7 International Conference on Electrical Engineering and Automation Control (ICEEAC 7) ISBN: 978--6595-447-9 Active Disturbance Rejection Control of Bearingless Induction Motor Wen-Shao BU, and Yong-Quan HUANG Electrical Engineering College, Henan University of Science and echnology, Luoyang, 473, China Information Engineering College, Henan University of Science and echnology, Luoyang, 473, China wsbu@63.com Keywords: Bearingless Induction Motor, Active Disturbance Rejection Control, Rotor Flux Orientation, Robtness. Abstract. o improve the dynamic control performance of bearingless induction motor (BLIM), the active disturbance rejection control strategy is presented. Based on the rotor flux orientation inverse decoupling strategy, an active disturbances rejection control (ADRC) system is designed to replace the PID control system. he cross coupling items, motor parameter change and load are all regarded as disturbance. he total disturbance is estimated by an extended state observer (ESO), and compensated by a nonlinear state error feedback (NLSEF) controller. Simulation results show that the system has better dynamic decoupling performance and strong robtness. Introduction Bearing less induction motor (BLIM) is a new type of motor with the rotary drive and rotor self-spension functions. In BLIM, there exist complex electromagnetic coupling, and its parameters are time variant. he PID regulator is easy to implement, but it is difficult to meet the needs of high performance control of BLIM. Many advanced control strategies have been studied for BLIM, but the existing control system either is complicate, or hard to determine. Jingqing Han proposes an active disturbance rejection control method (ADRC) in [5]. ADRC absorbs the essence of PID controller, i.e. eliminating error based on the error feedback; at the same time, it online estimates and compensates the total disturbances of system. he ADRC control law doesn t depend on the accurate model, it has a strong adaptability and resistance to the disturbance, and it can be ed for the linear, nonlinear and time-varying systems. Now, the ADRC has been successfully applied in the fields of aerospace, chemical process system, maglev system, motion control system and so on. W.F Su has explored the application problem of ADRC to the asynchrono motor control [6], the stronger robtness and anti-interference performance can be achieved. In reference [7], ADRC is applied to the spension system of bearingless alternate pole permanent magnet motor, and a good dynamic decoupling performance is obtained. In [4], the ADRC controller is designed for BLIM, the spension control performance is improved effectively. In this paper, to further improve the control performance of BLIM, based on the inverse system decoupling, the ADRC controller is designed for each pseudo linear system. he simulation results have shown that the control system has better dynamic decoupling control performance, and has stronger robtness. Inverse System Decoupling Control of BLIM For BLIM, if the system state variables x, input variables u and output variables y are defined as the followings: x = [ x, x, x, x, x, x, x, x ] = [, β,, β, i, i, ψ, ] 3 4 5 6 7 8 sd sq r () U = [ u, u, u, u ] = [ u, u, i, i ] () 3 4 sd sq sd sq 386
Y = [ y, y, y, y ] = [, β, ψ, ] (3) 3 4 r hen the BLIM state equation in dq synchrono coordinate system can be derived, and according to the Interactor algorithm, the system reversibility can be proved. If selecting the input of inverse system as follow: Y( u) = [ y, y, y, y ] = [ ν, ν, ν, ν ] (4) 3 4 3 4 And then the inverse system model of torque system can be obtained as follows: Lm δ x6 u = [ v3 + γ x5 δ ( ξη + ) x7 ( x8 + ) x6 ] ξ δ Lm Lm x7 u = [ v4 + γ x6 + x5x 8+ ξηx7x8 ] ξ µ x7 Lr u3 = [ L rl x6( mν + Fs β ) + ( x7 + Lr l x5 )( mν + Fs )] Lm Km[( x7 + Lr l x5 ) + ( Lr l x6 ) ] L r u4 = [ L rl x6( mν + Fs ) ( x7 + Lr l x5 )( mν + Fs β )] Lm Km[( x7 + Lr l x5 ) + ( Lr l x6 ) ] (5) Where: γ = R / σl + R / σl, δ = R / L, ξ = / σl, µ = p L / JL, η= L / L, σ = L /( L L ); i s s r r r r s m r m r m s r sd and i sq are currents components of torque windings; L m is mutual inductance of torque windings, L r is the self inductance of rotor; L s and L r are the leakage inductance of stator and rotor, r is the rotor time constant; p is the number of pole pairs, ψ r is rotor flux, is angular frequency of rotor, is the synchrono angular velocity, J: is moment of inertia, L is load torque; M is mass of rotor; F s and F sβ are and β axes spension force components. According to the inverse system principle, connecting the inverse system in series with the BLIM original system, the BLIM system can be decoupling for four second-order pseudo linear subsystems, include motor speed, rotor flux-linkage and two radial displacement subsystems. ADRC Design of BLIM he Structure and Operational Principle of ADRC he ADRC consists of three subsystems [3]; include a tracking differentiator (D), an extended state observer (ESO), and a nonlinear state error feedback (NLSEF). By D, the target value, is reasonably arranged, the transient process Z and its differential signal Z are output; ESO is the core of ADRC, its function is real-time estimate and compensate the total disturbances of the system, include internal disturbance and external disturbance. he function of NLSEF is nonlinearly combining the outputs of D and ESO reasonably, so as to improve the dynamic performance of control system. he -order ADRC diagram is shown in Fig. he discrete algorithm of tracking differentiator (D) can be expressed as follows: x( k+) = x( k) + x( k) x( k+) = x( k) + fst x( k) x( k) u( k) r h (,,,, ) (7) In (7): is sampling period, u (k) is the current input signal; r is a parameter that determines the tracking speed. When the input signal is polluted by noise, h is a parameter that determines the filtering effect. When r increases, the tracking speed increases, and the tracking error would be increased under the influence of random disturbance, this needs to increase the H value to carry on the error suppression. he fst () function can be calculated by the following formula step by step: 387
z t z e e u( ) u( t) z z z 3 Figure. Structure of second-order ADRC. δ = rh, δ = δ h y = x u + hx a δ 8r y, = + (8) x + y / h, y > δ = x +.5( δ ) sign( y), y > δ (9) r / δ, δ fst = rsign( ), > δ () he discrete algorithm of Extended State Observer (ESO) can be expressed as follows: z( k + ) = z( k) + [ z( k) βe( k)] z( k + ) = z( k) + [ z3( k) β. fal( e( k),/, δ ) + bu( k)] z3( k + ) = z3( k) β3 fal( e( k),/ 4, δ ) () Where: e( k) = z( k) y( k) ; he expression of function fal() is as follow: eδ, e δ fal( e,, δ ) = e sign( e), e > δ () In the discrete mathematic model of ESO, Z (k) and Z (k) are the estimations for the state variables of object. Z 3 (k) is the comprehensive prediction of external disturbances. he β, β and β 3 are adjtable parameters of controller, and the output error can be tuned by adjting the three parameters. he δ is the nonlinear function filter factor to eliminate noise; the is sampling period. he discrete algorithm of nonlinear state error feedback (NLSEF) can be expressed as follows:, e = v( k) z( k) e = v( k) z( k) u = β fal( e,, δ) + β fal( e,, δ) u( k) = u- z3( k) / b he function of NLSEF is to nonlinearly combine the outputs of D and ESO reasonably, and output the feedback of state error, and supplement the external disturbances observed by ESO. ADRC Controller Design of Velocity, Flux-Linkage and Radial Displacement he mathematical model of motor speed subsystem can be expressed as follow: (3) 388
d p L p = () dt JL J m ψ risq L r According to the ADRC control theory, the ADRC controller of motor speed can be constructed, include a first order D (omitted), a second-order ESO and a first-order NLSEF. he specific control algorithms are as follows: Second-order ESO: z = z β fal( z,, η) + bu( t) z = β fal( z,, η) (3) Second-order NLSEF: ( ) u ( t) = β fal( z,, η ) + bu t (4) he output control variable: u( t) = u ( t) z ( t) / b (5) After the inverse system decoupling, the obtained rotor flux-linkage and two radial displacement components subsystems are the same as the motor speed subsystem, which is the second-order integral subsystem. he design principle of ADRC is similar to that of the rotational speed subsystem. Figure shows the structure of the ADRC controller for motor speed, rotor flux and radial displacement. u( t) u( t) z z Figure. Structure diagram of ADRC controllers for velocity, flux-linkage and radial displacement. Structure of ADRC System β ψ r ( ) ν y ( ) ν y ( 3 3) ( y ) ν y ν 4 4 i s d i s q u s d u s q u sd u sq u s u sβ u s u sβ u sa u sb u sc u sa u sb u sc a b c a b c β ψ r - - x = [, β,, β, i, i, ψ, ] sd sq r Figure 3. ADRC control system of BLIM. 389
By connecting the inverse system in series with the original system, a pseudo linear composite system with linear transfer relation con be obtained. According to each decoupled pseudo linear subsystem, the ADRC controller is designed, and the ADRC inverse decoupling control system of BLIM can be constructed, so that the system has good dynamic decoupling control performance, and has stronger robtness to parameter variation and load. he control structure is shown in Fig.3. System Simulation and Analysis Simulation is made by Matlab/Simulink according to Fig.3; the controlled object is a four-pole BLIM with two-pole spension winding. he motor parameters are as shown in able. Setting the initial values of system as follows: =-.4mm, β =-.6mm; =-.4mm, β=-.6mm; n=5r/min, ψ r =.96 Wb; no load start. able. Parameters of BLIM. Rated power(kw) Rated speed(r/min) Rotor mass(kg) Moment of inertia(kg m ) Stator resistance(ω) Rotor resistance(ω) Stator leakage inductance(h) Rotor leakage inductance(h) Rotor time constant(s) Single-phase excitation inductance(h) Spension force coefficient Number of pole pairs orque winding. 3 8.5.4.6.43.43.43.69.859 Spension winding 8.5.4.7.398.398.3.3 FLUX/wb.5.5.5.5 speed/r/min 4 3 arget speed.5.5 Figure 4. Response curve of flux linkage Fig.5 Response curve of speed and torque. In order to verify the effectiveness of the proposed ADRC, the simulation contrast response curves of inverse decoupling control system that es PID controller are also presented. Comparison curve are described in Fig.4 to fig.7, the solid line represents the response curve of each variable when ADRC is adopted; the dotted line represents the response curve of each variable when PID controller is adopted. From the simulation results, there are following: ) From Fig.4: when the ADRC is adopted, the rotor flux reaches the given value faster and more smoothly. From Fig.5, when PID controller is adopted, there is an overshoot about %, when the ADRC controller is adopted, there is almost no overshoot. From Fig.6 and Fig.7, when the ADRC controller is adopted, the radial displacement reaches their steady state within.s, there is no overshoot; but when the PID controller is adopted, there is an overshoot of radial displacement about.5mm. he simulation results have shown that when the ADRC is adopted, the system has smaller overshoot and faster response speed. ) At different moment, the given values of rotor flux-linage, radial displacement are suddenly changed. From the simulation results, it can be known that when one of the four controlled variables changes, the other variables are almost unaffected. he simulation results have shown that the ADRC system can effectively improve the dynamic decoupling control performance. 39
3) In order to verify the disturbances rejection performance, the load torque is suddenly added N.m at.s, and reduced to at.3s. From Fig.5, it can be seen that the ADRC controller system can response more rapid, and the jitter is smaller. And then the ADRC system has stronger robtness and anti-interference ability. 4) Form Fig.6 and Fig.7, it can be seen that the radial displacement components are almost unaffected by the load torque, and then the dynamic decoupling performance of ADRC control system is stronger. x/mm..5 -.5 y/mm.5 -.5 -. -. -.5.5.5 -.5 -..5.5 Figure 6. Response curve of radial displacement. Figure 7. Response curve of β radial displacement. Conclions o overcome the impact of load change on the dynamic performance of the inverse controls system of BLIM, an active disturbance rejection control strategy based on inverse system decoupling is presented. he simulation results show that the ADRC control system can greatly reduce the overshoot and improve the response speed; and it can effectively improve the dynamic control performance of a BLIM, the system has better adaptability and robtness to the change of load disturbance. Acknowledgement his work was financially supported by National Natural Science Foundation of China (57753). References [] W.S Bu, C.L Zu, C.X Lu. Decoupling control strategy of bearingless induction motor under the conditions of considering current dynamic characteristics, Control heory & Applications, 4, 3():56-567. [] W.S Bu, Z.Y Li, C.X Lu, et al. A Convenient Vibration Compensation and Control Method of Bearingless Induction Motor, International Journal of Control and Automation, 6, 9(4):53-6. [3] C Li, H Bei, W Yanhong, et al. Active Disturbance Rejection Control for Spension System of Bearingless Motor with Rectifier Circuit, Fifth International Conference on Measuring echnology and Mechatronics Automation, Hong Kong, 3. [4] D.M Zhu, X.X Liu. Direct orque Control System Using Space Vector Modulation for Bearingless Induction Motor Based on Active Disturbance Rejection Controller echnology, Micro and special motor,, :54-57. [5] J.Q Han. Auto disturbance rejection control technology, Frontier science, 7, ():4-3. [6] W.F Su, X.D Sun, F.H Li. Vector control of inductjon motors with active disturbance rejection control, Journal of singhua University (Sci&ech), 4, 44(): 39-33. [7] Q Ding, X.L Wang, Cheng, P He. Displacement active disturbance rejection control for bearingless consequence-pole PMSM, Micro and special motor, 4, 4(8): 67-7. 39