechanical, Electrical & Inforation Engineering, Shandong University, Weihai 649, China Correspondence should be addressed to Song Wang; wangsong Received 6 August 3; Revised October 3; Accepted 3 Noveber 3 Acadeic Editor: Xi-Ming Sun Copyright 3 Song Wang. This is an open access article distributed under the Creative Coons Attribution License, which perits unrestricted use, distribution, and reproduction in any ediu, provided the original work is properly cited. The peranent-agnet synchronous otor (PMSM) is a coplex controlled object that is difficult to drive and control. In this study, the vector control strategy is adopted to drive the PMSM. The active disturbance rejection controller is used to achieve the closed-loop control of PMSM, which siplifies the coputational coplexity. A load torque observer and feedforward copensation coponent are designed to overcoe the PMSM speed fluctuation of the load disturbance. An experiental syste based on the DSP board is designed to test the controller perforance. The results validate the control algorith.. Introduction The peranent-agnet synchronous otor (PMSM) is a ultivariable, nonlinear, tie-varying, and strongly coupled syste.thecontrolethodanddrivestrategyofpmsmsare coplex.thethreeainpmsmdrivestrategiesareconstantfrequency ratio control (VVVF), field-oriented control (also called vector control (VC)) [], and direct-torque control (DTC). VVVF is called a variable-voltage and variable-frequency control; this strategy ostly adopts open-loop control [] and has a siple structure. The VVVF does not perfor well because of the lack of current and position feedback. VC and DTC belong to the high-perforance PMSM control strategy and are thus different fro VVFF [3]. VC requires an accurate PMSM odel. Vector transforation and large-syste calculations can be used to control PMSM but generally do not yield the desired effect. However, the use of high-precision encoders has significantly iproved PMSM control. The DTC ethod does not require coplex coordinate transforations [4] but has a large torque ripple coponent because it cannot generate a current loop or execute current protection. Therefore, DTC requires current-liiting easures. With the developent of a control theory, various alternative control ethods [5 8], including feedback linearization, sliding ode variable structure, neural network control, adaptive control, fuzzy control, and anti-step control, have been proposed. Most of these control ethods are based on the VC and DTC strategies. The PMSM control syste exhibits iproved perforance when cobined with these control ethods. In this study, we adopt the VC strategy to drive PMSM and use the double-loop (speed and current loops) control ethod to achieve a hybrid PMSM control syste. The speed loop uses the active disturbances rejection controller (ADRC), whereas the current loop adopts a D controller coposite with feedforward. ADRC is useful in analyzing nonlinear uncertain systes with unknown disturbances. Therefore, the ADRC of the speed loop can adequately handle unknown load disturbances. However, the paraeters of the ADRC are difficult to adjust. Thus, we propose a linear ADRC controller and design a load torque observer and feedforward copensation coponent to overcoe the PMSM speed fluctuation of load disturbances. A DSP is used to design an ebedded PMSM controller and perfor actual achine experients in order to evaluate the effectiveness and superiority of the ethod.. Matheatical Model of PMSM The atheatical odel of PMSM in a d, q two-phase rotating coordinate syste is shown below [9, ]. The voltage equation is u q =R s i q L q di q dt ωψ d, u d =R s i d L d di d dt ωψ q. ()

2 Matheatical Probles in Engineering V dc n n Speed controller i d = i q i q i d Torque controller Flux controller q d Park d, q α,β θ α β SVPWM UVW inverter i q d, q i α α,β i a i d α,β i β a, b, c i b Position and speed sensor PMSM Figure : Structure of a peranent-agnet synchronous otor (PMSM) vector control (VC) syste. When the PMSM is in a steady state, the voltage equation is given by u q =R s i q ωψ d, () u d =R s i d ωψ q, where u d and u q represent the stator winding shaft in a straight axis and the quadrature voltage, respectively; i d and i q are the direct-axis current and quadrature-axis current, respectively; R s is the stator phase resistance; ψ d and ψ q represent the syntheses of the agnetic fields in space-direct and quadrature-axis stator winding of the agnetic chain, respectively; L d is the straight axis inductance; and L q is the quadrature axis inductance. The agnetic linkage equation can be expressed as follows: ψ d =ψ f L d i d, (3) ψ q =L q i q, where ψ f is the peranent-agnet fundaental excitation agnetic field and stator winding of the agnetic chain. The electroagnetic torque of PMSM in the d, q coordinate is T e =n p (ψ d i q ψ q i d )=n p [ψ f i q (L d L q )i d i q ]. (4) When L d is equal to L q, the electroagnetic torque can be siplified as follows: T e =n p ψ f i q. (5) Figure shows the VC syste structure of PMSM when id =. The structure includes the current acquisition, rotor position, speed detection, speed control, torque control, flux controller, SVPWM odules, inverters, and PMSM. The siulation syste is established in MATLAB/ SIMULINK using a VC syste siulation odel of PMSM (Figure ). 3. Application of ADRC in PMSM Speed Control The ADRC technology is derived fro the D control theory. The ADRC has higher stability [ 3] and robustness than the D controller and has thus been used to address the inherent defects of classical D [4]. 3.. ADRC Controller. The ADRC consists of two parts. The first part is the tracking differentiator (TD), which tracks the syste reference input and reasonably arranges the transient process. The second part is the extended state observer (ESO), which controls the syste, observes the integrated disturbance of systes through the nonlinear-state error feedback (NLSEF) generalized error, and provides the corresponding feedforward copensation of the disturbance [5]. Figure 3 shows the structure of the ADRC controller. The ADRC can be widely used for the unknown disturbances of nonlinear uncertain systes, as follows: x (n) =f(x, x,...,x (n),t)ω(t) bu, y=x(t), where f(x, x,...,x (n),t) is the unknown function, ω(t) is the unknown disturbance, x(t) is the syste output (which can be easured), u is the control action of the syste, and b is the gain. 3.. ADRC Controller Design. Although ADRC ipleentation does not rely on the accurate atheatical odel of the object, (6) shows that the ADRC order can be deterined by the order of the controlled object. In addition, given the choice of different constructors, ADRC ipleentation can also be in various fors. (6)

3 Matheatical Probles in Engineering 3 Speed ref I q ref I d ref U q U d θ U α U β Discrete SV PWM generator U α U β Pulses Continuous powergui Signal builder Load torque Iabc Inv park is abc Idq DC voltage s g Signal builder A A Controlled VS N B B S C C Universal bridge Peranent agnet synchronous achine Gain3 T is qd s qd w θ T e Udq 4 Speed Gain w 4 I q I d Figure : Peranent-agnet synchronous otor (PMSM) vector control (VC) syste odel. TD n e e n NLSEF u /b Z n Z n Z u b ESO w Object Figure 3: Active disturbance rejection controller (ADRC) structure Tracking Differentiator (TD). The atheatical odel for the coonly used n-order TD is as follows [6]: e =z V, =z,. z n =r [fal (e,a,δ )β fal ( ) r, a,δ z n z β (n) fal ( r n )],,a n,δ n where V is the reference input, z is the trace output after the TD arrangeents, e is the difference between the TD trace output TD and the reference input, z z n is the output of each derivative signal for the TD tracking reference input, r and β β (n) are constants, and fal() is an error function. y (7) 3... Extended State Observer (ESO). The coonly used atheatical odel for the n-orderesoisasfollows: e =z y, =z β fal (e,a,δ ),. n =z (n) β n fal (e,a n,δ n )bu, (n) =β (n) fal (e,a (n),δ (n) ), where y is the syste output, z z n is the expansion state of the ESO observing systes, z (n) is the total nuber of syste disturbances observed by ESO, e is the difference between ESO observation and the syste output, β β (n) is a constant, u is the syste control function, and b is the gain of the control action. The n-order nonlinear feedback control rate of the state error is expressed as follows: u =k fal (e 3,a 3,δ 3 ) k n fal (e 3n,a 3n,δ 3n ) u=u b z (n), where e 3 e 3n is the error between the syste reference and the output of each order state; naely, e 3x =e x e x (x= n) and k k n is a constant. The nonlinear functions fal() are used in TD,ESO,and NLSEF [7], as follows: fal (x, a, δ) = { x { δ a, sign (x) x { a, x δ x >δ, (8) (9) () where sign(x) is the sign function, in which sign(x) = when x and sign(x) = when x<; a is the nonlinear factor

4 4 Matheatical Probles in Engineering and δ is the filter factor. When a<, fal(x, a, δ) has a large error with a sall gain or exhibits the characteristics of sall errors with a large gain ADRC-Based PMSM VC. The atheatical odel for PMSM in the two-phase d, q rotating coordinate syste can be derived as follows [8]: di d dt = (u L d R s i d ωl q i q ), d di q dt = (u L q R s i q ωl d i d ωψ f ), q dω dt = J (n p [ψ fi q (L d L q )i d i q ]n p T L Bω). () When designing the ADRC controller of PMSM, the current loop inverter and PMSM are considered as one control object. The third expression in () shows thatthe PMSM speed is affected by i q, i d, load torque, and friction coefficient. According to the ADRC principle, i q is due to the speed control, which is the ADRC output. i d,theloadtorque,andthefriction coefficient are considered syste disturbances and are given by a(t) = (/J)[n p (L d L q )i d i q n p T L Bω]. Therefore, the three expressions in ()canbewrittenas dω dt = J n p ψ fi q a(t) =bi q a(t), () where b = (/J)n p ψ f. In addition, the third expression in () shows that the PMSM speed loop is a first-order odel. Therefore, the ADRC controller of the PMSM speed loop is also in the first order, as shown in Figure 4. In Figure 4, ω is a given speed reference signal, z is the speed output after the TD transition procedure, z is the ESO speed output, z is the syste disturbance of the ESO observation, u is the control signal of the nonlinear feedback control law, and u is the control signal copensated by the perturbation, which is the current reference of the quadrature axis (i q ). The first-order ADRC controller of the PMSM speed loop canberealizedasfollows. TD: ESO: e =z ω, =rfal(e,a,δ ). e =z ω, =z β fal (e,a,δ )bu, =β fal (e,a,δ ). (3) (4) ω One step TD z e NLSEF u z z u One step ESO Figure 4: Peranent-agnet synchronous otor (PMSM) speed loop active disturbance rejection controller (ADRC) odel. Nonlinear-state error feedback-control law: e=z z, u =β 3 fal (e, a 3,δ 3 ), u=u z b. i q ω (5) The MATLAB/SIMULINK is used to build a siulation odel (Figure 5)based on theatheaticalodel.thespecific paraeters are as follows. The noinal voltage is U = 56 V, the stator phase resistance is R s =.4 Ω, the cross-axis inductance is L d =L q =.5 H, the agnetic chain of peranent agnets and stator winding is ψ f =.6784 V s, the oent of inertia is J = kg,therotordapingfactorisb =.69 4 N s, and the nuber of pole pairs is n p =4.Basedon these paraeters, the ADRC controller paraeters of ADRC can be calculated as follows: b= J n p ψ f = 6.3. (6) 3.4. Coparison between ADRC and a D Controller. The current loop adopts the D control ethod, whereas the speed loop uses the ADRC control strategy. This paper copares the overshooting, response tie, antiload disturbance, and other capabilities of the ADRC and D ethods of PMSM in a VC syste according to the requireents of the PMSM speed control. The DC voltage of the PMSM inverter stabilizes at the start of the rated voltage (56 V) of the otor, drops to 46 V within seconds, and then reverts to the rated voltage at.5 seconds. Moreover, this voltage increases to 66 V in 3 secondsandthenrevertstotheratedvoltageat3.5seconds.the load torque input starts to stabilize at.5 N, increases to 3N at second, and then drops to.5 N at.5 seconds. The PMSM speed is set to 5 r/in under the sae conditions. Figure 6 shows the speed output wavefor of the two strategies of the PMSM speed controller. Figure 6 shows that the speed output of the D controller in the PMSM speed loop has significantly overshot at 3 r/in and that the regulation tie is approxiately.6 s. The torque increases to 3 N and then suddenly decreases. Moreover, the speed output has nearly r/in fluctuations. The regulation tie is approxiately. seconds. However, the voltage fluctuations have no effect on the speed. The speed outputandspeedobservationofadrcarethesae,andno

5 Matheatical Probles in Engineering 5 wz Step TDw Continuous powergui u In Out NLSFEw z U q ref V Signal builder U U d ref α α Iabc U Pulses Load torque abc U abc U U o ref V β β θ Discrete SV PWM Machines easureent dqabc abcalβ generator deux g T DC voltage s is abc is A A qd s Signal builder B B N qd Hall effect w Controlled voltage source C C S θ T Universal bridge Peranent agnet e synchronous achine 4 p Idq w ESOw z w z -K- z u /b 4 p Figure 5: Peranent-agnet synchronous otor (PMSM) active disturbance rejection controller (ADRC) MATLAB odel Speed (n/) 5 55 fal() Tie (s) D speed control ADRC speed control ADRC speed observation Figure 6: Peranent-agnet synchronous otor (PMSM) speed output based on D. overshoot occurs when the otor starts. When the torque changes as above, the ADRC speed output changes to approxiately r/in. The voltage fluctuations also have no effect on the speed output. The following conclusion can be drawn fro the aforeentioned results. () The otor can start without an overshoot because of the TD arrangeents and the nonlinear control state and variables. The classic D control generates unavoidable overshoot even after adjusting the paraeters. () The load antidisturbance control by ADRC in the is greater than that by the D control Figure 7: fal(e,.5,.5) function. (3) The three-phase inverter DC voltage fluctuations do not affect the PMSM speed output ADRC Linearization. In siulation and practical applications, paraeter adjustent inconvenience is the ain factor that affects the ADRC control perforance. On the other hand, because of the presence of nonlinear functions and its two paraeters. Moreover, the calculation of nonlinear functions for ebedded controllers requires a large aount of CPU resources. Thus, this study has siplified the nonlinear functions to facilitate paraeter adjustent and calculations. The nonlinear function expressed in () is shown in Figure 7,whereα =.5, δ =.5,thex-axisistheerrorinput e,and the y-axis is the function value. This nonlinear function hasyields asallerrorandalargegain,andviceversa[5, 9]. The linear function of error y=eis instead that of the nonlinear function fal(e, α, δ);that is,a straight line throughthe origin is used in place of the curve in Figure 7. x

6 6 Matheatical Probles in Engineering Speed (n/) Tie (s) Speed (n/) TD output of linear ADRC TD output of noral ADRC Figure 8: Coparison of the tracking differentiator (TD) outputs of the linear active disturbance rejection controller (ADRC) and noral ADRC Realization of Linear ADRC. The linear first-order odelofadrcinthepmsmspeedloopofpmsmcanbe described as follows. TD: e =z ω, ESO: = re. e =z ω, =z β e bu, =β e. Control law of state-error feedback: e=z z, u =β 3 e, u=u z b. (7) (8) (9) As shown in Figure 8, the TD output of ADRC is soother than that of the linear ADRC under the sae r,and the duration of transition is longer. However, linear ADRC can track the reference signal given a suitable paraeter, and the transition tie arranged by TD in linear ADRC can be arbitrarily adjusted PMSM Siulation Based on Linear ADRC. Figure 9 showstheadrcspeedcontroloutputaswellasthelinear ADRC observations. The speed controller with the linear ADRC also shows no overshooting. Under the sae load disturbance, the linear and nonlinear ADRC controllers exhibit nearly siilar speed fluctuations. Moreover, the power fluctuation of the threephase inverter circuit has negligible effects on the linear ADRC.IntersofthespeedobservationofthelinearADRC, the ESO yields a ore coplete observation of the extended states Tie (s) ADRC speed control ADRC speed observation Figure 9: Speed output and observation of peranent-agnet synchronous otor (PMSM) linear active disturbance rejection controller (ADRC). d(t) y (t) e Feedback controller u (t) G FF (s) u(t) Object G YD (s) G YC (s) Figure : Feedforward and feedback controller. y(t) However, when the start or working process of PMSM is disrupted, the duration for which the syste returns to the steady state is relatively long. This duration corresponds to the characteristic of the fal() function, wherein the gain increases when the error decreases. Given that the error gain of the linear ADRC near the steady state is negligible, the changes in the control action are also relatively sall and the duration of the stabilization process is relatively long. Overall, the linear ADRC has achieved the expected iproveents. 4. PMSM Control Syste Based on ADRC and Feedforward Control Feedforward control is used [] to increase the load antidisturbance in the PMSM speed control (Figure ). The observation and copensation of the load torque are used to achieve greater speed control. The feedforward controller of the load torque achieves the hybrid control of PMSM. Thus, a PMSM load torque observer, such as a state observer, should be constructed to achieve state reconstruction [8,, ].

7 Matheatical Probles in Engineering Full-Diensional State Observer of the Load Torque. A state observer is constructed to achieve a state observation. The diension of the state observer is the sae as that of the control syste and is called a full-diensional state observer. AstateobserverforPMSMisconstructedaccordingtothe state reconstruction principle. According to the otion equation (4)ofthePMSMdrive syste, the electrical angle w is used instead of a echanical angular velocity ω, which is expressed as follows: u B Σ(A,B,C) G x C y ŷ dω dt = B J ω J T L J T e. () A x Suppose that the PMSM state is x=[wt L ] T,theinputisu= T e,andtheoutputisy=w.thevariationinthepmsmtorque is unknown, and the torque paraeter is assued to be constant; that is, the rate of torque change is zero. Therefore, the speed syste of PMSM can be described as where x=axbu, y=cx, () B A=[ J J ], B = [ J ], C = [ ]. () [ ] [ ] According to the syste Σ(A, B, C), the new syste Σ(A, B, C) canbeconstructedasfollows: x =A xbu, y =C x, (3) where x represents the state Σ, whichiscalledtheobserver value of x. Therefore, x x =A(x x), the solution of which is x x =e At [x() x()]. Under noral conditions, the initial conditionsarenotalwaysthesaebecauseoftheassuption thatthetorqueisconstant.toeliinatethestateerror,the feedback of the error x x is used based on the new syste, naely, the error y y.thus,g is the feedback atrix of the state observer. Figure shows the structural diagra of the state observer. The state equation is expressed as x =A xg(y y) Bu = (AGC) xbugy. (4) The state-estiated variables yield accurate approxiations of the true value as long as the eigenvalues of the coefficient atrix (A-GC) in (4)to(6)ofthestateobserverhave negative real parts. Let G=[g,g ] T.Then,thestateequationoftheobserver canbeexpressedas si (AGC) =s ( B J g )s g J =. (5) Figure : Structural diagra of the state observer. If the expected poles of the state observer are α and β,then g = B J (αβ), g =Jαβ. (6) Figure shows the MATLAB-established full-diensional state observer odel of the load torque. Given the known paraeters J and B of the PMSM in MATLAB, the rational poles of the observer can be used to deterine the PMSM state observer, in which inputs are the echanical angular velocity and torque of the otor and the load torque and the echanical angular velocity are the outputs. 4.. Direct Calculation of the Load Torque. Although the load torque observation in previous studies [, ] is ainly designed using a full-diensional or reduced-order observer, theloadtorquecanbecalculateddirectlyandstraightforwardly by using the PMSM drive equation [3]. ThedriveequationofPMSMcanberewrittenasfollows, andtheexpression[], of the load torque can be calculated using the following equation: T L =T e J dω Bω dt. (7) Figure 3 shows a odel diagra of the load torque observer, which is established using MATLAB via direct calculation. Equation (7) shows that the ethod of directly calculating the load torque requires the sae paraeters and inputs as those used for the full-diensional state observer, except for the speed observation Coparison of the Two State Observers of Load Torque. To copare the perforances of the two load torque observers, we siulate a state observer via calculation and via fullorder observation. The load torque is initially set at.5 N, is increased to 4 N at.5 s, and is returned to.5 N ats. Figure 4 shows the observations of the two load torque state observers.

8 8 Matheatical Probles in Engineering -K- T e Gain3 w k Gain s Integrator w k Gain s Integrator -K- Gain Gain4 -K- T L Figure : Full-diensional state observer of the load torque. W T e du/dt Derivative -K- Gain Add T L where the control input is i q, which can be considered as an electroagnetic torque, and the disturbance is the load torque. According to (8), G YD (s) = /(JsB) and G YC (s) = n p ψ f /(Js B) can yield the following: G FF (s) = G YD (s) G YC (s) = n p ψ f. (9) Figure 3: Load torque observer obtained via direct calculation. Torque (M ) Tie (s) Torque Torque by full-order observer Torque by calculation Figure 4: Coparison of the load torque observers Load Torque Feedforward Controller. The two current loops, the inverter, and the PMSM are regarded as generalized controlled objects. Moreover, the current loop is approxiated to a proportional eleent with a ratio of. Then, the expression of the controlled object is a odification of the PMSM otion equation and is given by dω /dt = (B/J)ω (/J)T L (/J)T e.ati d =or L d =L q,this equationcanberewrittenas dω dt = B J ω J T L J n pψ f i q, (8) Equation (8) shows that once the load torque changes after copensation of the sae electroagnetic torque, the righthand side of the equation becoes constant to ensure a constant speed. The feedforward observer can then be expressed as follows: i q = T L n p ψ f. (3) After verification, (3) is shown to have the sae relationship as (9) Siulation of PMSM Based on ADRC and Feedforward Control. The load torque observer and feedforward controller consist of the load torque copensation. The output is the copensation of i q once the load suddenly changes. The linear ADRC in the PMSM speed loop achieves the feedback control for speed, the output of which is the reference for i q. This output and the copensation of the load feedforward controller consist of the reference input of i q. Figure 5 shows the odel for the PMSM control syste based on ADRC and feedforward control, which are established using MATLAB. TheDcontrolisusedinthecurrentloop,andthespeed reference is set at 5 r/in (Figure 5). Moreover, the DC voltagefluctuationsoftheinverterhavenoeffectontheentire syste and are thus directly set to 56 V. Figure 4 shows the setting of the load torque, and Figure 6 shows the PMSM speed output. Figure 6 showstheresultsofacoparisonoftheactual outputs of the speed using D, ADRC, and ADRC with the feedforward speed control. The ADRC and feedforward control have not exhibited overshooting and have shown nearly negligible speed fluctuations when the load suddenly

9 Matheatical Probles in Engineering 9 Step wz TD Continuous powergui z 5 k u U q ref V Signal builder U d ref α U α Iabc U Pulses abc U abc Torque U U o ref V β β θ Discrete SV PWM Machines easureent dqabc abcalβ generator deux g T Signal s is abc is A A qd s Signal builder3 B B N qd Hall effect w Controlled voltage source C C S θ Universal bridge Peranent agnet T e synchronous achine Idq Idq 4 p z -K- /b ESO w u z z w 4 p Gain -K- T L observer W T L T e Figure 5: Modeling of the peranent-agnet synchronous otor (PMSM) vector control (VC) based on active disturbance rejection control (ADRC) and feedforward control. Speed (n/) D speed control ADRC and feedforward speed control ADRC speed control Tie (s) Figure 6: Peranent-agnet synchronous otor (PMSM) speed output based on the active disturbance rejection control (ADRC) and feedforward control. changes. These results confir that the ADRC controller with thefeedforwardloadtorquecopensationexhibitsastable perforance and antidisturbance ability when PMSM starts. The speed controller output is not constant even when the feedforward copensation is added under ideal conditions because of the speed and the differential signal used in designing the load torque observer. That is, the output of the load torque observer changes and copensates when the speed output changes. In addition, the results of the siulation are acceptable as long as the otor odel in MATLAB is accurate. However, because an accurate odel and paraeters cannot be obtained in practical applications, so the feedforward control cannot fully copensate for the effects of changes in the load torque. Table : Peranent-agnet synchronous otor (PMSM) paraeters. Rated voltage V Rated current 4 A Rated power 6 W Rated speed 3 r/in Rated torque N Phase resistance.97 Ω Phase inductance.89 H Pole pairs 4 Inertia.33 kg 5. Experients The PMSM used in this paper is the Wuhan ST-M3 otor, which has a surface-type package peranent agnet rotor. Moreover, the direct-axis inductance of this otor is thesaeasitsquadrature-axisinductance,itsstatorwindings are star wirings and do not have neutral wires, and the su of its three-phase currents is zero. In addition, the otor is packaged with a copound increental encoder to detect the rotor position. The paraeters of the otor and encoder are presented in Table. TheDSPboardandIPMdriverboardforthePMSMcontrol syste testing in the experients are shown in Figure 7. During the test, the PMSM is connected to a ZC hysteresis dynaoeter (Guangzhong Electrical Equipent Co. Ltd.) via couplings to detect the otor speed conveniently and add load to the otor iediately.

10 Matheatical Probles in Engineering (a) DSPcontrolandcurrentacquisition (b) IPM diver board Figure 7: Main hardware control equipent. We conducted otor starting experients and load tests toverifythecontrolethod.thepmsmspeedreferenceisset at 5 r/in. Figure 8 showsthechangesinthespeed,output torque, and output power recorded by the collecting syste under a N loadinput. Curves and in Figure 8 show the relationship between otorspeedandoutputtorqueandbetweenoutputpower and output torque, respectively. The two curves exhibit the relations of speed and power with the changes in the output power. The relationship of speed and power with the torque shows the following. () When the otor starts, the PMSM output torque overcoes the load torque and increases the speed. As a result, the output torque is higher than that of the no-load. When the otor speed is kept equal to the reference speed, the output torque becoes lower than that of the noload (if the effects of the rotor-daping factor are ignored). Thus,curve,whichisdrawnfror/into5r/in,represents the decrease in the output torque. The difference between the two curves is that the output torque is reduced with the D controller when the speed reaches the set value, whereas the output torque reaches its axiu value with the ADRC controller when the speed increases. These phenoena can also explain the occurrence of an overshoot in the D controller but not in the ADRC controller. When the output power changes with the product of the output torque and speed, the change trends are decided by the control ethod and are consistent with the changes in the output torque. The output power for the D controller reaches its axiu value when the speed approaches the set value. By contrast, the output torque for the ADRC controller reaches its peak and reains constant when the otor starts. () The speed can return to the set value because of the closed-loop regulation when the load changes. The changes in the output power vary with the changes in the load torque and thus illustrate the linear relationship between the two paraeters. However, because of the greater changes in the speed with the D control, the output power of this controller is relatively larger than that of the ADRC controller. In the D control syste of PMSM, the overshoot is 5 r/in. Figure 8(a) shows the speed change when a sudden load is added. The output torque reaches the axiu and the axiu speed decreases to 7 r/in. The change in P (w) P (w) n (rp) n (rp) M (N ) (a) D test results M (N ) (b) Linear active disturbance rejection controller (ADRC) test results Figure 8: Load test results. speed when the added load suddenly disappears is shown in the upper portion of Figure 8(a). When returned back to the no-load torque, the axiu change in speed reaches r/in. The overshoot is negligible with ADRC (Figure 8(b)). When a sudden load is added, the speed drop is 4 r/in.

11 Matheatical Probles in Engineering Table : Changes in speed with the different control ethods under sudden load. Control ethod D ADRC ADRC and feedforward Decrease in the speed upon load addition (r/in) Increase in the speed under decreasing load (r/in) 5 4 P (w) n (rp) M (N ).5 Figure 9: Results for the active disturbance rejection controller (ADRC) and feedforward controller. Figure : Line voltage and current wavefor. 6. Conclusions Whentheloaddisappears,theaxiuspeedis5r/in.In addition, the output torque of ADRC begins to decrease before the speed reaches the set value, whereas the output powerisnearlykeptconstanttoensurethatnoovershoot occurs when PMSM starts. These results confir that ADRC perfors better than D. The coparison results are shown intable. The perforance iproves when a copound control of ADRC or D with a PMSM feedforward control of PMSM is used (Figure 9). The axiu speed change decreases to 3 and4r/inwhentheloadincreasesanddisappears,respectively.thefeedforwardcontrolrequiresanaccuratepmsm odel, such as the inertia, daping, stator flux, and real-tie i q. i q is necessary in the easureent of fixed paraeters. However, this current is inaccurate because of the inaccurate easureent of the three-phase current as well as the nonideal utual difference of between the three-phase current.therefore,theeasureentoftheloadtorqueisinaccurate and results in the insufficient copensation of the feedforward control and of the speed changes caused by the load torque. Thus, the test results are not accurate as the siulation perforance. Figure shows the line voltage and line current wavefor of the PMSM, as easured by a FLUKE 43B power quality analyzer. In Figure, the line voltage and current wavefor are approxiately equal to the sinusoidal signal, which has a frequency of 33.4 Hz and is nearly equal to the Hz frequency set by the speed set value. This result further confirs the suitability of the PMSM VC. PMSMisdifficulttodrivebecauseofthesynchronicityrequireent. The ADRC is an excellent controller in industrial control. In this study, we use ADRC to achieve a closed-loop control of PMSM. A linearization ethod is also adopted to siplify the coputational coplexity. To achieve load antidisturbance, a feedforward coponent is designed by observing the load change. The siulation results show the excellent perforance of the cobined ADRC and feedforward coponent. The load disturbance has no effect on the PMSM speed. An ebedded controller based on DSP is designed to validate the practical application of the new controller. The cobined ADRC and feedforward coponent shows higher perforance than the D in ters of the steady-state and dynaic characteristics. Although the results are proising, additional research, particularly on the online paraeter estiation of PMSM, is necessary to iprove the accuracy of the PMSM odel. Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper. References [] K.-Y. Chen, J.-S. Hu, C.-H. Tang, and T.-Y. Shen, A novel switching strategy for FOC otor drive using ulti-diensional feedback quantization, Control Engineering Practice,vol.,no.,pp.96 4,.

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