Hendrik.VanBrussel@mech.kuleuven.ac.be
1. Abstract
Linear motors experience a real breakthrough in machine tools. They have outspoken advantages compared to traditional rotary servomotor/ball screw drives, the main one being the high control bandwidths that can be achieved. There are also drawbacks however, e.g. load variations and disturbances are directly felt by the motor. Robust or adaptive controllers are needed to cope with these drawbacks.
The different types of linear motors and their salient features are presented in the first part of the paper. Consequently a number of innovative robust/adaptive control algorithms are presented, such as H-infinity and sliding mode controllers. The robustness of these controllers against disturbances of several kinds (cutting forces, friction, cogging, change in load inertia) are demonstrated by means of real-life examples.
2. Introduction
The use of linear motors in machine tools is on the upswing. Many machine tool manufacturers already offer machines with linear drives. Linear motors are particularly suitable for feed drives in highprecision, high-speed, high-reliability machine tools.
There are several outspoken advantages in using linear motor drives. The first is that very high positioning loop bandwidths can be obtained. This is due to the fact that the dynamics of the moving body are very simple. In fact, a machine tool table on roller guideways, directly driven by a linear motor, is nothing more than a damped mass, subject to a force. The low-frequency structural resonances, coming from lead screw transmissions in traditional rotary servomotor drives, and limiting the positioning bandwidth, are completely absent in linear drives. The remaining residual modes, e.g. coming from the position sensor connections, occur at very high frequencies and have no detrimental influence on the bandwidth. These higher control bandwidths, however, require a higher encoder bandwidth and servo sampling frequency.
A second advantage is that friction and backlash in transmission mechanisms (gear boxes, harmonic drives, rack-and-pinion systems, etc) is absent, so that the total system friction is reduced to the (low) friction in the guideways. This is an advantageous feature for high-accuracy machines. It partially explains why ultra-precision machines are mostly equipped with direct-drive systems, (and with aerostatic guideways eliminating the friction altogether).
There are also a few important drawbacks associated with linear motors. The main drawback is that the disturbances, such as cutting forces in machine tools, or friction forces in the guideways, are directly felt by the motor. The drive stiffness in the motion direction is entirely determined by the servo controller stiffness.
A second negative feature is that from the viewpoint of optimal power transfer from the motor to the load, a direct drive is usually not optimal. (Application of the optimal power transfer theorem to direct linear drives would require that the load inertia and the slider inertia are equal, which is never the case in practical applications.) The consequence is that, in linear drives, load inertia variations have a considerable influence on the behaviour of the drive.
A third disadvantage associated with some types of linear motors, particularly the iron-core brushless servomotors (see further) is their high level of heat generation and high attraction forces between slider and track. Ironless motors do not have these problems but their thrust force density is markedly lower. The high attraction forces and the heat removal problem require special design considerations about the way how the motors are to be incorporated into the machine structure.
A final issue requiring special attention from machine designers is the management of the (steel) chips attracted by the magnets on the linear motor tracks.

3. Linear motors for servo control
The same types exist in linear as in rotary electric motors. The main rotary motor types used for servo applications in machine tools are: (i) the permanent magnet DC motor, (i) the brushless DC (or
AC if you like) motor, with trapezoidal or sinusoidal excitation, (iii) the induction or asynchronous motor, and (iv) the variable reluctance or hybrid stepping motor. Linear versions of each of these types exist; they can be considered as the ‘unrolled’ version of the corresponding rotary motor.
An exception is the voice coil or Lorentz motor which only exists in its linear version. An example of a Lorentz motor is a loudspeaker. Voice coil motors (VCMs) are increasingly used in high-precision mechatronic positioning systems because of their excellent controllability and high bandwidth. They provide constant force over the full stroke, contrary to solenoids. Their use in computer peripherals
(disc drives) is widespread.
The DC brushed linear servomotors (Figure 1) are not widespread due to the necessity of regularly replacing the wear-prone brushes, like in rotary DC servomotors. An advantage, however, is that, because commutation is taken care of in the motor itself, simple linear of PWM-amplifiers can be used.
Figure 1. Brushed linear DC servo motor
Figure 2. Linear brushless servo motor with iron core
The brushless linear servomotors are the linear equivalents of the brushless DC (BLDC) servomotors. They consist of a stationary magnetic track with a cascade of magnets arranged with alternative polarity on a back iron plate to produce the main magnetic field. The moving part, called the slider, consists of (3-phase) coils wound on a steel lamination (iron-core motor) or fixed by resin/epoxy
(ironless motor) to carry the currents producing the thrust force. The iron-core motor is usually laid out as in figure 2 with an air gap of about 0.5 mm to be maintained by proper guideways. These latter also have to withstand the high attraction forces between track and slider. These motors exhibit a so-called
‘cogging’ effect due to the layout of the magnets in the track and to end effects during slot-teeth interaction. One can feel this effect when moving the slider of a switched-off motor. (The force ripple is a similar effect but different in origin. It results from variations in the force constant with position due to the non-perfect sine distribution of the magnetic field.)
Ironless coils allow to lay out the motor in a symmetrical way, with the slider moving in a U-shaped magnetic track as shown in figure 3 This configuration makes that there are no magnetic attraction forces transmitted to the outside world and cogging is minimal or absent. However, the thrust forces are markedly smaller than in an iron-core motor.
Commutation is achieved electronically by means of Hall sensors built into the slider coils at appropriate places, to trigger the switching between phases. Two commutation schemes are used: trapezoidal and sinusoidal. In the trapezoidal scheme the motor acts like a stepping motor, in the sinusoidal case like an AC synchronous motor. A sinusoidally commutated linear motor runs smoother and generates less heat than a trapezoidally commutated one.
The linear induction motor consists of a primary, moving coil assembly, comprised of steel laminations and phase windings, and a secondary, stationary reaction plate, corresponding to the squirrel cage of a rotary induction motor. The reaction plate can be made of aluminium or copper plate bonded to a steel backing. Variable frequency inverters are used for velocity control and vector control schemes for motion control applications.
The linear stepping motor is mostly of the variable reluctance type or of the hybrid type. It consists of a stationary platen (bar or tube) with (photo-chemically etched) teeth filled with epoxy and ground flatly

afterwards. The slider or forcer of a hybrid type stepping motor is made of multiple laminated steel cores slotted with teeth like the platen. Magnetisation is obtained with coils and with permanent magnets. Figure 4 shows the functional principle.
Figure 3. Linear brushless servo motor with ironless core, symmetrically arranged
A dual-axis or planar stepping motor can be made by making the platen as a checkerboard arrangement of teeth etched in a grid pattern. The forcer consists of two single-axis forcers arranged orthogonal to each other. An air bearing separates slider and platen.
Stepper motors mainly work open loop, making them simple to use. Adding a position sensor may increase the reliability. Microstepping improves the positioning accuracy.
Figure 4. Linear hybrid stepping motor
Table 1 summarizes the salient features of the different linear motor types.
Feature
Table 1. Salient features of frequently used linear motor types
Iron-core
BLDC
Ironless
BLDC
Induction
(Asynchronous)
Nom. thrust force F
Peak thrust force
Force density (N/cm
Attractive force
Cogging
Acceleration (typ.)
Max. speed (typ.)
Heat generation
Cooling system
2 )
High
300%
2.5
5-10F
Yes
10g
5m/s
High
Water
Low
300%
1.5
None
No
10g
5m/s
Very low
Air (forced or convection)
10 Air gap (mm) 0.1-1.0
4. Accurate position control with linear drives
Up to very high
500%
1.0
None
No
1g
>5m/s
Low
Air or water
>1mm
Stepping
Very low
100%
1.5
5-10F
Yes
1g
2m/s
Low
Air
<0.05
As stated above, because of their favourable properties, linear motors are increasingly used to drive moving elements in machine tools. These moving elements are tables in conventional machine tools, or struts in parallel kinematics machines (see figure 5). The considerations in the sequel are restricted to traditional machine tool tables. As a linear motor is directly subject to all disturbances acting in the

motion direction, alternative motion controllers are needed in order to ensure robustness. In machine tools, the disturbances are:
(i) external disturbances resulting from the process, like e.g. cutting forces in machining centers,
(ii) internal disturbances, like friction in the guideways,
(iii)
(iv) load variations due to different causes: varying mass of the workpiece, variable load inertia due to changes in the machine configuration, and variations due to the trend towards modular design (Figure 6).Using this design approach, autonomous, linear single-axis building blocks, containing the complete drive electronics
(control computer, power amplifier, position sensor, diagnosis sensors) are combined into various machine configurations and controlled with a distributed control scheme (see
Section 8). As the inertial load of a module is not known during the manufacture of the module, the motion controller has to be made robust against load variations.
Figure 5. Parallel kinematic machine with linear motors
Figure 6. Modular machine design
5. Performance measures for machine tool drives
The performance of machine tool drives is expressed by three important parameters that have a direct influence on the quality of the machined workpiece. These parameters are (i) the tracking error,
(ii) the stiffness in the motion direction , and (iii) the positioning bandwidth.
The most important feature that characterizes a feed drive is its position loop gain k v
, also called the velocity gain. It expresses the relation between the feed rate v and the resulting tracking error e t
: e t
= v/k v
. This means that when milling with a feed rate of 100 mm/s on a drive with k v
= 100 s -1 , a tracking error of 1mm occurs. Circular contouring with a radius R at a contouring speed v c
, results in a radial error e r
= v c
2 /2Rk v
.
A high k v
is beneficial for a low tracking error, but also for a high stiffness and a high bandwidth.
In rotary motor/ballscrew feeddrives, the achievable positioning bandwidth is limited by the lowfrequency mechanical resonances in the machine and drive structure. As these resonances are absent in linear drives, the reachable bandwidth is much higher in linear drives. This allows to adopt high k v
values, and hence high drive stiffness and low tracking errors.
6. Robust motion controllers with linear motors
Traditional PI- and pole placement controllers (block C in figure 7) are frequently used to control linear drives with a constant inertial load. However, when load variations occur, e.g. workpieces with different mass are mounted on the machine tool table, the positioning performance normally deteriorates for masses other than the one for which the controller has been designed. Cascade controllers, consisting of an internal velocity feedback loop and a position feedback loop around it are difficult to apply because of the unavailability of linear tachometers. The use of a Ferraris sensor has become popular recently as a tachometer. A Ferraris sensor measures the relative acceleration; integration of its output yields a velocity signal.

Figure 7. General motion control scheme. C represents the controller; G represents the drive and load to be controlled; d is the external disturbance (cutting force, friction, …); y ref
is the reference trajectory and y is the resulting trajectory
Socalled robust controllers are needed to make the drive’s performance independent of the disturbances described above. Controller structures that satisfy those requirements have been developed recently. Two of them are discussed further: the H ∞ -controller and the socalled ‘sliding mode’ controller. H
∞
is a method in which optimal controllers are designed by an optimization process, where the system uncertainties (disturbances) are taken into account by defining frequencydependent sensitivity functions chosen such that the influence of the disturbances is reduced. The choice of these sensitivity functions is quite delicate and requires a good understanding of the method and of the disturbance frequency characteristics. The sliding mode controller is a nonlinear controller where the system state tries to reach a so-called switching line (surface) and then slides along (in fact chatters around) that line to reach the final system state. The consequence of this control mode is that, during sliding, the control behaviour becomes completely independent from the system dynamics, and hence also from the disturbances acting on the system. This explains the inherent robustness of sliding mode control. More details on the application of both methods to control feed drives with linear motors can be found in reference [1].
A comparative study of robust control of linear drives has been carried out on a linear BLDC motor
[1]. The slider had a mass of 12 kg and was supported by two roller element guideways containing an incorporated magnetic position encoder with a resolution of 1 micrometer. The robustness of the H  - and sliding mode controllers against load mass variations was tested and compared with a standard pole placement controller. The load mass was increased from 12 to 35 kg in steps of 7 kg, by adding weights to the slider. Four controllers were tested: a pole placement controller taken as reference, a traditionally designed  -controller, an H  -controller based on a modified sensitivity function, and a sliding mode controller. As can be seen from figure 8 the worst performing controller is the pole placement controller, the best one is the sliding mode controller. The originally designed H  -controller performed very poorly. Slight modifications to the sensitivity function resulted in a robust controller, almost as good as the sliding mode controller (Figure 8).
Figure 8. Robust behaviour of different motion controllers for changing load mass
In the framework of the EU-project MOTION [4], a modular XY-table with linear drives was built, as shown in figure 9. The results of some interesting contouring experiments are discussed hereafter.
The controller structure is shown in figure 10. A traditional PID controller has been used. Velocity and acceleration feedforward have been added to enhance the contouring performance. The notch filters

are added to increase the positioning bandwidth by eliminating the influence of the high-frequency modes. Open-loop bandwidths of around 80 Hz have been achieved.
Velocity &acc.
Setpoint
Position
Setpoint sensor position delay setpoint
Figure 9. Modular XY-table with linear drives calculate position error estimate velocity error velocity filter feed forward
PID controller second notch filter lowpass filter apply saturation level first notch filter
Figure 10. Controller structure for the XY-table experiments output
+
Figure 11 shows some contouring results. A circular contour with a radius of 20 mm was covered with a circumferential feed rate of 0.2 m/s. This implies a maximum axis acceleration of 2 m/s 2 . Figure
11a shows the result with pure feedback. The maximum contour error is about 50 microns. This large error is due to the fact that in the absence of feedforward, the feedback loop is totally responsible for the generation of the acceleration force, which implies large tracking and contour errors. Adding acceleration feedforward makes the maximum tracking error drop drastically to 10 micron (figure 11b).
Adding also velocity feedforward reduces the contour error to 2 microns (Figure 11c). The remaining contour error is due to cogging forces in the linear motors.

Servo contour erro r
0.175
0.17
0.165
0.16
0.155
0.175
0.17
0.165
Setpoin t
Zoomed in co nto ur error
5 m icron errorband
Servo contour erro r
Setpoin t
Zoomed in co nto ur error
5 m icron errorband
0.15
0.145
0.16
0.175
Ser vo contour erro r
0.14
0.135
0.13
0.155
0.15
0.145
0.17
0.165
0.16
0.155
Setpoin t
Zoomed in co nto ur error
5 m icr on errorband
0.125
0.14
0.105
0.11
0.115
0.12
0.125
0.13
0.135
0.14
0.145
0.15
0.155
0.135
0.15
0.145
0.13
0.14
0.125
0.135
0.105
0.11
0.115
0.12
0.125
0.13
0.135
0.14
0.145
0.15
0.155
0.13
0.125
0.105
0.11
0.115
0.12
0.125
0.13
0.135
0.14
0.145
0.15
0.155
Figure 11: Contour errors. (a) Pure feedback,
(b) Feedback +acceleration feedforward, (c) Feedback + acceleration + velocity feedforward
The robustness of sliding mode controllers against friction forces in the guideways has been convincingly demonstrated on the XY-table of figure 9. The quadrant glitches occurring around motion reversal of the axes, due to pre-rolling friction in the guideways, is reduced from 115 microns with a traditional cascade controller (position and tacho feedback) to 27 microns with the sliding mode controller (Figure 12). Feedforward with a pre-rolling friction model could alleviate the problem with the cascade controller, but the sliding mode controller is so robust that no model is needed at all [3].
Figure 12. Quadrant glitch during contouring, left: with cascade controller, right: with sliding mode controller

The sliding mode control scheme yields drive stiffnesses (a few hundreds of N/micron) that are more than an order of magnitude better than cascade controllers (a few tens of N/micron).
Another interesting case, illustrating the performance of linear drives, is shown in figure 13. It concerns a linear toolholder module for unround turning. An air-cooled ironless linear motor drives a toolholder with a total mass of 25 kg. A position loop bandwidth of 100 Hz was achieved allowing accelerations up to 10g. The linear motor is synchronized with the spindle motor via a CAN bus (see further), resulting in a high-performance electronic cam functionality. Course-pitch screw threads for application in the oil industry were machined at speeds up to 550 rpm. This system allowed a doubling of the productivity compared to the traditional mechanical solution [4].
Figure 13. Add-on toolholder with fast linear drive for unround turning
7. Motion and vibration control of systems with variable dynamics
The high accelerations occurring in contemporary high-speed machine tools excite the machine structure up to high frequencies. The resulting structural vibrations need to be damped if accurate positioning and trajectory tracking are to be achieved. An additional problem is that the dynamic behaviour of the machine tool depends on the position of the tool as a consequence of the varying machine configuration during machining. Such time-varying behaviour cannot be controlled by classical linear control methods, as these methods require a linear time invariant (LTI) model of the system. One solution to this problem is to design robust controllers that perform well for all configurations. Another method consists of switching between different locally optimised controllers as the configuration changes.
Figure 14. Gantry pick-and-place machine with linear drives
Figure 15. Robust motion and vibration control for variable configurations
An example of the control of the X-axis of a 4-axis pick-and-place assembly machine (Figure 14) shows that it is possible to simultaneously control robustly the position and damp out the vibrations of the tool, for varying position of the quill along the Z-axis. The machine consists of a gantry driven by

two linear motors controlling the Y-motion. The X-motion of the carriage over the gantry is also driven by a linear motor. The vertical Z-motion is a traditional rotary motor. The quill, holding the tool, can move up and down, resulting in variable natural frequencies.
Figure 15 shows the results of a gain scheduling H
∞
–controller controlling a specified trajectory in
X-direction while simultaneously damping the vibrations of the toolholder resulting from the acceleration and deceleration along the X-axis [2, 6].
8. Modular motion control systems
Mass customization has triggered the tendency towards modular machine design. Each module is supposed to be independent but able to communicate with its peers to achieve a global system goal.
Linear motors are eminently suitable as a building block in single-axis motion control modules. Each axis module is provided with a robust controller that it performs well in every possible application.
Combination of such modules results in reconfigurable and extendable multi-axis machines provided the modules are able to communicate with each other in an appropriate way. A solution for this communication problem has been worked out in the framework of the EU-project MOTION. Figure 16 illustrates the general idea. A PC-based mo tion controller plans the trajectory and ‘projects’ this trajectory on the motion axes. This information is sent through a fieldbus (e.g. CAN-Open) to the different axis control modules. Each axis controller has its own interpolator, the output of which serves as input to the axis controller. The fieldbus only has to have ‘soft’ real time capabilities while the ‘hard’ real-time interpolation calculations are done on the local axis processors. However, such a decentralized scheme needs a synchronization mechanism that links the different axis interpolators.
The scheme developed in the MOTION project [5,7] has a maximum synchronization error of a few microseconds. This allows real-time interpolation at feed rates up to 1 m/s. The results shown in figure
11 have been obtained with this system. To show the scalability of the concept, a 10 degrees-offreedom walking robot has been controlled with the same decentralized controller structure, by adding axis modules.
9. Conclusion
Figure 16. High-performance decentralized motion control system
Linear motors of different types offer, when properly controlled, excellent opportunities for the design of high-accuracy, high-speed, high-reliability, modular machine tools. They allow to achieve high bandwidths of the positioning systems, and high robustness against varying load mass, friction in the guideways, varying geometric configurations. They are finally very suitable for the development of modular machines using a decentralized and scalable motion control structure.

10. Acknowledgements
The substantial research contributions of Pieter Van den Braembussche, Bob Koninckx, Wim
Symens and Jian Wang, and the financial support by the Interuniversity Attraction Pole programme of the Belgian Federal Science Policy Office, by the Fund for Scientific Research of Flanders, and by the
EU through projects MOTION and MECOMAT are gratefully acknowledged.
References
[1] H. Van Brussel, P. Van den Braembussche, Robust control of feed drives with linear motors, CIRP
Annals, Vol. 47(1), 1998, 325-328.
[2] W. Symens, H. Van Brussel, J. Swevers, Gain-scheduling control of machine tools with varying structural flexibility, CIRP Annals, Vol. 53/1, 2004, 321-324.
[3] J. Wang, Robust tracking controller design with application to the motion control of an XY-feed table for high-speed machining, PhD thesis KULeuven, ISBN 90-5682-468-6, 2004.
[4] B. Koninckx, H. Van Brussel, J. van Eijk, N. Meijerman, Modular technologies for intelligent motion unit with linear motor and axis control, Transactions of the North American Manufacturing Research
Institution of SME, Vol. XXIX, 2001, 493-499.
[5] B. Koninckx, H. Van Brussel, B. Demeulenaere, J. Swevers, Closed-loop, fieldbus-based clock synchronisation for decentralised motion control systems, Proc. of CIRP, 1st International Conference on Agile, Reconfigurable Manufacturing, Michigan, 2001, CD-ROM.
[6] W. Symens, Motion and vibration control of mechatronic systems with variable configuration and nonlinear friction, PhD thesis KULeuven, ISBN 90-5682-493-7, 2004.
[7] R. Koninckx, Modular distributed motion planning, interpolation and execution, PhD thesis
KULeuven, ISBN 90-5682-439-2, 2003.