Induction motor fault detection and isolation through unknown input observer

Transcription

1 Scientific Reearch and Eay Vol. 5(2), pp , 18 October, 21 Available online at ISSN Academic Journal Full Length Reearch Paper Induction motor fault detection and iolation through unknown input oberver Khalaf Salloum Gaeid* and Hew Wooi Ping Department of Electrical Engineering, Univerity of Malaya, Kuala Lumpur, 563, Malayia. Accepted 5 October, 21 Unknown input oberver (UIO) can be ued in the model-baed fault detection and iolation (FDI) cheme to reduce or almot eliminate the effect of unknown diturbance on the multi input multi output (MIMO) plant/ytem. In thi paper, a new FDI of the MIMO ytem wa carried out in a well a the deign of many fault iolation bank of UIO ha been done. hee bank are ued to generate reidual that are inenitive to unknown diturbance or noie. o make ure bet detection and iolation of the fault, thee bank generate reidual, which are enitive to only one fault. he fault in the actuator i detected and iolated with a lower fale alarm rate effectively. Key word: Fault detection and iolation, induction motor, MIMO plant, reidual, unknown input oberver. INRODUCION Nowaday, there i a demand for high performance electric drive. hee derive can be capable of accurately achieving peed command. hi ha necearily lead to more ophiticated control method to deal with uch an iue. Special attention wa directed induction motor becaue of known reaon uch a ize, cot, efficiency (Khalaf et al., 29). Fault detection and iolation (FDI) have received a great deal of attention in the lat 2 year. A a control ubject, the diagnoi i baed on the model of the ytem under tudy. he model-baed FDI approach involve two main tep: reidual generation and deciion making. hi model uually repreent the normal behavior of the ytem, in the abence of any fault. Detection of udden or developing fault which occur in actuator, enor, or other component may be economically reaonable and may contribute to a afe operation or provide a fault ride through capabilitie (Combatel et al., 22). In the literature, the linear oberver who are completely independent of the immeaurable diturbance are known a unknown input oberver (UIO). he principle of (UIO) i to make the tate etimation *Correponding author. alim_hazim2@iwa.um. edu.my. el: error de-coupled from the unknown input (diturbance). An oberver can be defined a an UIO for the ytem decribed by equation (1), if it tate etimation error vector e ( approache zero aymptotically, regardle of the preence of the unknown input (diturbance) in the ytem. he ytem with unknown input oberver play a vital role in robut model-baed fault detection the baic idea behind the ue of oberver for fault detection to form reidual from the difference between the actual ytem output and the etimated output uing an oberver (Patton and Chen, 1997). he fault of the aircraft actuator are detected and iolated uing (UIO) (Stefen et al., 25). he deigned S oberver i ued for detection and recontruction of fault, which can affect a non-linear model and can be applied directly for fault detection and iolation of actuator fault (Dan and Kai-Yew, 26). he uncertainty of the model i till a big problem for election and adaptation of threhold of the model-baed fault detection and iolation (Mohammed et al., 28). he fault detection and iolation problem (FDIP) in dynamic ytem conit of generating a diagnotic ignal, which ha to be different from zero during a pecific fault occurrence and inenitive to other input, uch a diturbance and other fault ignal (Guang- Hong, 27). Benloucif and Balaka (26) preented a cheme of

2 Gaeid and Ping 3153 oberver with nonlinear decoupling ued for reidual generation to detect the fault in the induction machine. rzynadlowk (21), preented nonlinear oberver ued in the fault diagnoi of the induction motor. Sarah K. Spurgeon (28) preented liding mode oberver have unique propertie, in that the ability to generate a liding motion on the error between the meaured plant output and the output of the oberver. Chung-Wei et al. (26) developed a fault detection procedure baed on the PI controller of the torque oberver tructure and the dicrete wavelet tranform (DW) method to detect a ervomechanim fault. Jaon and Pieter (26) tudied a fault detection, iolation, and recovery (FDIR) ytem, in the cae of an aircraft elevator redundancy control ytem, and demontrate how to trace requirement to a deign, create tet baed on thoe requirement. Zhengang et al. (25) propoe a novel cheme of enor and actuator (FDI) for multivariate dynamic ytem in the preence of proce uncertaintie. Wang (21) preented new approach in enor fault etimation of the UIO baed fault cla iolation and etimation. he aim of thi paper i to implement fault detection and iolation of induction motor oberver-baed approache uing unknown input oberver. Induction motor modeling he tate pace of the induction motor in the preent of fault i:. X = Ax + B v + Ed I = Cx + f x R n m i the tate vector, I R i the output vector, r q v R i the known input vector and d R i the unknown input (or diturbance) vector. A, B, C and F are known matrice with appropriate dimenion, according to the ytem hown in (S.M. Bennett et al., 22 and Hafiz Bilal Ahmad, 25). x ] = [ i λ (2) i ] = [ id iq (3) λ = [ λ d λq ] (4) λ d, λ q are direct and quadrature tator flux component v ] = [ vd vq (5) (1) A = A A ; A ] (6) [ A 22 he value of ( A, A, A, A ) a follow: 22 A = 1/ σ[1/ τ + (1 σ ) / τ I ] (7) 11 Where,, r are the total leakage factor, tator time, rotor time contant repectively. A = L m / σ L Lr [(1/ τ r) I ω o ] (8) 12 J L m, L, L r i the magnetizing inductance, tator inductance, and rotor inductance repectively, Andrzej, (21). A = ( Lm / ) I 21 τ (9) A = (1/ τ r I + 22 ) ω o J (1) I i an identity matrix and J= [ -1; 1 ] B = B ] (11) [ 1 B 1 = (1/ σ L ) I (12) C = [I ] (13) Deign of the general tructured UIO he firt major goal of thi paper i to deign a full-order unknown input oberver (UIO) baed on the tructure of equation (2).he tructure of the unknown input oberver (UIO) a follow: z. = Fz( + Bu( + Ky( t ) (14) x ˆ = z( + Hy( (15) xˆ i the etimated tate vector, z i the tate of thi full-order oberver, and F,, K, H are matrice to be deigned for achieving unknown input de-coupling and other deign requirement. he oberver decribed by equation (2) i illutrated in Figure 1. he error between the plant tate vector and etimated tate vector i e (. e( = x( xˆ( he dynamic error i: (16)... e( t ) = x( t ) xˆ ( t ) (17) Subtituting the above equation in equation (17) yield:

3 3154 Sci. Re. Eay here i exiting gain matrix K uch that the etimation of the error: e( = x( xˆ(, will converge to zero when t heorem2. he econd condition of heorem 1, which tate that the pair (A1, C) i detectable, i equivalent to Rank of: I A C E = n + m (25) Figure 1. Induction motor with unknown input oberver. (n, m) i the order of the ytem and dimenion of the E matrix repectively.. e ( = ( A HCA K1C ) e( + [ F ( A HCA K1C ) z( + [ K 2 HCA K1C ) H ] y( + [ ( I HC)] Bu( u) + [ HC I ) Ed ( K = K1 + K 2 (19) ( (18) he gain matrix K 1 i found uing bilinear feedback to cancel the firt two column in the error dynamic. K2 can be calculated uing equation (21) (Zhengang et al., 25) K = FH (2) 2 F 1 = A HCA K C (21) If all Eigen value of F are table then the error e ( will approach zero aymptotically, thi mean that the oberver i an unknown input oberver for the original ytem (Floquet et al., 27). he mot important thing of the model-baed FDI i the generation of reidual. o provide ueful information for FDI, the reidual hould be: r e ( if and only if f ( (22) hen the fault can be detected by comparing the function of reidual generated with the threhold (J. Chen, 28). here are two theorem control the operation condition of the unknown input oberver. heorem1. here are two condition hould be atified: 1. Rank (E*C) hould be equal to the rank (E). (he checking prove that the rank (C*E) = 1), and the rank of (E = 1) o the firt condition i atified. 2. (A1, C) i detectable. A = A 1 (23) = I HC (24) Fault detection and iolation algorithm Fault detection he claical oberver-baed fault detection cheme i to contruct an oberver, which take the input and output of a ytem and generate a ignal called reidual. hi ignal i proceed to decide if the ytem i faulty or healthy (Saverio Armeni et al., 28). Fault detection and iolation technique for induction motor i decribed in the beginning, the tate pace matrice of the induction motor. Uing MALAB to find the tate feedback controller (K) by pole placement method: [ K l ] = lqr( A, B, Q, R, N ) (26) he calculation of the tate gain K i choen to minimize the following cot function. j = 1/ 2 ( X ( k) QX ( k) + u ( k) Ru( k)) K = (27) he matrix N in equation (26) i et to zero for implicity. Furthermore, returned are the olution of the aociated algebraic Riccati equation and the cloed-loop Eigen value. = eig( A BK ) (28) k l = =

4 Gaeid and Ping 3155 = 1.e + 2* i i i i In the deign of UIO, the deired location of the pole were elected at (= -2,-3,-4,-5). Figure 2. Additive actuator fault. F = he rank condition of the (C*E) = rank (E) mean that the correponding tate coupled with unknown input mut be obtainable through the meaurement output. So, it hould be noticed that the number of output ignal no le than the number of unknown input (Young-Real et al., 1994). For table ytem the following condition hould be atified. M = A F kc = (29) Figure 3. Senor fault on tator current (Iq) no uncontrollable tate (healthy ytem). Due to equation (3), the controllability matrix i: 1.e - 12 * M = Fault iolation cont = 1.e + 6 * [ ; ; ; ] he detection of any fault hould be followed by the fault iolation, which will ditinguih (iolate) a particular fault from other, the meaning of fault iolation i imply to find which reidual not atify the fault condition (Shao-Kung Chang et al., 1997). o prove the ability to track the output, controllability of the ytem and the uncontrollable tate in the preence of fault hould be teted, according to the following formula: cont = ctrb( A, B) (3) he number of uncontrollable tate (UC) i: UC=length (A)-rank (con In thi paper, the length of the matrix A i 4 and the rank of the controllability matrix i 4. hi mean there i he imulation of actuator fault a additive fault will be hown in Figure 2, the bia fault for enor for the quadrature or direct component of the tator current a will be hown in Figure 3. RESULS AND DISCUSSION he nonlinear propertie of induction motor are neglected a well a conidering a pure inuoidal input ource. Simulink implementation of UIO fault detection baed for (MIMO) ytem i carried out. In the preence of the actuator or enor fault, thi approach could decouple any fault. Figure 1 how the unknown input oberver coupled with the induction motor.

5 3156 Sci. Re. Eay Figure 4. Reidual generation and data converion. Figure 5. Propoed tructure. Figure 2 repreent the additive actuator fault circuit. Figure 3 repreent the tator current enor (Iq) circuit. Figure 4 how the reidual generation with the monitoring ytem. Figure 5 repreent the propoed tructure of the ytem. Figure 6 repreent actuator fault detection after the repone of the tate exceed the

6 Gaeid and Ping fault detection of tate State Iteration Figure 6. Actuator fault detection. 1 Fault detection and threhod.5 tate x 1-15 reidual Figure 7. Healthy cae output and reidual. threhold (.3), Conequence of a fault in the actuator would mot likely be intability (fluctuation). Figure 7 repreent the healthy cae. All tate are within the threhold, and the tet of controllability of the ytem prove that. o check the number of uncontrollable tate for the healthy ytem, the difference between length of matrix (A) and rank of controllability equal zero (no uncontrollable tate). According to the reult of equation (26) and (27) the ytem pole' location were to left hand ide of -plane, which prove that the ytem table for all value of a in Figure 8. Figure 9 how the reult of fault iolation when the fault occur in the actuator at.4. It how that the reidual generation method can detect the fault with reaonable accuracy. he nonzero (M) reult of equation (29) may be due to uncertainty of ome parameter of induction motor. In thi paper, the induction motor wa 4 th order. able 1 give the parameter of the

7 3158 Sci. Re. Eay Figure 8. Stability checking after the fault iolated..1.9 Amplitude of the iolated fault a m p litu d e o f th e i o la te d fa u lt iteration Figure 9. Actuator fault iolation. Iteration

8 Gaeid and Ping 3159 able 1. Induction motor parameter. Item Value Unit Power 3 Hp Stator reitance.534 Ohm Rotor reitance.816 Ohm Stator inductance 73e-3 Henry Rotor inductance 71e-3 Henry Magnetizing inductance 69e-3 Henry frequency 5 Hz Speed 1725 RPM Voltage 22 volt induction motor. CONCLUSIONS here have been a number of technique developed for fault detection and iolation bae oberver named qualitative and quantitative over the pat decade for fault detection and iolation variou ytem. he ytem have performance pecification and uncertain characteritic, o it cannot be modeled perfectly. hi paper ha introduced the unknown input oberver-baed approach for fault detection of induction motor. MALAB/SIMULINK implementation of the propoed tructure had confirmed the effectivene of thi UIO of the FDI method. he unknown input oberver can be detecting more fault like intrument fault uch a gain and bia change. For detection of fault, one filter i enough but for iolation a et of a filter bank are needed. When one or more fault in proce parameter are directly iolated, it i required to etimate the degree of thoe fault to take appropriate fault accommodation action, which i part of the fault tolerant control. REFERENCES Bennett SM, Patton RJ, Daley S, Newton DA (22). orque and Flux Etimation for Rail raction Sytem in the Preence of Intermittent Senor Fault, IEE Int. Conf. Control (UKACC), pp Chen J (28). Robut Fault Detection uing Unknown Input Oberver, lecture from 8th IRS coure, Brunel Univerity, UK. Chung-Wei C, Wen Peng, Mi Ching (26). Servomechanim Fault Detection Baed on Load orque Oberver and Dicrete Wavelet ranform, JSME Int. J., Serie C, 49(2): Combatel SL, Petropol S, Gentil S (22) Model-Baed and Wavelet Approache to Induction Motor on-line Fault Detection. Control Eng. Pract. J., 1(5): Dan W, Kai-Yew L (26). Adaptive Unknown Input Oberver Approach for Aircraft Actuator Fault Detection and Iolation, Int. J. Adaptive Control Signal Proce., 21: Floquet, Edward C, Spurgeon SK (27). On Sliding Mode Oberver for Sytem with Unknown Input. Int. J. Adaptive Control Signal Proce., pp Guang-Hong Y, Heng W (27). An LMI-baed Approach to Fault Detection for Uncertain State Feedback Control Sytem, IEEE Int. Conf. Control Appl., CCA, pp Hafiz BA (25). UIO baed Fault Detection and Iolation in Dynamic Sytem Jaon G, Pieter JM (26). Applying Model-Baed Deign to a Fault Detection, Iolation, and Recovery ytem, Military Embedded Syt. J., pp Khalaf SG, Hew WP, Haider A, Mohamed F (29). Indirect Vector Control of a Variable Frequency Induction Motor Drive (VCIMD), IEEE Conf., ICICI-BME, pp Mohammed C, Abdelkader A, Didier M, Joe R,.Young M (28). Fuzzy Oberver for Fault Detection and Recontruction of Unknown Input Fuzzy Model. Int. J. Modeling Identification Control, 3: Patton RJ, Chen J (1997). Oberver -Baed Fault Detection and Iolation: Robutne Appl., Control Eng. Pract. J., 5: Sarah KS (28). Sliding Mode Oberver: A urvey, Int. J. Syt. Sci., 39(8): Saverio A, Aleandro C, Edoardo M (28). Robut Fault Detection and Iolation Filter Deign with Senitivity Contraint, Int. J. Adaptive Control Signal Proce., 23(1): Shao-Kung C, Wen-ong Y, Pau-Lo HSU (1997). Deign of General Structured Oberver for Linear Sytem with Unknown Input, J. Franklin Intitute, 334B (2): Stefen H, StanilawH Z, Shao-Kung C, Nicole R (25). Oberver Deign for Sytem with Unknown Input, Int. J. Appl. Math. Comput. Sci., 15(4): Wang Z (21). Unknown Input Oberver Baed Fault Cla Iolation and Etimation IEEE, Proceeding of the 29th Chinee Control Conf., pp Young-Real K, Seung-Ki S, Min-Ho P (1994). Speed Senorle Vector Control of Induction Motor Uing Extended Kalman Filter. IEEE ran. Indutry Appl., 3(5): Zhengang H, Weihua L, Sirih LS (25). Fault Detection and Iolation in the Preence of Proce Uncertaintie. Control Eng. Pract. J., 13: Andrzej M (21). Control of Induction Motor, Academic Pre, Univerity of Nevada. Benloucif ML, Balaka H (26). Robut Fault Detection for an Induction Machine, IEEE Conf. (WAC), pp. 1-6.