Frequency Response Analysis of Linear Active Disturbance Rejection Control

Transcription

1 Senor & Tranducer, Vol. 57, Iue, October 3, pp Senor & Tranducer 3 by IFSA Freuency Repone Analyi of Linear Active Diturbance Reection Control Congzhi HUANG, Qing ZHENG School of Control and Coputer Engineering, North China Electric Power Univerity, Beiing, 6, China Electrical and Coputer Engineering Departent, Gannon Univerity, Erie, PA 654, USA Tel.: , fax: E-ail: hcz9@ncepu.edu.cn Received: July 3 /Accepted: 5 Septeber 3 /Publihed: 3 October 3 Abtract: In thi paper, the deign of linear active diturbance reection control (LADRC) for high order yte i preented and the freuency repone i analyzed. Firt, the LADRC for iniu-phae procee i introduced, and the paraeterization of tuning parater, which reduce the tuning paraeter to controller bandwidth and oberver bandwidth, i given. With the tranfer function of the LADRC, the cloed-loop tranfer function, diturbance channel a well a enitivity tranfer function are derived, followed by the freuency repone analyi. An illutrative exaple for an eighth order proce i given to deontrate the effectivene of LADRC. Copyright 3 IFSA. Keyword: Linear active diturbance reection control (LADRC), Extended tate oberver (ESO), Tranfer function, Freuency analyi.. Introduction Due to the iple tructure and eay tuning feature of PID control, it reain the prevailing control approach in practical indutrial application []. In order to eet the increaing need of higher control accuracy and better perforance, a great nuber of ophiticated control trategie have been developed in the pat everal decade. However, ot of the depend on the odel accuracy of the controlled procee, or they are difficult to be ipleented in practical application. To build a bridge between the, one feaible olution to thi proble i the new idea active diturbance reection control (ADRC) propoed by Han []. The baic idea of ADRC i to deign an extended tate oberver (hort for ESO hereinafter) to etiate and cancel the total diturbance in real tie [3], which include the internal dynaic and external diturbance. In the fraework of ADRC, all the proble, including the etpoint tracking iue, diturbance reection, a well a dealing with the uncertaintie in the proce, can be treated a a diturbance reection proble [4], and therefore a atified perforance can often be achieved by uing the ADRC in variou type of yte, uch a ultivariable yte with tie delay [5], nonlinear yte with uncertainty [6], variable yte with diturbance [7], a well a the fault diagnoi iue of nonlinear yte [8]. Succeful application of ADRC can alo be found in practical indutrial ection, uch a the actuator [9, ], otion control [, ], power plant [3], power filter [4], power converter [5], etc. 346 Article nuber P_436

2 Senor & Tranducer, Vol. 57, Iue, October 3, pp The key of ADRC propoed by Han i to force the total yte behave a a erie of cacaded integrator by etiating the total ditance with ESO and cancelling it in the control law in real tie. The paraeterization, which greatly iplifie the tuning procedure, lead to linear active diturbance reection control (LADRC) and ake it uite practical [6-8]. In the LADRC, there are only two paraeter to be tuned, including the controller bandwidth and oberver bandwidth. It doe not reuire the accurate atheatical odel of the yte and it i eay to put into practical engineering proble, uch a gyrocope [9-], wate heat recovery yte [3], uperconducting RF cavitie [4], etc. The LADRC ha alo been forulated into a diturbance decoupling approach for ultivariable yte [5]. The recent thereotical analye of LADRC are dicued in [6, 7]. The freuency repone of the LADRC for the econd order yte wa analyzed in [8], which explicitly explained the intrinic reaon for the robutne and trong diurbance reection ability of LADRC in the preence of paraeter variation of the proce fro the perpective of freuency analyi. The robutne of the LADRC for the rotor haft poition of NASA high peed haft flywheel uing active agnetic bearing wa utified by freuency doain analyi [9]. To iprove the control perforance of the fat tool ervo yte for noncircular achining in preence of variou uncertaintie and diturbance, a control trategy cobining the LADRC and feedforward control wa propoed by Wu [3], in which the tranfer function deduction of the econd-order LADRC wa deontrated and the cloed-loop tability wa analyzed in freuency-doain [3]. The uantitative dynaic perforance analyi for the feedback control loop with the econd order ESO baed LADRC and the firt order lag proce wa propoed with regrad to non-overhoot characteritic, and the reult obatined indicated that the LADRC wa uch ore uperior than the tratidioanl PI in ot cae [3]. The iilar analyi wa alo perfored for the firt order plu dead tie procee [33]. The freuency perforance of the linear ESO wa analyzed by Zhao [34], which proved that the reuired tate at the deigned peed in pite of a large range of uncertaintie can be etiated by the linear ESO. The developent on ADRC wa reviewed and coprehenive coparion were propoed in the fraework of controlling uncertain yte [35]. An LADRC-baed control approach wa propoed in [36] for the load freuency control iue, and it perforance uperiority over the well tuned PI controller by genetic algorith linear atrix ineualitie (GALMI) in [37]. The robutne and excellent tie-doain perforance of LADRC wa alo utified fro the perpective of freuencyanalyi. However, the expreion of the tranfer function of the arbitrary order LADRC baed feedback control yte wa not explicitly propoed. The ain obective of the paper i to preent the baic forulation of the LADRC for a general noniniu phae proce, develop it unifor tranfer function for for a yte cobining the LADRC and a general iniu phae proce, and then earch for the intrinic reaon for the excellent perforance of LADRC in tie doain fro the perpective of freuency analyi. The effectivene of the propoed approach will be validated by the an illutrative exaple of the eighth order proce. Thi paper i organized a follow. Section focue on the developent of the LADRC. In Section, baed on the correponding tranfer function of the arbitrary order LADRC, the loop tranfer function, diturbance reection a well a enitivity tranfer function are derived. The freuency repone analye are hown in Section 3. In Section 4, the perforance coparion of LADRC and PID further validate the analyi. Finally, concluion and future reearch direction are given in Section 5.. Linear Active Diturbance Reection Control The forulation of the LADRC for a general iniu phae proce will be preented in thi ection. The cloed-loop yte i hown in Fig., where d i the external diturbance and w i the noie. For a iniu-phae dynaic yte, the plant can be decribed a b + b + + b+ b G () = ( n ) p n n + an + + a + a () where a, a,,a n-, b, b,,b are the poitive real nuber. Fro E. (), one can get y + a y + + a y + a y = bu + b u + + bu+ bu ( n) ( n ) n ( ) ( ) () Define f=-a n- y (n-) - -a y'-a y+b u () +b - u (- ) + + b u'+(b-b )u, we can obtain (3) () n ( n) ( n) y f(, t yy,,, y =, uu,,, u, dw, ) + bu where f i denoted a the total diturbance, b i the approxiate value of the high gain freuency b. r u + + Controller Proce w Fig.. Block diagra of a cloed-loop yte. d y 347

3 Senor & Tranducer, Vol. 57, Iue, October 3, pp Forulation of the Augented Proce Define an augented tate vector x=[x, x,, x n, x n+ ] T, where x =y, x =y,, x n = y (n), x n+ =f, and h=f. The augented tate pace repreentation of the controlled proce i: x = Ax + Bu + Eh, (4) y = Cx r + + k p b z z + k d kdn ( ) z n + z n + u ( ABCD,,, ) ( ABCD,,, ) Fig.. Block diagra of the (n+) th order LADRC baed yte. y where I A = n, B=[,,, b,] T, E=[,,,,] T, C=[,,,, ] T... Extended State Oberver Deign The key idea of the LADRC i to deign an ESO to etiate the total diturbance and actively cancel it in the control law in real tie. To etiate the tate in E.(4), the (n+) th order ESO i deigned a. z = Az+ Bu+ L( y z) y = Cz (5) where z=[z, z,, z n, z n+ ] T i the etiated tate and L i the oberver gain with L=[α, α,, α n, α n+ ] T. To iplify the tuning of the ESO, all the oberver pole are placed at w o. Thi yield: α =(n+)w o, α =.5n(n+)w o,, α n =(n+)w o n, α n+ =w o n+. With thi paraeterization, the oberver bandwidth w o i the only tuning paraeter in the ESO. The output of the proce and it derivative, a well a the total diturbance f can be etiated accurately baed on the controller output u and the proce output variable y provided the oberver bandwidth w o i appropriately elected..3. The Control Law Deign With the well tuned ESO, the total diturbance f can be etiated accurately. To copenate for the etiated total diturbance f, a tate feedback control law i deigned to ake the yte behave a a erie of cacaded integrator, the control law i deigned a u z u b = ( n+ + )/ (6) Then, the yte behave a a erie of cacaded integrator, which can be eaily controlled by u = kp ( r z) kdz kd z n n z n+ (7) To iplify the tuning, all the cloed-loop pole are placed at-w c. Thi yield k p =w c n, k d =nw c n-,, k dn- =nw c. The block diagra of the (n+) th order LADRC i hown in Fig.. A hown in Fig., the output variable y and it derivative, a well a the total diturbance f can be etiated in real tie baed on the extracted input and output data of the controlled proce with a uitable oberver bandwidth w o. Then, the etiated diturbance f can be fully copenated for with the PD controller by electing a uitable controller bandwidth w c. 3. Freuency Repone Analyi of the LADRC Syte 3.. Tranfer function Derivation of the (+) th Order LADRC A hown in [38], the (+) th order ESO baed LADRC can tabilize the n th order iniu-phae proce, where i an integer between and n. The correponding tranfer function block diagra of Fig. i hown in Fig. 3, where G p () i the n th order proce, and the (+) th order LADRC i deigned accordingly. D () R() G () U() + + Y() G () c Gp () f W() Fig. 3. Block diagra of the LADRC baed yte. In Fig. 3, R(), D(), and W() repreent the etpoint, the external diturbance, and the enor noie, repectively. G f () and G c () repreent the prefilter and feedback controller, repectively. Fro Fig., one can obtain: U() = G () G () R() G () Y() (8) f c c Let k p =k d, α =, k d =. Fro E. (5), E. (6), E. (7), and E. (8), one can get: G () = c C + + C + C n n n bcd + + Cd+ Cd (9) 348

4 Senor & Tranducer, Vol. 57, Iue, October 3, pp H H + H G k H H H H + n ( ) n n f () = p d + + d + d + d i, () where Cni = kdα ++ i, Cdi = kd ( + i) α, i for i=,,,. α =, α =(+)w o, α =.5 (+)w o,, α =(+)w o, α + =w o +. H di = C ni, i=,,, ; H nk = α (+-k), k=,,, +. Particularly, for the third order ESO baed LADRC, it i eay to derive. C + C + C n n n c() = bcd + Cd+ Cd G H + H + H + H 3 n3 n n n f() = p Hd + Hd+ Hd G k, () where C n =k p α +k d α +α 3, C n =k p α +k d α 3, C n =k p α 3 ; C d =, C d =k d +α, C d =k p +k d α +α ; H n3 =, H n =α, H n =α, H n =α 3 ; H d =C n, H d =C n, H d =C n. 3.. Freuency Repone Analyi of the (+) th Order LADRC Syte In thi ection, the perforance of the LADRC yte i analyzed in the freuency doain. In ot cae, the dynaic of a iniu-phae controlled proce can be repreented by E. (), where p=n- i it relative order, a n =, and aue b i an accurate etiation of b. In addition, all the coefficient in G p () are poitive real nuber. Without lo of generality, it i aued that all the pole and zeroe are negative real nuber. Otherwie, oe conugate coplex nuber ay appear and the following reult reain the ae. In other word, the proce can be rewritten a follow: ( + ) b λ G n i= i p () = ( ) n a ( + ) µ, () G () = c C n k = bcd l= ( + ) θk ( + ) ρ l (3) Cn C where θk =, d k = C ρl =. n l= Cd Then, cobining E. () and E. (3) yield the open loop tranfer function: G () = bc ( + ) ( + ) θ λ n k= k i= i Loop n bac d ( + ) l= ρl µ ( + ) (4) where the open loop gain i coputed a K=b C n /(ba C d ). Theore For the feedback control yte coniting of the nth order proce hown in E. () and the ( +) th order LADRC in Section 3. with a given ESO bandwidth w o and a given controller bandwidth w c, the open loop tranfer function ha the following freuency repone characteritic: (a) In the low freuency part of it Bode plot, the lope i nearly - db/dec, but the croover point between it or it extenion line and the vertical axi ove down a the value a increae. Particularly, the low freuency part are the ae with the preence of perturbation in all the proce paraeter regardle of a and b value provided b i an accurate etiation of b. (b) In the high freuency part of it Bode plot, the lope i the ae a -(p+)db/dec. The croover point between it or it extenion line and the vertical axi ove up a the value b increae. Proof. Firt, the open loop tranfer function G Loop () ha an integrator; therefore it ha an ayptote with a lope of - db/dec in the low freuency part of the freuency repone. In addition, the croover point between the low freuency part or it extenion line in the Bode plot of G Loop () and the vertical axi i up to where λ i and µ are the poitive real nuber and b λi =, i= b n µ = a. b lg K = lg ba k α p k d + α. In Fig., the proce i repreented by E.(); the (+) th order LADRC i eployed, where i an integer between and n. It i eay to follow that all the pole and zero of G c () have negative real part for a typical lower order LADRC with a or, and it i aued that all of the are negative real nuber for the facility of analyi. Otherwie, the following reult reain the ae. And thu, the feedback controller can be written a follow: In other word, in the low freuency part of the ayptote of Bode plot of G Loop () with different procee, the lope are the ae. With the value of b /(ba ) increaing, the croover point between the ayptote and the vertical axi ove up. Particularly, the low freuency part are the ae with the preence of perturbation in all the proce paraeter regardle of a provided that b i an accurate etiation of b. 349

5 Senor & Tranducer, Vol. 57, Iue, October 3, pp Second, in the high freuency part of the Bode plot of G Loop (), it ayptote can be rewritten a: ρ µ L w K p w l l= ( ) = lg ( + )lg n θk λ k= b = lg k dα+ ( p+ )lg w. b n (5) Finally, it can be obtained that the lope of the high freuency part i -(p+) db/dec, and b /(b) deterine the croover point between it or it extenion and the vertical axi. QED. Lea. Given a erie of given procee hown in E.() with the three coefficient a and b fixed, the low freuency part in the Bode plot of the correponding open loop tranfer function are the ae with the preence of all the other proce paraeter variation provided that b which i an accurate etiation value of b. In addition, the high freuency part in the Bode plot are iune to all the other paraeter variation except b. Theore. For the feedback control yte with the nth order proce hown in E. () and the (+) th order LADRC preented in Section 3., aue b i an accurate etiation of the proce paraeter b, the diturbance reection tranfer function G YD () ha the following great freuency characteritic: a) in the low freuency part of the Bode plot of G YD (), it ha an ayptote with a lope a + db/dec. the lope are the ae but the value of the croover point ha oething to do with the coefficient b, a well a the tuning paraeter of the LADRC, while it ha nothing to do with all the other coefficient. b) The high freuency part of the ayptote of Bode plot of G YD () can be coputed by lgb - plgw, which explicitly indicate that it only depend on the coefficient b, a well a the relative order p. Proof. The tranfer function fro the diturbance input to the controlled output in Fig. i coputed by: G YD + Y () bb ( + + bc d) () = = n+ + D () b + + bc n (6) In the diturbance channel tranfer function G YD (), there i a differential eleent, and thu in the low freuency part of the Bode plot of G YD (), it ha an ayptote with a lope a + db/dec. The open loop gain i coputed a b C d /C n, which ean that the croover point between the extenion line of the low freuency part in the Bode plot of G YD () and the vertical axi i up to lg b kdα /( kpα + ). In = other word, in the low freuency part of the ayptote of Bode plot of G YD () for different procee, the lope are the ae but the value of the croover point i deterined by the coefficient b, a well a the tuning paraeter of the LADRC, while it ha nothing to do with all the other coefficient. On the other hand, following the ae analyi approach in Theore, the high freuency part of the ayptote of Bode plot of G YD () can be coputed by lgb -plgw, which explicitly indicate that it only depend on the coefficient b, a well a the relative order p. In addition, it ha nothing to do with the other coefficient of the controlled proce, which obviouly how that the great freuency characteritic and the robutne of the propoed LADRC againt the diturbance inerted into the control loop or the proce paraeter variation. Lea. Given a erie of given procee hown in E. () with a fixed paraeter b and all the other coefficient perturbated, the Bode plot of the correponding diturbance reection tranfer function are the ae. Theore 3. For the feedback control yte with the proce hown in E. () and (+) th order LADRC propoed in Section 3., aue b i an accurate etiation of the proce paraeter b, the enor noie tranfer function G UW () ha the following great freuency characteritic: (a) in the low freuency part of the Bode plot of G UW (), it ha an ayptote with a lope a db/dec. The lope are the ae but the value of the croover point i only deterined by the coefficient (a /b ), a well a the tuning paraeter of the LADRC, while it ha nothing to do with all the other coefficient. (b) The high freuency part of the ayptote of Bode plot of G UW () can be coputed by lg( kdα + / b ) lg w, which explicitly indicate that it only depend on the coefficient b. Proof. The tranfer function fro the enor noie to the proce output in Fig. i: G UW n+ U() Cn + + a C () = = n+ + W() b + + bc n n (7) For the enor noie tranfer function G UW (), it doe not have any integrator or differential eleent, and thu in the low freuency part of G UW () it ha an ayptote with a horizontal line. The open loop gain i coputed a a /b, which ean that the croover point between the extenion line of the low freuency part of the Bode plot of G UW () and the vertical axi i up to lg(a /b ). In other word, in the low freuency part of the ayptote in the Bode plot of G UW () with different procee, the lope are the ae but the value of the croover point ha oething to do with the coefficient a /b, while it ha nothing to do with all the other coefficient and the tuning paraeter of the LADRC. 35

6 Senor & Tranducer, Vol. 57, Iue, October 3, pp On the other hand, the high freuency part of the ayptote of the Bode plot of G UW () can be obtained a lg( k / b ) lg w, which explicitly dα + indicate that it only depend on the coefficient b, a well a the LADRC tuning paraeter w o and w c. In addition, it ha nothing to do with the other coefficient of the controlled proce and the relative order p. It i hown that the great freuency characteritic and the robutne of the propoed LADRC againt the enor noie inerted into the control loop or the proce paraeter variation. Lea 3. Given a erie of given proce hown in E. () with fixed coefficient a and b, all the other coefficient are perturbated, the Bode plot of the correponding enor noie tranfer function are the ae. 4. Illutrative Exaple An illutrative exaple will be preented to deontrate the effectivene and robutne of the propoed LADRC approach in an eighth order proce in [39]. The perforance i copared with the PID control approach propoed in [4]. In addition, the robutne of the propoed LADRC yte for the eighth order proce i hown fro the perpective of freuency analyi. 4.. Tie-Doain Repone of LADRC Conider the eighth order proce a follow [39]: G () = (8) The third order LADRC i applied to the proce hown in E. () and the perforance i copared to the PID controller in [4]. The choen paraeter are a follow: b =9448, w c =95.5 rad/, and w o = 99rad/. The perforance of the LADRC and the PID controller i hown in Fig. 4, where the tep diturbance with a agnitude of.5 i applied at.3 and a band-liited white noie with a noie power of -9 i applied. A can be een fro Fig. 4, the perforance of the yte with the propoed third order LADRC trategy i uch better than the PID control trategy in [4]. The LADRC yte deontrate excellent reference tracking perforance, trong diturbance reection ability, and robutne to noie. Fig. 5. Note that all the coefficient of the proce vary ±3 % except keeping the four paraeter unchanged: a, b, a 8, b 7. In Fig. 5, the ae third order LADRC i applied without changing the tuning paraeter. Output y.5 (a) Noinal value.5 PID LADRC.5. Tie(ec.) (b) +3% variation.5.5 (c) -3% variation.4. Output y.5 Output y.5 Output y Tie(ec.).5. Tie(ec.) Fig. 5. The unit tep repone of the LADRC and PID control yte..4. PID LADRC Tie(ec.) Fig. 4. Repone of yte with LADRC and PID controller. To tet the robutne of the propoed LADRC approach, the unit tep repone of the yte with paraeter variation in the proce are hown in A hown in Fig. 5, with the propoed third order LADRC trategy, the yte reain excellent perforance in the preence of paraeter variation in the proce. The robutne and perforance uperiority of the propoed LADRC over the PID control trategy are alo validated. 4.. Freuency-Doain Repone of LADRC To deontrate the intrinic reaon for the robutne of the propoed LADRC trategy, the 35

7 Senor & Tranducer, Vol. 57, Iue, October 3, pp Bode plot of the open loop, diturbance reection, a well a the noie enitivity tranfer function of the yte with proce paraeter variation are hown in Fig. 6, Fig. 7, and Fig. 8, repectively. Magnitude (db) Phae (deg) Magnitude (db) Phae (deg) Noinal value +3% variation -3% variation Bode Diagra Freuency (rad/ec) Fig. 6. Bode plot of G Loop () for LADRC with proce paraeter variation Bode Diagra Freuency (rad/ec) Noinal value +3% variation -3% variation Fig. 7. Bode plot of G YD () for LADRC with proce paraeter variation. A can be een fro Fig. 6, Fig. 7, and Fig. 8, the Bode plot of G Loop (), G YD () and G UW () for the yte with the propoed LADRC approach are nearly the ae in the preence of large variation in the proce paraeter. A hown in Fig. 6, in the preence of large variation of the proce paraeter, the low freuency part and high freuency part for the Bode plot of the open loop tranfer function G Loop () are nearly the ae, which confir the freuency analyi reult. The Bode plot of the diturbance reection tranfer function G YD () are iune to the paraeter variation, and it utifie the trong diturbance reection ability of the LADRC approach. The Bode plot of the noie enitivity tranfer function G UW () of the three cae deontrate the trong robutne of LADRC to noie. 5. Concluion In thi paper, the LADRC for a general iniuphae high order proce i forulated, followed by the derivation of the tranfer function. The freuency repone of the LADRC baed feedback control yte are analyzed. The iulation reult of LADRC on the eighth order proce further validated the theoretical analyi and deontrate it excellent perforance in diturbance reection and robutne. Acknowledgeent Thi work i upported by the National Natural Science Foundation of China (Grant No. 6344) and the Contruction Fund fro Beiing Municipality,China.The author would like to thank Prof. Zhiiang Gao at ClevelandStateUniverity for hi inightful and valuable uggetion.the anonyou reviewer coent are alo greatly appreciated. 5 Bode Diagra Reference Magnitude (db) Phae (deg) Freuency (rad/ec) Fig. 8. Bode plot of G UW () for LADRC with proce paraeter variation. Noinal value +3% variation -3% variation []. K. J. Åtrö, T. Hägglund, PID controller: theory, deign, and tuning, Intruent Society of Aerica, 995. []. J.-Q. Han, Control theory: i it a theory of odel or control? Syte Science and Matheatical Science, Vol. 9, Iue 4, 989, pp (in Chinee) [3]. J.-Q. Han, Fro PID to active diturbance reection control, IEEE Tranaction on Indutrial Electronic, Vol. 56, Iue 3, 989, pp (in Chinee) [4]. D. Sun, Coent on active diturbance reection control, IEEE Tranaction on Indutrial Electronic, Vol. 54, Iue 6, 7, pp [5]. Y.-Q. Xia, P. Shi, G.-P. Liu, D. Ree, J.-Q. Han, Active diturbance reection control for uncertain ultivariable yte with tie-delay, IET Control Theory & Application, Vol., Iue,, pp

8 Senor & Tranducer, Vol. 57, Iue, October 3, pp [6]. B.-Z. Guo, Z. Zhao, On the convergence of an extended tate oberver for nonlinear yte with uncertainty, Syte & Control Letter, Vol. 6, Iue 6,, pp [7]. D. Wu, T. Zhao, K. Chen, X. Wang, Application of active diturbance reection control to variable pindle peed noncircular turning proce, International Journal of Machine Tool and Manufacture, Vol. 49, Iue 5, 9, pp [8]. B. Yan, Z. Tian, S. Shi and Z. Weng, Fault diagnoi for a cla of nonlinear yte via ESO, ISA Tranaction, Vol. 47, Iue 4, 8, pp [9]. X.-X. Shi, S.-Q. Chang, Preciion otion control of a novel electroagnetic linear actuator baed on a odified active diturbance reection controller, Proceeding of the Intitution of Mechanical Engineer Part I Journal of Syte and Control Engineering, Vol. 6, Iue I5,, pp []. H.-L. Xing, J.-H. Jeon, K. C. Park, Il-Kwon Oh, Active diturbance reection control for precie poition tracking of ionic polyer-etal copoite actuator, IEEE/ASME Tranaction on Mechatronic, Vol. 8, Iue, 3, pp []. G. Tian, Z.-Q. Gao, Benchark tet of active diturbance reection control on an indutrial otion control platfor, in Proceeding of the Aerican Control Conference (ACC' 9), St. Loui, Miouri, USA - June, 9, pp []. S. L. Li, X. Yang, D. Yang, Active diturbance reection control for high pointing accuracy and rotation peed, Autoatica, Vol. 45, Iue 8,, pp [3]. Y.-Q. Xia, B. Liu, M.-Y. Fu, Active diturbance reection control for power plant with a ingle loop, Aian Journal of Control, Vol. 4, Iue,, pp [4]. Q. Zhong, Y. Zhang, J. Yang, J. Wu, Non-linear auto-diturbance reection control of parallel active power filter, IET Control Theory & Application, Vol. 3, Iue 7, 9, pp [5]. B.-S. Sun, Z.-Q. Gao, DSP-baed active diturbance reection control deign for a -kw H-bridge DC DC power converter, IEEE Tranaction on Indutrial Electronic, Vol. 5, Iue 5, 7, pp [6]. Z.-Q. Gao, Scaling and bandwidth-paraeterization baed controller tuning, in Proceeding of the Aerican Control Conference (ACC' 3), pp [7]. Z.-Q. Gao, Active diturbance reection control: A paradig hift in feedback cotnrol yte deign, in Proceeding of the Aerican Control Conference (ACC 6), 6, pp [8]. X. Chen, D. H. Li, Z.-Q. Gao, C.-F. Wang, Tuning ethod for econd-order active diturbance reection control, in Proceeding of the Chinee Control Conference (CCC' 6), pp [9]. Q. Zheng, L.-L. Dong, D. H. Lee, Active diturbance reection control for MEMS gyrocope, IEEE Tranaction on Control Syte Technology, Vol. 7, Iue 6, 9, pp []. Q. Zheng, L.-L. Dong, D. H. Lee, Z.-Q. Gao, Active diturbance reection control for MEMS gyrocope, in Proceeding of the Aerican Control Conference (ACC 8), 8, pp []. L.-L. Dong, David Avaneian, Drive-ode control for vibrational MEMS gyrocope, IEEE Tranaction on Indutrial Electronic, Vol. 56, Iue 4, 9, pp []. L.-L. Dong, Q. Zheng, Z.-Q. Gao, On control yte deign for the conventional ode of operation of vibrational gyrocope, IEEE Senor Journal, Vol. 8, Iue, 8, pp [3]. J.-H. Zhang, J. Feng, Y. Zhou, F. Fang, H. Yue, Linear active diturbance reection control of wate heat recovery yte with organic Rankine cycle, Energie, Vol. 5, Iue,, pp [4]. J. Vincent, D. Morri, N. Uher, Z. Gao, S. Zhao, A. Nicoletti, Q. L. Zheng, On active diturbance reection baed control deign for uperconducting RF cavitie, Nuclear Intruent and Method in Phyic Reearch Section A: Accelerator, Spectroeter, Detector and Aociated Euipent, Vol. 643, Iue,, pp. -6. [5]. Q. Zheng, Z.-Z. Chen, Z.-Q. Gao, A practical approach to diturbance decoupling control, Control Engineering Practice, Vol. 7, Iue 9, 9, pp [6]. F. J. Goforth, Q. Zheng, Z.-Q. Gao, A novel practical control approach for rate independent hyteretic yte, ISA Tranaction, Vol. 5, Iue 3,, pp [7]. Q. Zheng, L.-Q. Gao, Z.-Q. Gao, On validation of extended tate oberver through analyi and experientation, Journal of Dynaic Syte, Meaureent, and Control, Vol. 34, Iue,, pp. 455 (6 page). [8]. G. Tian, Z.-Q. Gao, Freuency repone analyi of active diturbance reection baed control yte, in Proceeding of the 6 th IEEE International Conference on Control Application Part of IEEE Multi-conference on Syte and Control, 7, pp [9]. B. X. S. Alexander, R. Rarick, L.-L. Dong, A novel application of an extended tate oberver for high perforance control of NASA HSS Flywheel and fault detection, in Proceeding of the Aerican Control Conference (ACC'8), pp [3]. D. Wu, C. Ken, X.-K. Wang, Tracking control and active diturbance reection with application to noncircular achining, International Journal of Machine Tool & Manufacture, Vol. 47, Iue 5, 7, pp [3]. D. Wu, C. Ken, Deign and analyi of preciion active diturbance reection control for noncircular turning proce, IEEE Tranaction on Indutrial Electronic, Vol. 56, Iue 7, 9, pp [3]. R.-G.Yang, M.-W. Sun, Z.-Q. Chen, Active diturbance reection control on firt-order plant, Journal of Syte Engineering and Electronic, Vol., Iue,, pp [33]. R.-G. Yang, M.-W. Sun, Z.-Q. Chen, Perforance analyi of active diturbance reection control on the firt-order-plu-dead-tie plant, ICIC Expre Letter, Vol. 5, Iue 4B,, pp [34]. C.-Z. Zhao, X.-X. Yang, J. Xiong, X.-R. Lin, Capability of the extended tate oberver for iniu phae plant with unkown order and uncertain order and uncertain relative degree, in Proceeding of the Chinee Control Conference,, pp [35]. Y. Huang, W. Xue and C.-Z. Zhao, Active diturbance reection control ethodology and theoretical analyi, Journal of Syte Science and Matheatical Science, Vol. 3, Iue 9,, pp. -9. (in Chinee) [36]. L.-L. Dong, Y. Zhang, Z.-Q. Gao, A robut decentralized load freuency controller for 353

9 Senor & Tranducer, Vol. 57, Iue, October 3, pp interconnected power yte, ISA Tranaction, Vol. 5, Iue 3,, pp [37]. D. Rerk Preedapong, A. Haanovic, A. Feliachi, Robut load freuency control uing genetic algorith and linear atrix ineualitie, IEEE Tranaction on Power Syte, Vol. 8, Iue, 3, pp [38]. C.-Z. Zhao, Capability of ADRC for plant with unkonwn order and/or uncertain relative degree: theory and application, Doctoral diertation, Intitute of Syte Science, Acadey of Matheatic and Syte Science, Chinee Acadey of Science, June. (in Chinee) [39]. V. Sehadri Krihnaurthy, Model reduction uing routh tability criterion, IEEE Tranaction on Autoatic Control, Vol. 3, Iue 4, 978, pp [4]. S. N. Deepa, G. Suguaran, Deign of PID controller for higher order continuou yte uing MPSO baed odel forulation techniue, International Journal of Electrical and Electronic Engineering, Vol. 5, Iue 4,, pp [4]. P. Kundur, Power yte tability and control, McGraw-Hill, 994. [4]. W. Tan, Unified tuning of PID load freuency controller for power yte via IMC, IEEE Tranaction on Power Syte, Vol. 5, Iue,, pp Copyright, International Freuency Senor Aociation (IFSA). All right reerved. ( 354