AC Servo Motor Based Position Sensorless Control System Making Use of Springs

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1 Extended Summary pp AC Servo Motor Based Position Sensorless Control System Making Use of Springs Akira Shimada Senior Member (Dept. of Electrical System Engineering, Polytechnic University) Yu Kishiwada Non-member (Mitsubishi Electric Corporation) Michiyo Arimura Non-member (Dept. of Electrical System Engineering, Polytechnic University) Keywords: position sensorless conrol, AC servo motor, observer, vector control This paper describes a position sensorless control technique on AC servo motor position control systems. We have previously presented a paper on the DC servo motor position sensorless control technique using mechanical springs. It is based on a point of view that mechanical springs form the key components for the observability. On the basis of the result obtained from the successful experiment, we come to a conclusion that the AC servo motor position sensorless control system applying the vector control method is identical as in the case of the DC motor. Using vector control, the presented controller needs the data of magnetic pole position on rotor of AC servo motor. By using the AC servo motor perfect position sensorless control technique, the controller should estimate both the magnetic pole position and mechanical position. In this paper, we demonstrate the simulation and expreimental results for the latter as an initial step in a new control technology. And Fig. 4 shows the experimental result. They are successfully worked out. Note: Fig. 1, 2 indicate a block diagram of AC servo motor and mechanical plant and the experimental apparatus. Fig. 3, 4 shows the block diagram of control system and the experimantal result. u q1 and u q2 are decoupling inputs. z r, z and ẑ are position reference, real position and its estimation. v q and i q mean the q-axis driving voltage and electrical current. The observer can estimate position, velocity, and q-axis current. Fig. 3. Block diagram of control system Fig. 1. Block diagram of AC servo motor and mechanical plant Fig. 2. View of experimental apparatus Fig. 4. control Experimental result of position sensorless 7

2 AC AC Servo Motor Based Position Sensorless Control System Making Use of Springs Akira Shimada, Senior Member, Yu Kishiwada, Non-member, Michiyo Arimura, Non-member This paper describes a position sensorless control technique on AC servo motor based position control systems. Shimada et al. had previously presented a paper on a DC servo motor based position sensorless control technique using mechanical springs. It was based on a point of view that mechanical springs form the key components for the observability. On the basis of the result obtained from the successful experiment, we assumed that the AC servo motor position sensorless control system would be identical. Using vector control, the controller needs the data of the magnetic pole position on the rotor of the AC servo motor. It is not perfect sensorless control, since it use a rotary encoder. However, we introduce it and demonstrate the expreimental results as an initial step in the new control technology. AC Keywords: position sensorless conrol, AC servo motor, observer, vector control 1. AC DC (1) (2) (3) (4) AC AC Dept. of Electrical System Engineering, Polytechnic University Hashimotodai 4-1-1, Sagamihara Mitsubishi Electric Corporation Marunouchi 2-7-3, Chiyoda-ku, Tokyo (3) (4) F = k x F = G i 3 AC AC (7) (9) 2π rad D

3 2π rad 2π rad AC DC (5) (6) DC (1) (4) 2 (7) (9) π rad AC AC (1) (12) 2. AC DC AC dq Fig. 1 (5) 1 Fig. 2 z v ω m M D k n f τ 1 L a 1 R a p Φ fa d Fig. 1. Block diagram of AC servo motor and mechanical plant Fig. 2. View of experimental apparatus q Fig. 1 v d = u d u dd v q = u q + v qd u dd = v dd = pl a i q v/r v qd = v q1 + v q2 = pφ fa v/r + pl a i d v/r u d u q i d i q 1/(sL a + R a ) q v q q i q z z q i q Fig. 1 z n k 1/(sM + D) v v 1/r p v qd 1/(sL a + R a ) i q q v v qd v d = u d u dd = u d pl a r v q = u q + u q2 = u q + pl a r i q v (1) i d v (2) Fig. 3 i d i q i dr i qd Fig. 4 (4) 988 IEEJ Trans. IA, Vol.127, No.9, 27

4 AC t u d = K pi (i dr i d ) + K ii (i dr i d )dt (3) t u q = K pi (i qr i q ) + K ii (i qr i q )dt + u q1 (4) i dr = q 1/(pΦ fa ) Fig. 5 q ẋ 1 = [z,v,i q ] T u 1 = u q y 1 = i q (5) (6) ẋ 1 = A 1 x 1 + B 1 u 1 (5) y 1 = C 1 x 1 (6) 1 nk M D pφ fa M Mr, B 1 =, 1/L a A 1 = C 1 = [ 1 ] pφ fa L a r M = J r 2 + m, D = D m r 2 R a L a + D z x 2 = [z,v] T u 2 = τ y 2 = z (7) (8) (5) (6) (7) (8) Fig. 3. Equivalent system to DC servo motor system ẋ 2 = A 2 x 2 + B 2 u 2 (7) y 2 = C 2 x 2 (8) A 2 = 1 nk M D, B 2 = 1, M Mr C 2 = [ 1 ] 3. Fig. 4. Fig. 5. Current feedback system Equivalent control plant (5) (6) n, k > (1) det(u o ) = p 2 φ 2 fa /(L2 ar 2 ) nk/m (5) (6) C 1 A 1 (13) (5) (6) (9) (1) (11) (12) Fig. 6. Block diagram of control system D

5 x 1 [i + 1] = A d1 x 1 [i] + B d1 u 1 [i] (9) y 1 [i] = C d1 x 1 [i] (1) ˆx 1 [i + 1] = A d1 ˆx 1 [i] + B d1 u 1 [i] + H d (y[i] ŷ[i]) (11) ŷ 1 [i] = C d1 ˆx 1 [i] (12) A d1 = e A 1 T s R 3 3 B d1 = T s e A1τ dτ B 1 R 3 1 C d1 = C 1 R 1 3 T s H d ẑ (7) (8) (13) (14) x 2 [i + 1] = A d2 x 2 [i] + B d2 u 2 [i] (13) y 2 [i] = C d2 x 2 [i] (14) (15) A d2 = e A 2 T s C d2 = C 2 R 1 2 R 2 2 B d2 = T s e A 2τ dτ B 2 R 2 1 Fig. 6 z r T s T s z r ẑ δ(i + 1) = δ(i) + T s (z r ẑ) (7) (8) δ x 2 = [z,v] T x 3 = [z,v,δ] Q d R d LQ τ r = Kx 3 + K p z r K = [F b K i ] F b K i K p S elector1 S elector2 ˆx 1 = [ẑ, ˆv, î q ] T ˆx 2 = [ẑ, ˆv] T ẑ PI q PI = K pi + K ii /s d u q1 u q v q u q1 PI i q DC (1) (4) d, q (5) DC 4. Table 1 Table 2 Table 2 2 Fig. 7 Fig. 7. Table 1. Variables Mass of the cart M Coefficient of viscosity D z Radius of pulley r Coef. of elasticity k Number of spring n Armature resistance R Armature self inductance L E.M.F. constant K e Torque constant K T Phisical parameters of the plant Values of the parameters.165 [kg].35 [N s/m].8825 [m] 16 [N/m] 1or [Ω] 9.5 [mh].35 [Vs/rad].35 [Ns/rad] Rotor inertia J [kgm 2 ] Coef. of rotor viscosity D m [Nms/rad] Current control gain K pi 1 Current control integral gain K ii 8 Maximum magnetic flux φ fa.3 Number of pole pairs p 4 Variables Table 2. Sampling time T s Control parameters Values of parameters.1 [ms] Weight function Q d Diag(1, 1, 1 6 ) Weight function R d 1 State feedback gain F b [7.25, ] Integral gain K i Observer gain H d [.16,.2883,.3331] Feedfoward gain K p 55. Simulation result of position sensorless control 99 IEEJ Trans. IA, Vol.127, No.9, 27

6 AC (a) t=.25 [s] Fig. 8. Structure of hardware system (b) t=.75 [s] (c) t=1.25 [s] (d) t=1.75 [s] Fig. 9. Experimental result of position sensorless control (e) t=2.25 [s] 5. PE- PRO MWINV-4R22 PWM C PE-PRO DSP TI TMS32C25 PWM DC2 V 1 khz AC 2 W 248 /, SY-3 12 A/D.1ms Fig. 9 Fig. 1 (e) t=2.75 [s] Fig. 1. Pictures on the experiment Fig. 7 Fig. 9 ±25 mm ±3mm 6. AC DC AC (7) (9) D

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