PRESENTED AT PCIM-97 EUROPE CLOSED LOOP CONTROL OF THE LINEAR STEPPING MOTORS G.Kanevsky HTA Technologies, Inc. ABSTRACT Linear stepping motors (LSM), also known as Sawyer motors by the name of their inventor, have found numerous industrial applications due to their simplicity and ease of control. The majority of described applications are of open loop controls, and there have been applications using feedback to improve dynamic performance of the linear stepping motor 1. Inherently, motors have a position error associated with motor manufacturing and magnetic structure. Mapping techniques and current waveform modifications 2 are used to improve positioning accuracy of the LSM based systems. Some applications use linear encoders for position verification and after move correction. The present paper offers another perspective on the control of the linear stepping motors - being a two phase (or more) motor without brushes, it can be viewed as polyphase brushless electric machine and controlled as such 3. The described application uses real time closed loop electronically commutated linear stepping motor (LSM) based positioning system with Digital Signal Processor controls. A dual resolution feedback is obtained from a standard 20 µm linear scale to provide position information for the motor commutation and submicron resolution for positioning accuracy. Present application uses a variety of single and multiaxis air bearing LSM s topologies applied to the semiconductor and electronic assembly equipment and wafer steppers. Figure 1
FORCE MECHANISM Force produced by the two phase (A and B) hybrid LSM motor [Figure 2] F = K * I *sin( α) a f a F = K * I *cos( α) b f a F = F F m a b If we apply to to the motor phase currents such as: I I a b = I = I m m *cos( β) *sin( β) where α is an angle of the PM field from motors' phase A equilibrium position β is an angle of the electric field from motors' phase A equilibrium position K f is motor force constant Ia and Ib are motor phase currents Im phase peak current Fm = K f * I m* *sin( α β) If the angle difference between magnet vector and electrical vector α-β=0, the microstepping controls (phase controls) is obtained, and with α-β=90 the servo controls (magnitude control) is exercised. The stiffness of the LSM: S = K * I *cos( α β) f m With microstepping stiffness is high (inherent to the stepping motor). With servo controls the stiffness is zero (inherent to the servo motor) and must be provided by closed servo loop with feedback. Fa PM field α β Electric.field (microstepper) Fb Electric.field (servo motor) Figure 2
CONTROLLER ARCHITECTURE The servo controller has been designed to control simultaneously 3 LSM motors with a servo update rate of 250 mksec (4000 Khz). The design is based on the TI floating point DSP TI320C32 and features industry standard VME interface, 2K x 16 dual port RAM for interprocessor communication, on board 32K x 32 EPROM and 32K x 32 RAM for program and data storage, interface to commutator and absolute position feedback [Figure 3]. Figure 3 axis 1 phase A VME bus VME I N T E R F A C E Dual port RAM 2Kx16 32Kx32 zero wait RAM DSP TI TMS320 C32 current magnitude control phase B current magnitude control commutator to current amp 32Kx32 EPROM enc.i/f abs. position register from encoder axis 2 axis 3 Improved continuous sliding mode control law with adaptive gain feedback 4 was chosen for this application due to the presence of system parameter variations and external disturbances. It was augmented with velocity and acceleration feedforward compensator [Figure 4]
Figure 4 S 2 Kp Kaff S Kvff feedforward compensation position generator e Kp F 1 F 1 Amp 1/S 1/S - Ki/S - antiresonance filters adaptive gains 1Kv1* V Kv SL= es*ksl*e velocity generator - Velocity velocity estimate Position S K sl sliding mode controller
where K K p _ v a r i _ v a r S l = * K S l δ S l = 1 S l δ p S l * * S l K i S l = C e e. The presence of structural resonances required implementation of digital filters in a form: y(n) = a 0 x(n)a 1 x(n-1)a 2 x(n-2)b 1 y(n-1)b 2 *y(n-2) to increase velocity loop bandwidth [Figure 5]. Disk Util Def Disk: Internal Format Date: 03-31-95 Time: 12:02:00 PM A: Freq Resp X:564.399 Hz Y:-9.333 10 Date: 03-31-95 Time: 12:39:00 PM A: Freq Resp X:143.649 Hz Y:-13.954 10 Mag 10 /div Mag /div 10-90 10Hz B: Freq Resp X:564.399 Hz Y:177.218 180 999.999Hz -90 10Hz B: Freq Resp X:143.649 Hz Y:-138.362 180 999.999Hz Phase 36 /div Phase 36 /div -180 10Hz 999.999Hz -180 10Hz 999.999Hz Figure 5
FEEDBACK AND COMMUTATOR Linear stepping motors are manufactured with a pitch size 0.64 mm or 0.040". At high speed applications with a software commutated motor 5 force loss up to 30% can occur. Therefore, a hardware based commutator [Figure 6] has been designed for this application. The commutators' phase control counter receives pulses from the encoder and maintains a 90 angular displacement of the current vector from the magnet vector. Initial displacement of the current vector is performed in the beginning of the servoing by writing it into a phase advance register, which is also used to compensate for commutation angle loss at higher velocities. A standard linear encoder with a 20 µm grating pitch and analog voltage output is used as a feedback device and an proprietary interpolator [Figure 7] has been developed to provide dual resolution positioning information (10 µm to commutate the motor and 0.15625 µm for positioning accuracy). Interpolator design is based on the phase discriminator principle and provides 128 times resolution of basic grating pitch of the encoder.
Figure 6 from DSP current magnitude control 10 µm pulses from encoder UP DOWN phase counter sine ROM multiplying DAC to phase A amplifier from DSP phase advance counter cosine ROM multiplying DAC to phase B amplifier
Figure 7 α - position on encoder grating sin α cos ωt cos α diff amp diff amp X X sin (ωt-α) phase α measurement circuit absolute position register (14 bits) 0.15625 µm 0.3125 µm sin ωt (2 14-1) 0.15625 µm ω-reference frequency 125 Khz pulse generator UP count 10 µm DOWN count
MOTION PROFILE S-curve jerk limited profiles 6, created for current limited drives, were modified to accomodate the motors' dynamic characteristics, when used with a voltage limited amplifier [Figure 8]. Normalized jerk LSM Accel vs Speed 25 0.008 20 0.006 15 motor F/V 0.004 0.002 10 5 profile F/V 0 0-0.002 200 400 600 800-0.004 0 0 0.1 0.2 0.3 0.4 0.5-0.006 Normalized acceleration 1.20E00 1.00E00 8.00E-01 6.00E-01 4.00E-01 2.00E-01 0.00E00 0 100 200 300 400 500 600 700 800 Normalized velocity 5.00E-01 4.00E-01 3.00E-01 2.00E-01 1.00E-01 0.00E00 0 200 400 600 800 Figure 8
PERFORMANCE The motion control system presented in this paper is based on an LSM with 100N static force. The motor has an air bearing for frictionless operation and can develop speed up to 0.5 m/sec (presently limited by power amplifier voltage) and peak acceleration of 2 G with a 5 kg load. The positioning system performed with a static error less than 1 µm and a dynamic trajectory error of 15 µm [Figure 9]. It took 5-7 msec to settle to 5 mkm band after the motion completion. sync. pulse vel trajectory error sync.puls e 15 mkm during deccel. accel 10 mkm during accel. Figure 9 REFERENCES 1 Edmond Pelta, Direct linear and cartesian coordinate stepping motors, MotorCon, 1985 2 A. Leenhouts, Microstepping currents in hybrid step motors, IMCSD, 1991 3 Dr. Claude Oudet, D.Ettelman, An alternative to choosing between DC and Stepper motor, Power Conversion International, 1985 4 Y. Dote, Servo motor and motion control using digital signal processors, Prentice Hall, 1990 5 Thomas Bucella, A single chip solution for sine wave brushless motion control, IMCSD,1992 6 David Robinson, High performance motion profiles, PCIM, 1989