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Optimal design issues in high-speed high-precision motion servo systems
Mechatrot#cs Vol. 1, No. 2, pp. 187-201, 1991
0957-4158/91 $3.fD+0.00 © 1991 Pergamon Press plc
Printed in Great Britain
OPTIMAL DESIGN ISSUES IN HIGH-SPEED HIGH-PRECISION MOTION SERVO SYSTEMS
SABRI
CETINKUNT
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680, U.S.A.
(Received 11 July 1990; accepted 21 November 1990)
Abstract--High speed and precision requirements in servo driven multi-axis motion control systems are such that optimal design consideration of not just the servo motor, but all of the system components is necessary in order to achieve the best possible performance from the available technology. In general, speed and precision are conflicting requirements in incremental motion control systems. The current state of the art in servo systems, their performance characteristics, ultimate performance limitations, optimal design and selection criteria are discussed for high-speed high-precision incremental motion control applications such as assembly machines and x - y table based machines.
1. I N T R O D U C T I O N Applications of multi-axis motion servo control systems cover a wide range from web processing in the paper and film industry to the assembly machines and machine tool industry. The motion type can be classified in two groups: (1) continuous motion; (2) incremental motion. In continuous motion, servos move at precisely controlled constant speeds for hours and days without frequent stops. The speed reference may be constant, or the speed of another machinery which is to be tracked. In incremental motion, however, the servos move in " s t a r t - m o v e - s t o p " cycle. The cyclic motion of " s t a r t - m o v e - s t o p " may continue for long periods. This is the type of motion encountered in assembly machines. Consider the schematics of an assembly machine station shown in Fig. la, (a typical x - y table based automatic insertion machine schematics is shown in Fig. lb). This is the essential station of an assembly machine for connector assembly. The station is driven by a five axis servo system. The insertion head (driven by servo #1) drives a cam or crank mechanism to perform cut and insert operations of the contacts being inserted to the housing. The other servos feeding the contacts from a continuous roll (servos # 4 and #5), and the servos ( # 2 and #3) feeding the connector housing in a continuous line (hence, these machines are given the name of in-line assembly machines) must be synchronized relative to the insertion head tool. That is, the contacts must be fed within the acceptable positioning accuracy before the cutting begins and must not move until insertion is complete. Similarly, the connector housing must be positioned before the insertion begins and must be in position until the insertion is completed. Clearly, one insertion cycle is divided into portions where each servo must make its move and hold its position during the remaining part of the cycle. Consider a realistic state of art assembly machine which makes 1200 cycles of insertion per minute. That 187
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means 50 msec for one insertion cycle. This 50 msec is further divided between contact feed, housing feed, and insertion head as function of the cam/crank mechanism design and they may have some overlap between them. A typical timing chart for synchronization is shown in Fig. 2. The motion of the multi-axis servo must be position synchronized according to this timing chart. The generally used name timing chart is somewhat misleading. Since the synchronization must be based on the relative position of the insertion head during one cycle (effective cam position) for reliable operation, this should be called cam chart. In fact, old assembly machines used to be synchronized by cams. Now, the synchronization is made through the real-time software simulation of the cams. The advantage is that if a different product to be manufactured requires different synchronization, one does not have to change a whole set of cams and belts which may be impossible, but merely changes the control software. Due to position synchronization, the system will still work even if there are variations in the speed of the insertion head. As shown in Fig. 2, some servos must perform their incremental motion within a 15-20 msec period (also called index time). Therefore, it is expected that index times of under 10 msec will be demanded by the next generation of assembly machines. Hence, a complete systems design approach for optimal design becomes an important issue in order to get the most out of the available technology in mechanical-system design, servo motor, and controllers area.
2. OPTIMAL DESIGN ISSUES IN HIGH-SPEED HIGH-PRECISION
INCREMENTAL MOTION CONTROL SYSTEMS Optimal design and/or selection issues can be divided into two groups: (1) design of mechanical drive system and sizing of servo motor: (2) design and/or selection of the controller. The first group is essentially a optimization problem where the fundamental relationship is the Newton's Second Law. Given a task which may be identified as moving a part in certain incremental distances within a given time, and positioning accuracy, the part inertia and other resisting loads (either as inertia or force/torque) in the motion determines the torque history required from the motor as function of desired motion. The fundamental relationship is: Teff -- Jeff0,
(1)
where Teee is the effective torque delivered, that is motor torque minus the resistive torques such as friction, viscous, gravity, load resistance etc., Jeff is the effective inertial load seen by the motor, that is the motor inertia, plus the part inertia, plus the effective inertia of the kinematic mechanism coupling the load to the motor. For a given part and its defined desired motion, the design of the kinematic coupling system, and selection of appropriate servo motor to deliver the specified motion, is the remaining question. The next issue is regarding the controller design and/or selection. The first group of design problems mainly determine the mechanical capability of the servo system in terms of responsiveness and power in delivering a commanded motion. Commanding the desired motion, i.e. triggering a servo to perform a predefined incremental
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motion, turns out to be an important factor affecting the speed of operation in multi-axis servo systems. In an application such as assembly machines, where a servo has about 20 msec to perform its move, the time delay associated with the processing of synchronization signals is very important. Consider that the synchronization signal is sensed by a fast response inductive proximity switch which would have about 0.5-1 msec time delay in its response. This signal triggers the servo controller to perform a predefined incremental move. The time period from the moment the servo is triggered to the moment the servo motor actually starts to receive current from the drive is due to the signal-processing delay associated with the servo controller. There are a wide range of servo controllers in the market where this time delay varies from 50 msec (which would be impossible to use in high speed assembly machines of the type discussed here) to under 1.0 msec. The other criteria in the servo controller are the servo loop update time that affects precision especially in contouring applications such as CNC machine tools and coordinated path tracking control of robots. Typical servo loop update time of industrial servo systems is in the range of 2.0 msec-200 microsec [9-11].
3. DESIGN ISSUES CONCERNING THE MECHANICAL COMPONENTS
A block diagram of servo motor and load coupling is shown in Fig. 3. The kinematic coupling mechanism has the function of transforming the rotational motor motion to the desired motion of the load. This may take the form of gears, timing belts, lead-screws etc. (Table 1). Now we will discuss the dynamic characteristics of the each block of Fig. 3.
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3.1. Dynamic characteristics of the servo motor The dominant features of the dynamics of the servo motors are described by their electrical and mechanical time constants. An idealized model of a D.C. motor is shown in Fig. 4. The dynamic relationship between the input terminal voltage, V, and current following through the windings, i, of the motor is given by:
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electrical time constant in most low-inertia servo motors is in the order of 0.1 msec. This time constant is further reduced by the current feedback loop in the servo amplifiers, hence further increases the bandwidth of the torque control. The mechanical time constant is a measure of the time delay between the applied current [torque, Eqn (3)] and the occurrence of the actual movement in the motor shaft. In small moves, that is the time it takes for the motor respond to reach 63% of a step change in speed command. This is the time constant which is important in position control mode and determines the position control bandwidth of the motor. It is important to recognize that the mechanical time constant is a function of the total inertia seen by the motor [Eqn (7.b)]: J
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Therefore, in order to have a high bandwidth control capability, motor and load inertia must be minimized. Load inertia includes the inertia of the part and the kinetic coupling mechanism. As the effective gear ratio increases, the effective load inertia acting on the motor decreases, but the amount of motor rotation necessary to perform the same part movement increases, which may be a limiting factor in high cycle rate incremental motion control systems.
3.2. Characterization of the load for servo system design The characteristics of the load that matters for the servo system design are the following: (1) inertia and torque/force associated with the part itself to be moved, not including the effects of the kinetic coupling mechanism; (2) incremental motion distance (index distance) and the available time period to perform the motion (index time), and time period the load stays stationary within a cycle (dwell time); (3) positioning accuracy required (i.e. +0.0005 in typically required in linear positioning). One of the fundamental problems in mechanics is not being able to accurately model and predict the Coulomb friction [3, 4]. Hence, the active control and accurate compensation of friction effects is not possible [5]. Clearly, if the force/torque associated with the load is of Coulomb type, that may reduce the servo motor positioning accuracy due to stiction and result in cyclic oscillations about the nominal desired position [6]. In fact, in high-speed assembly machine applications, there is no
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time for occurrence of cyclic oscillations generated by integral action of the servo control. The result is poor positioning accuracy by the motor. In order to compensate for the poor motor accuracy due to friction, the kinematic coupling mechanism may have to be designed with higher effective gear ratio. Higher gear ratio for the sake of accuracy will require more rotation at the motor shaft to perform the same motion at the load end. Longer motor rotation will require longer time, and the cycle rate of the servo system will be lower. Therefore, the design of the mechanical system around the load should be such that factors affecting accuracy such as friction should be minimized [7, 8]. The friction alone can reduce the cycle rate by a factor of two. If considered in the content of high-speed assembly machines, that may mean having a machine with 600 cycle per minute rate as opposed to 1200 cycles per minute!
3.3. Characteristics of the kinematic coupling mechanism The function of the kinematic coupling mechanism is to translate the rotary motion from the motor to the desired type of motion of the part (Fig. 3). The effective gear ratio has influence over the part positioning accuracy, motor index distance, and load seen by the motor. The first requirement that must be satisfied in servo-system design is the accuracy requirement. The servo system must provide the positioning accuracy specified to begin with, regardless of the type or size of motors, or coupling system used. The positioning accuracy needed for the part is determined by the task, and is given. The motor positioning accuracy at the motor shaft is determined by the servo motor control technology. Under favourable conditions, servo controllers can guarantee positioning accuracy of _+2-3 counts of the feedback device resolution, i.e. if a 12-bit sampling of resolver feedback is used, the motor would have + 1 0 - 1 5 arcmin of positioning accuracy. If a much higher resolution feedback device is used, such as 24,000 count/rev encoders, the motor positioning accuracy can be significantly improved. However, the Coulomb friction can be a major limitiation in positioning accuracy. In the presence of large Coulomb friction, a higher resolution feedback device alone will not improve the positioning accuracy of the motor. The motor will oscillate about the nominal desired position in a limit cycle due to not being able to control stiction friction [3-5, 8]. In summary, the given part positioning accuracy needed, A/part , a n d the available motor positioning accuracy, A0m, determine the minimum effective gear ratio that must be provided by the kinematic coupling mechanism. Effective gear ratios of typical kinematic coupling mechanisms are shown in Table 1. Accuracy specification requires that (considering the last mechanism in the Table 1 as an example):
(r2/rl)/rw > AOm/Alpart,
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which means that the larger the effective gear ratio, the better the positioning accuracy of the part. On the other hand, the amount of rotation the motor must make to achieve the given amount of part motion increases with the increasing effective gear ratio:
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Notice that in high-speed (high-cycle rate) applications, there is a limited amount of
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time to make each move determined by the cycle rate and the cam chart of the synchronization. Increasing gear ratio for the sake of accuracy may result in m o t o r index distances which may be impossible to perform within the available index time. For instance, state of art servo motors with low inertias (brushless or moving-coil types) can reliably perform 1/10 rev incremental move within 10 msec under no load. If the load is pure inertial and 3 times that of m o t o r rotor inertia, the same move would take 20 msec. Clearly, if it is required to move 1.0 rev in 20 msec as a result of a large gear ratio, it would be impossible to find a m o t o r to make that move. Therefore, the accuracy and speed requirements are conflicting performance specifications. In the limit, one may have to make a compromise in one specification for a gain in the other. That is, lower positioning accuracy will allow higher cycle rate of operation, or lower cycle rate of operation will allow higher positioning accuracy. The state of art performance can be judged by the following two generic measures in any high-speed incremental motion control application: (1) the ratio between incremental index distance and the positioning accuracy: (2) the index time to make the index distance while providing the required positioning accuracy. Clearly, if the cycle rate, or index time, was not a concern the first ratio can be made as large as is needed. What limits the first ratio is the availability of the index time period. Since the ultimate actuation and control capability lie in the servo m o t o r and the controller, these two measures can be used to judge the relative merits of different servo systems as far as high-speed high-precision incremental motion control applications are concerned. A typical high-performance servo system on the market would have the following performance characteristics: 1/10rev in 10msec with + 15 arc min accuracy.
4. DESIGN AND SELECTION ISSUES IN SERVO CONTROLLERS
Controllers provide the p r o g r a m m a b l e intelligence in servo systems. There are no size considerations as there are for servo motors/drives, and kinematic coupling systems for each application. For every application whether it is in assembly machines, machine tools, or web applications, the design of a kinematic coupling mechanism, and sizing and selection of servo motors and drives, must be analysed specifically for that particular application. The question of selection of an appropriate servo controller can be answered for a class of applications, but need not be analysed for each particular application within that class. In high-speed high-precision incremental motion control systems, the important factors to consider for controller selection are as follows (Fig. 5): (1) response time to trigger signals: (2) servo loop update time: (3) software programming capabilities. Consider the five axis servo station of an assembly machine discussed in the Introduction (Fig. la). The index time for some of the servos are in the 15-20 msec range. Each slave servo receives its trigger signal from another servo (master axis) or
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a proximity switch which senses the appropriate cam position from the master axis. When the master axis is at the appropriate cam position, the follower servo must be triggered (Fig. 5, instant 1), recognize the trigger signal (instant 2), process it (instant 3), command the motion (instant 4) and send out a signal to other servos (instant 4'), start moving (instant 5), and complete the move (instant 6). The time delay from the trigger signal instant to the instant where servo drive commands the motor to move (from instant 1 to instant 4) is purely a result of signal processing delay in the controller. In multi-axis synchronized servo control applications where some index times are under 20 msec, this time delay can be a very significant factor. There are wide range of servo controllers in the market with time delays from 50 msec to under 1.0 msec. Servo loop update time is especially important in contouring, machine tool, and path tracking robotic applications. If the multi-axis operated tool is to follow a path in space, the servo loop update time will be important in accurate tracking. However, in point to point control applications this is not a significant factor. As long as each servo gets to the desired final position within the allowed index time and final positioning accuracy, the tracking accuracy while it was making the move is not important. Software aspects of the controller should not be overlooked, since more than 80% of the application development time is spent in software. In fact, the main advantage of servo systems over mechanical cams is their programmability. The effectiveness of the programmability is determined by the software environment of the controller. Most single-axis servo controllers on the market today have commands to perform the following functions: (1) H o m e - - t o establish zero reference: (2) Stop; (3) Jog-constant speed motion: (4) M o v e - - m a k e a predefined motion: (5) Wait for a trigger signal or period of time; (6) Turn O N / O F F some of Output signals--which may be used by other servos for synchronization [9-11]. Recent servo controllers equipped with more powerfull microprocessors, and digital signal processors, provide all of the programming structures of high level programming l a n g u a g e s - - I F . . . T H E N . . . ELSE IF . . . E N D IF control structures, D O . . . L O O P U N T I L . . . iterative statements and their nesting, constant, variable, and array definitions, operators, functions, sub-routines, operator I/O support. Clearly, availability of these high level languages structures increases the level of programmable intelligence of the servo systems, and reduces the application software development time.
5. AN ILLUSTRATIVE EXAMPLE
In order to illustrate the conflict between accuracy and speed requirements in servo systems, consider the servo # 2 in Fig. la which is used to feed the contacts for insertion. The kinematic coupling mechanism between the servo motor and the contact trip is shown in Fig. 6. Contacts are on a continuous stip. During every cycle, servo # 2 moves the contact to the insertion head on trigger from the master axis based on the cam chart. Then, the contact is cut and inserted by a cam mechanism driven by servo #1. For continuous reliable operation, the contact must be positioned within the desired positioning accuracy before the cutting action begins, which is precisely determined by the cam chart.
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As a example, consider that the contact must be fed /part = 0.25 in every cycle with a positioning accuracy A/part. Let us assume that a state of the art low inertia, brushless D.C. servo m o t o r is available with a positioning accuracy of _+(10/60) ° at the m o t o r shaft. The goal is to design the kinetic coupling mechanism, and select an appropriate servo m o t o r to p e r f o r m the desired motion. H e r e , we will consider three different cases of performance specifications to illustrate the conflict between accuracy and speed:
A/part /'index
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Case 2
Case 3
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On one hand, a large effective gear ratio is desirable to increase the positioning accuracy of the part [Eqn (8)]. On the other hand, a small gear ratio is desirable to perform the desired part motion with minimal m o t o r rotation [Eqn (9)]. The material of pulley rolls are considered to be aluminium, and the drive wheel is steel. The widths of the rolls and the wheel are taken an 0.5 in and 0.125 in, respectively. Based on accuracy requirements, the radius dimensions selected for the mechanism and the m o t o r rotation necessary to move the part for the specified distance are shown below:
r i(in) r2(in) r~(in) 0m(°)
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A high performance servo motor series is considered for this application (Yaskawa, S-series brushless D.C. servo motors). The servo motor sizing analysis results are illustrated below. None of the motors could deliver the performance specified in case 1. In case 2, the speed requirement is relaxed compared to case 1 (100 msec cycle time as opposed to 50 msec), whereas in case 3, the accuracy requirement is relaxed compared to case 1 (_+0.001 in accuracy as opposed to +0.0005 in). One servo motor would be able to deliver either of the required performance of case 2 or 3. From this example it is clear that the accuracy or speed can be improved at the expense of the other. Motor performance
Required performance
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6. CONCLUSIONS Optimal design issues of servo systems for high-speed high-precision incremental motion systems are discussed. The high-speed assembly machines are one area of application of such control systems. It is shown that optimal design in high-speed high-precision applications includes not only optimal sizing of servo motors, but also the design of kinematic coupling mechanism, and appropriate selection of the servo controller with specific requirements of high cycle rate applications. It was also shown that the precision and speed are conflicting requirements. Increase in one requires compromise in the other requirement. The current state of the art servo motor technology is evaluated for high cycle rate applications using the time it takes to make 1/10 rev, and the positioning accuracy of the servo system. The effect of mechanicalsystem design and friction considerations and their impact on the final system peformance is discussed. Acknowledgements--This work was supported in part by the Campus Research Board, and Manufacutring Research Center of the University of lllinois.
REFERENCES 1. DC Motors, Speed Controls, Servo Systems. Electro-Craft Corp., Hopkins, MN, Fifth ed. (1980). 2. Dote Y., Servo Motor and Motion Control Using Digital Signal Processors. Prentice Hall and Texas Instruments (1990). 3. Tou J. and Schultheiss P. M., Static and sliding friction in feedback systems, J. Appl. Phys. 24, 1210-1217 (1953). 4. Nelson W. L., Pulse-width relay control in sampling systems. J. Basic Engng. March 65-76 (1961). 5. Yang S. and Tomizuka M., Adaptive pulse width control for precise positioning under the influence of stiction and coulomb friction. A S M E J. Dyn. Syst. Measmt. Contr. 110, 221-227 (1988). 6. Gawthrop P. J., Self-turning PID controllers: algorithms and implementation. IEEE Trans. on Auto. Control, Vol. AC-31, No. 3, pp. 201-209 (1986). 7. Gawthrop P. J. and Nomikos P. E.. Automatic turning of commercial PID controllers for single-loop and muhiloop applications. IEEE Control. Syst. Magazine January, 34-42 (1990).
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8. Ulsoy A. G. and Koren Y., Applications of adaptive control to machine tool process control, 1EEE Contr. Syst. Magazine June, 33-37 (1989). 9. Emerson EMC Positioning Drives & Motors Manual. Emerson Electronic Motion Controls, Chanhassen, MN (1989). 10. BRU-200 Seried Brushless Servo Systems Users' Manual. Electro-Craft Corp., Hopkins, MN (1989). 11. Generation lI1 Multi Axis Motion Controller Users' Manual. ORMEC Systems Corp., Rochester, NY (1990).
0957-4158/91 $3.fD+0.00 © 1991 Pergamon Press plc
Printed in Great Britain
OPTIMAL DESIGN ISSUES IN HIGH-SPEED HIGH-PRECISION MOTION SERVO SYSTEMS
SABRI
CETINKUNT
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680, U.S.A.
(Received 11 July 1990; accepted 21 November 1990)
Abstract--High speed and precision requirements in servo driven multi-axis motion control systems are such that optimal design consideration of not just the servo motor, but all of the system components is necessary in order to achieve the best possible performance from the available technology. In general, speed and precision are conflicting requirements in incremental motion control systems. The current state of the art in servo systems, their performance characteristics, ultimate performance limitations, optimal design and selection criteria are discussed for high-speed high-precision incremental motion control applications such as assembly machines and x - y table based machines.
1. I N T R O D U C T I O N Applications of multi-axis motion servo control systems cover a wide range from web processing in the paper and film industry to the assembly machines and machine tool industry. The motion type can be classified in two groups: (1) continuous motion; (2) incremental motion. In continuous motion, servos move at precisely controlled constant speeds for hours and days without frequent stops. The speed reference may be constant, or the speed of another machinery which is to be tracked. In incremental motion, however, the servos move in " s t a r t - m o v e - s t o p " cycle. The cyclic motion of " s t a r t - m o v e - s t o p " may continue for long periods. This is the type of motion encountered in assembly machines. Consider the schematics of an assembly machine station shown in Fig. la, (a typical x - y table based automatic insertion machine schematics is shown in Fig. lb). This is the essential station of an assembly machine for connector assembly. The station is driven by a five axis servo system. The insertion head (driven by servo #1) drives a cam or crank mechanism to perform cut and insert operations of the contacts being inserted to the housing. The other servos feeding the contacts from a continuous roll (servos # 4 and #5), and the servos ( # 2 and #3) feeding the connector housing in a continuous line (hence, these machines are given the name of in-line assembly machines) must be synchronized relative to the insertion head tool. That is, the contacts must be fed within the acceptable positioning accuracy before the cutting begins and must not move until insertion is complete. Similarly, the connector housing must be positioned before the insertion begins and must be in position until the insertion is completed. Clearly, one insertion cycle is divided into portions where each servo must make its move and hold its position during the remaining part of the cycle. Consider a realistic state of art assembly machine which makes 1200 cycles of insertion per minute. That 187
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means 50 msec for one insertion cycle. This 50 msec is further divided between contact feed, housing feed, and insertion head as function of the cam/crank mechanism design and they may have some overlap between them. A typical timing chart for synchronization is shown in Fig. 2. The motion of the multi-axis servo must be position synchronized according to this timing chart. The generally used name timing chart is somewhat misleading. Since the synchronization must be based on the relative position of the insertion head during one cycle (effective cam position) for reliable operation, this should be called cam chart. In fact, old assembly machines used to be synchronized by cams. Now, the synchronization is made through the real-time software simulation of the cams. The advantage is that if a different product to be manufactured requires different synchronization, one does not have to change a whole set of cams and belts which may be impossible, but merely changes the control software. Due to position synchronization, the system will still work even if there are variations in the speed of the insertion head. As shown in Fig. 2, some servos must perform their incremental motion within a 15-20 msec period (also called index time). Therefore, it is expected that index times of under 10 msec will be demanded by the next generation of assembly machines. Hence, a complete systems design approach for optimal design becomes an important issue in order to get the most out of the available technology in mechanical-system design, servo motor, and controllers area.
2. OPTIMAL DESIGN ISSUES IN HIGH-SPEED HIGH-PRECISION
INCREMENTAL MOTION CONTROL SYSTEMS Optimal design and/or selection issues can be divided into two groups: (1) design of mechanical drive system and sizing of servo motor: (2) design and/or selection of the controller. The first group is essentially a optimization problem where the fundamental relationship is the Newton's Second Law. Given a task which may be identified as moving a part in certain incremental distances within a given time, and positioning accuracy, the part inertia and other resisting loads (either as inertia or force/torque) in the motion determines the torque history required from the motor as function of desired motion. The fundamental relationship is: Teff -- Jeff0,
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where Teee is the effective torque delivered, that is motor torque minus the resistive torques such as friction, viscous, gravity, load resistance etc., Jeff is the effective inertial load seen by the motor, that is the motor inertia, plus the part inertia, plus the effective inertia of the kinematic mechanism coupling the load to the motor. For a given part and its defined desired motion, the design of the kinematic coupling system, and selection of appropriate servo motor to deliver the specified motion, is the remaining question. The next issue is regarding the controller design and/or selection. The first group of design problems mainly determine the mechanical capability of the servo system in terms of responsiveness and power in delivering a commanded motion. Commanding the desired motion, i.e. triggering a servo to perform a predefined incremental
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motion, turns out to be an important factor affecting the speed of operation in multi-axis servo systems. In an application such as assembly machines, where a servo has about 20 msec to perform its move, the time delay associated with the processing of synchronization signals is very important. Consider that the synchronization signal is sensed by a fast response inductive proximity switch which would have about 0.5-1 msec time delay in its response. This signal triggers the servo controller to perform a predefined incremental move. The time period from the moment the servo is triggered to the moment the servo motor actually starts to receive current from the drive is due to the signal-processing delay associated with the servo controller. There are a wide range of servo controllers in the market where this time delay varies from 50 msec (which would be impossible to use in high speed assembly machines of the type discussed here) to under 1.0 msec. The other criteria in the servo controller are the servo loop update time that affects precision especially in contouring applications such as CNC machine tools and coordinated path tracking control of robots. Typical servo loop update time of industrial servo systems is in the range of 2.0 msec-200 microsec [9-11].
3. DESIGN ISSUES CONCERNING THE MECHANICAL COMPONENTS
A block diagram of servo motor and load coupling is shown in Fig. 3. The kinematic coupling mechanism has the function of transforming the rotational motor motion to the desired motion of the load. This may take the form of gears, timing belts, lead-screws etc. (Table 1). Now we will discuss the dynamic characteristics of the each block of Fig. 3.
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3.1. Dynamic characteristics of the servo motor The dominant features of the dynamics of the servo motors are described by their electrical and mechanical time constants. An idealized model of a D.C. motor is shown in Fig. 4. The dynamic relationship between the input terminal voltage, V, and current following through the windings, i, of the motor is given by:
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3.2. Characterization of the load for servo system design The characteristics of the load that matters for the servo system design are the following: (1) inertia and torque/force associated with the part itself to be moved, not including the effects of the kinetic coupling mechanism; (2) incremental motion distance (index distance) and the available time period to perform the motion (index time), and time period the load stays stationary within a cycle (dwell time); (3) positioning accuracy required (i.e. +0.0005 in typically required in linear positioning). One of the fundamental problems in mechanics is not being able to accurately model and predict the Coulomb friction [3, 4]. Hence, the active control and accurate compensation of friction effects is not possible [5]. Clearly, if the force/torque associated with the load is of Coulomb type, that may reduce the servo motor positioning accuracy due to stiction and result in cyclic oscillations about the nominal desired position [6]. In fact, in high-speed assembly machine applications, there is no
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time for occurrence of cyclic oscillations generated by integral action of the servo control. The result is poor positioning accuracy by the motor. In order to compensate for the poor motor accuracy due to friction, the kinematic coupling mechanism may have to be designed with higher effective gear ratio. Higher gear ratio for the sake of accuracy will require more rotation at the motor shaft to perform the same motion at the load end. Longer motor rotation will require longer time, and the cycle rate of the servo system will be lower. Therefore, the design of the mechanical system around the load should be such that factors affecting accuracy such as friction should be minimized [7, 8]. The friction alone can reduce the cycle rate by a factor of two. If considered in the content of high-speed assembly machines, that may mean having a machine with 600 cycle per minute rate as opposed to 1200 cycles per minute!
3.3. Characteristics of the kinematic coupling mechanism The function of the kinematic coupling mechanism is to translate the rotary motion from the motor to the desired type of motion of the part (Fig. 3). The effective gear ratio has influence over the part positioning accuracy, motor index distance, and load seen by the motor. The first requirement that must be satisfied in servo-system design is the accuracy requirement. The servo system must provide the positioning accuracy specified to begin with, regardless of the type or size of motors, or coupling system used. The positioning accuracy needed for the part is determined by the task, and is given. The motor positioning accuracy at the motor shaft is determined by the servo motor control technology. Under favourable conditions, servo controllers can guarantee positioning accuracy of _+2-3 counts of the feedback device resolution, i.e. if a 12-bit sampling of resolver feedback is used, the motor would have + 1 0 - 1 5 arcmin of positioning accuracy. If a much higher resolution feedback device is used, such as 24,000 count/rev encoders, the motor positioning accuracy can be significantly improved. However, the Coulomb friction can be a major limitiation in positioning accuracy. In the presence of large Coulomb friction, a higher resolution feedback device alone will not improve the positioning accuracy of the motor. The motor will oscillate about the nominal desired position in a limit cycle due to not being able to control stiction friction [3-5, 8]. In summary, the given part positioning accuracy needed, A/part , a n d the available motor positioning accuracy, A0m, determine the minimum effective gear ratio that must be provided by the kinematic coupling mechanism. Effective gear ratios of typical kinematic coupling mechanisms are shown in Table 1. Accuracy specification requires that (considering the last mechanism in the Table 1 as an example):
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time to make each move determined by the cycle rate and the cam chart of the synchronization. Increasing gear ratio for the sake of accuracy may result in m o t o r index distances which may be impossible to perform within the available index time. For instance, state of art servo motors with low inertias (brushless or moving-coil types) can reliably perform 1/10 rev incremental move within 10 msec under no load. If the load is pure inertial and 3 times that of m o t o r rotor inertia, the same move would take 20 msec. Clearly, if it is required to move 1.0 rev in 20 msec as a result of a large gear ratio, it would be impossible to find a m o t o r to make that move. Therefore, the accuracy and speed requirements are conflicting performance specifications. In the limit, one may have to make a compromise in one specification for a gain in the other. That is, lower positioning accuracy will allow higher cycle rate of operation, or lower cycle rate of operation will allow higher positioning accuracy. The state of art performance can be judged by the following two generic measures in any high-speed incremental motion control application: (1) the ratio between incremental index distance and the positioning accuracy: (2) the index time to make the index distance while providing the required positioning accuracy. Clearly, if the cycle rate, or index time, was not a concern the first ratio can be made as large as is needed. What limits the first ratio is the availability of the index time period. Since the ultimate actuation and control capability lie in the servo m o t o r and the controller, these two measures can be used to judge the relative merits of different servo systems as far as high-speed high-precision incremental motion control applications are concerned. A typical high-performance servo system on the market would have the following performance characteristics: 1/10rev in 10msec with + 15 arc min accuracy.
4. DESIGN AND SELECTION ISSUES IN SERVO CONTROLLERS
Controllers provide the p r o g r a m m a b l e intelligence in servo systems. There are no size considerations as there are for servo motors/drives, and kinematic coupling systems for each application. For every application whether it is in assembly machines, machine tools, or web applications, the design of a kinematic coupling mechanism, and sizing and selection of servo motors and drives, must be analysed specifically for that particular application. The question of selection of an appropriate servo controller can be answered for a class of applications, but need not be analysed for each particular application within that class. In high-speed high-precision incremental motion control systems, the important factors to consider for controller selection are as follows (Fig. 5): (1) response time to trigger signals: (2) servo loop update time: (3) software programming capabilities. Consider the five axis servo station of an assembly machine discussed in the Introduction (Fig. la). The index time for some of the servos are in the 15-20 msec range. Each slave servo receives its trigger signal from another servo (master axis) or
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a proximity switch which senses the appropriate cam position from the master axis. When the master axis is at the appropriate cam position, the follower servo must be triggered (Fig. 5, instant 1), recognize the trigger signal (instant 2), process it (instant 3), command the motion (instant 4) and send out a signal to other servos (instant 4'), start moving (instant 5), and complete the move (instant 6). The time delay from the trigger signal instant to the instant where servo drive commands the motor to move (from instant 1 to instant 4) is purely a result of signal processing delay in the controller. In multi-axis synchronized servo control applications where some index times are under 20 msec, this time delay can be a very significant factor. There are wide range of servo controllers in the market with time delays from 50 msec to under 1.0 msec. Servo loop update time is especially important in contouring, machine tool, and path tracking robotic applications. If the multi-axis operated tool is to follow a path in space, the servo loop update time will be important in accurate tracking. However, in point to point control applications this is not a significant factor. As long as each servo gets to the desired final position within the allowed index time and final positioning accuracy, the tracking accuracy while it was making the move is not important. Software aspects of the controller should not be overlooked, since more than 80% of the application development time is spent in software. In fact, the main advantage of servo systems over mechanical cams is their programmability. The effectiveness of the programmability is determined by the software environment of the controller. Most single-axis servo controllers on the market today have commands to perform the following functions: (1) H o m e - - t o establish zero reference: (2) Stop; (3) Jog-constant speed motion: (4) M o v e - - m a k e a predefined motion: (5) Wait for a trigger signal or period of time; (6) Turn O N / O F F some of Output signals--which may be used by other servos for synchronization [9-11]. Recent servo controllers equipped with more powerfull microprocessors, and digital signal processors, provide all of the programming structures of high level programming l a n g u a g e s - - I F . . . T H E N . . . ELSE IF . . . E N D IF control structures, D O . . . L O O P U N T I L . . . iterative statements and their nesting, constant, variable, and array definitions, operators, functions, sub-routines, operator I/O support. Clearly, availability of these high level languages structures increases the level of programmable intelligence of the servo systems, and reduces the application software development time.
5. AN ILLUSTRATIVE EXAMPLE
In order to illustrate the conflict between accuracy and speed requirements in servo systems, consider the servo # 2 in Fig. la which is used to feed the contacts for insertion. The kinematic coupling mechanism between the servo motor and the contact trip is shown in Fig. 6. Contacts are on a continuous stip. During every cycle, servo # 2 moves the contact to the insertion head on trigger from the master axis based on the cam chart. Then, the contact is cut and inserted by a cam mechanism driven by servo #1. For continuous reliable operation, the contact must be positioned within the desired positioning accuracy before the cutting action begins, which is precisely determined by the cam chart.
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As a example, consider that the contact must be fed /part = 0.25 in every cycle with a positioning accuracy A/part. Let us assume that a state of the art low inertia, brushless D.C. servo m o t o r is available with a positioning accuracy of _+(10/60) ° at the m o t o r shaft. The goal is to design the kinetic coupling mechanism, and select an appropriate servo m o t o r to p e r f o r m the desired motion. H e r e , we will consider three different cases of performance specifications to illustrate the conflict between accuracy and speed:
A/part /'index
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On one hand, a large effective gear ratio is desirable to increase the positioning accuracy of the part [Eqn (8)]. On the other hand, a small gear ratio is desirable to perform the desired part motion with minimal m o t o r rotation [Eqn (9)]. The material of pulley rolls are considered to be aluminium, and the drive wheel is steel. The widths of the rolls and the wheel are taken an 0.5 in and 0.125 in, respectively. Based on accuracy requirements, the radius dimensions selected for the mechanism and the m o t o r rotation necessary to move the part for the specified distance are shown below:
r i(in) r2(in) r~(in) 0m(°)
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A high performance servo motor series is considered for this application (Yaskawa, S-series brushless D.C. servo motors). The servo motor sizing analysis results are illustrated below. None of the motors could deliver the performance specified in case 1. In case 2, the speed requirement is relaxed compared to case 1 (100 msec cycle time as opposed to 50 msec), whereas in case 3, the accuracy requirement is relaxed compared to case 1 (_+0.001 in accuracy as opposed to +0.0005 in). One servo motor would be able to deliver either of the required performance of case 2 or 3. From this example it is clear that the accuracy or speed can be improved at the expense of the other. Motor performance
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6. CONCLUSIONS Optimal design issues of servo systems for high-speed high-precision incremental motion systems are discussed. The high-speed assembly machines are one area of application of such control systems. It is shown that optimal design in high-speed high-precision applications includes not only optimal sizing of servo motors, but also the design of kinematic coupling mechanism, and appropriate selection of the servo controller with specific requirements of high cycle rate applications. It was also shown that the precision and speed are conflicting requirements. Increase in one requires compromise in the other requirement. The current state of the art servo motor technology is evaluated for high cycle rate applications using the time it takes to make 1/10 rev, and the positioning accuracy of the servo system. The effect of mechanicalsystem design and friction considerations and their impact on the final system peformance is discussed. Acknowledgements--This work was supported in part by the Campus Research Board, and Manufacutring Research Center of the University of lllinois.
REFERENCES 1. DC Motors, Speed Controls, Servo Systems. Electro-Craft Corp., Hopkins, MN, Fifth ed. (1980). 2. Dote Y., Servo Motor and Motion Control Using Digital Signal Processors. Prentice Hall and Texas Instruments (1990). 3. Tou J. and Schultheiss P. M., Static and sliding friction in feedback systems, J. Appl. Phys. 24, 1210-1217 (1953). 4. Nelson W. L., Pulse-width relay control in sampling systems. J. Basic Engng. March 65-76 (1961). 5. Yang S. and Tomizuka M., Adaptive pulse width control for precise positioning under the influence of stiction and coulomb friction. A S M E J. Dyn. Syst. Measmt. Contr. 110, 221-227 (1988). 6. Gawthrop P. J., Self-turning PID controllers: algorithms and implementation. IEEE Trans. on Auto. Control, Vol. AC-31, No. 3, pp. 201-209 (1986). 7. Gawthrop P. J. and Nomikos P. E.. Automatic turning of commercial PID controllers for single-loop and muhiloop applications. IEEE Control. Syst. Magazine January, 34-42 (1990).
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8. Ulsoy A. G. and Koren Y., Applications of adaptive control to machine tool process control, 1EEE Contr. Syst. Magazine June, 33-37 (1989). 9. Emerson EMC Positioning Drives & Motors Manual. Emerson Electronic Motion Controls, Chanhassen, MN (1989). 10. BRU-200 Seried Brushless Servo Systems Users' Manual. Electro-Craft Corp., Hopkins, MN (1989). 11. Generation lI1 Multi Axis Motion Controller Users' Manual. ORMEC Systems Corp., Rochester, NY (1990).