Motion control of a two-axis linear motor driven stage ...

Please cite this paper as: M. S. Heydarzadeh, S. M. Rezaei, N. A. Mardi, and A. Kamali E, “Motion control of a two-axis linear motor-driven stage in the micro-milling process,” Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng., vol. 0, no. 0, pp. 1–12, Dec. 2016. DOI: 10.1177/0954408916683976

Motion control of a two-axis linear motor driven stage in the micro-milling process Mohammad Sadegh Heydarzadeh1, Seyed Mehdi Rezaei2, Noor Azizi Mardi3, Ali Kamali E4 Abstract The application of linear motor driven stages (LMDSs) as the feed drivers of CNCmicro milling machine tools is growing. In addition to employ high speed and high precision equipment such as LMDSs, the precision of the machined contours is highly dependent on the capabilities of the servo controllers. In this paper, the design of a precise controller for a two-axis LMDS has been investigated for micro-milling applications. In such feed drives, disturbances such as friction, force ripples, and machining forces have adverse effects on the workpiecepositioning precision

1

Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran,

[email protected] 2

Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran,[email protected]

3

Department of Engineering, Mechanical Engineering, University of Malaya, Kuala Lumpur,

Malaysia,[email protected] 4

Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran,[email protected]


due to the direct drive concept behind them. Therefore, in order to have an acceptable transient response and disturbance rejection properties, a Two-Degree-Of-Freedom (2DOF) proportionalintegral-derivative (PID) controller was employed for each axis. To design this controller the zero-placement method was used. To compensate disturbances and machining contour errors, the utilization of Kalman filter (KF)observers, neural networks (NN), cross-coupled controllers (CCC), and different integration of them were studied. The controllers were experimentally examined for circular motions in two conditions; in the laboratory, and in the real machining experiments. An integrated controller consisted of a Kalman filter disturbance observer, acrosscoupled controller, and a well-designed 2DOF PID controller resulted in a high contouring and tracking precision. The controller could also reduce the spikes caused by the friction at the motion reversal points such as the quadrants in circle trajectories. Keywords: CNC machine tools, micro-milling, Linear motors, Controller, Kalman filter, cross-coupled controller, modified PID controller, precision motion control List of abbreviations LMDS

linear motor driven stages

DOF

Degree-Of-Freedom

PID

proportional-integral-derivative

PD

proportional-derivative

ZPETC

Zero Phase Error Tracking Controller

CCC

crossed-coupled controller

DOB

Disturbance observer


1

PEC

position error compensator

KF

Kalman filter

NN

neural network

RMS

root mean square

PIDD

PID controller in feedforward path and a derivative in the feedback path

Introduction Rapid technology advancements have resulted in some complicated products with

miniature components. Mechanical micro milling is one of machining processes that is widely employed to manufacture such products. This process has advantages such as high dimensional precision, high production rate, capability of manufacturing 3-D features and machining of almost all engineering materials. Such advantages make this process prominent among other similar processes and have attracted the attention of many researchers. Up to now, many investigations have been carried out on the improvement of the precision of this process. Employing linear motors as feed drivers in CNC micro milling machines is one result of such researches. The precision of the machined products is highly dependent on the precision of generated contours. Therefore,servo controlling of such feed drives have been studied by some researchers. There are two main approaches to increasing the precision of the contours generated by multi-axis CNC machines1. In one approach called tracking control, the main focus is on the reduction of the tracking errors of each axis by designing of individual controllers for each


axis2.To this end, among common feedback controllers, proportional-derivative (PD), and PID controllers have been used extensively2.To achieve perfect tracking in a wide control loop bandwidth, feed forward controllers were then added to the feedback controllers. The most significant research in this field was done by Tomizukaand led to the introduction of the Zero Phase Error Tracking Controller (ZPETC)3.Modern control schemes such as H∞ synthesis

4–8

,

and sliding mode controller and its modifications9–13 have been developed to obtain robustness against model parameter variations and disturbances. For cases that a trajectory should be traced for several times,repetitive control has been employed

8,14

. Some researchers have

offered controllers to reduce harmful effects of the friction and backlash on the tracking precision 15–17. In the other approach, the main goal of the control loop is the direct reduction of overall contouring errors instead of reducing each individual axis tracking errors. Inspired by this idea, the crossed-coupled controller (CCC) was proposed by Koren18 and was investigated in many types of research19–27.Different multi-axis contour controllers have been reviewed up to 2012 by Tang and Landers28. The integration of both approaches has also been explored by a few researchers.Yeh et al. integrated a PI controller in the feedback control loop, a ZPETC in the feedforward path, a digital disturbance observer (DOB), and CCC to improve contouring precision

29

. Su and

Cheng developed the position error compensator (PEC) approach and then combined it with a modified version of CCC, and a fuzzy-logic-based feed rate regulator

23

.Ghaffari and Ulsoy


proposed a novel dynamic contour error estimation method and feedback modification and used it in an integrated controller to reduce the absolute contour errors at very high feed rates30,31.

The selection of a motion controller is dependent on the requirements of the application.Typical requirements are precision, travel speed range, the computational power of motion control hardware, disturbance rejection, and motion characteristics (e.g., repetitiveness), etc28. Machine tools are subjected to process loads that can affect the motion characteristics. Most of the contour control research studies are conducted under no load condition and are evaluated on laboratory set-ups. thus, the aforementioned factors are ignored28.Just a few research have been reported with experiments conducted on machine tools 7,19,29,32,33. A few researchers have probed the servo controllers of micro milling machine tools. Crosscoupling control was employed in a miniaturized NC micro milling machine tool

34

.A non-

linear command shaping technique was proposed to reduce the vibrations in the micro-milling process 35. Dynamic dislocation compensation in micro milling machine tools was studied in ref.36. Linear motors are widely used in feed drives of micro milling machine tools.The main contribution of this paper is to propose a suitable controller for a two-axis stage driven by linear motors capable of achieving the requirements of micro milling.The proposed controller evaluated in real micro milling experiments on stainless steel parts.To this end, four strategies and their integrations were investigated: a) Design of a precise feedback controller in order to achieve high precision and highspeed motion. The basic controller should have a proper transient response plus


excellent disturbance rejection. For this purpose, a 2DOF PID controller was designed for each axis. b) Study of neural networks to estimate and compensate for friction and force ripples, which are two permanent sources of disturbances in linear motors. c) Utilization of a disturbance compensator to reduce the effects of cutting forces and uncertainties. A Kalman filter (KF) disturbance observer was employed for that purpose. d) Employing the cross-coupled controller to eliminate the contouring errors due to the mismatched dynamics of the two different axes. Cross-coupled controller and its integrations to other components were also investigated. 2

Experimental setup In this research, a two-axis stage (PlanarDL 100XY) manufactured by “Aerotech Co” was

used. Two linear motors of this stage are driven by two individual “Soloist CP” amplifiers. Specifications of this stage is given in Table 1. Matlab™ and Simulink™ were utilized to design and implement of controllers. A“dSpace 1104CP” data acquisition platform was used to make connections between the host computer and the amplifiers. The mentioned devices were employed in two configurations. After tuning the controller, the stage was mounted on a highspeed milling machine for evaluation in micro milling experiments (Fig.1, Fig.2). The connections within the setup are shown in Fig.3.

Please cite this paper as: M. S. Heydarzadeh, S. M. Rezaei, N. A. Mardi, and A. Kamali E, “Motion control of a two-axis linear motor-driven driven stage in the micro-milling micro process,” Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng.,, vol. 0, no. 0, pp. 1–12, 1 Dec. 2016. DOI: 10.1177/0954408916683976

Fig.1. Experimental setup

Fig.2.. Stage installed on the CNC machine


Table 1- Specification of the stage Units

Values

Lower Axis

kg

8.4

Upper Axis

kg

2.9

Maximum Speed (Upper Axis)

mm/s

500

Maximum Acceleration

g

1.5

Continuous Force (per motor)

N

12.9

Peak Force (per motor)

N

51.4

BEMF Constant

V/m/s

4.77

Continuous Current

Amppk (Amprms)

3.10 (2.19)

Peak Current, Stall

Amppk (Amprms)

12.40 (8.77)

Force Constant, Sine Drive

N/Amppk (N/Amprms)

4.15 (5.87)

Motor Constant

N/√W

1.59

Inductance

mH

0.87

Maximum Bus Voltage

VDC

80

Moving Mass

(No Load / Upper Axis)


Fig.3. Connections within the setups

3

Modeling of the stage Ignoring some nonlinear effects, the dynamical model of linear motors can be presented by

the following transfer function from input voltage commands to the displacement of the axis37: =

+

1


Where

and

are two parameters need to be identified.

There are some methods to identify two parameters of this model38. Herein,two simple PID controllers based on the nominal specifications of the motors werefirstly designed and implemented for each axis. Then, some successive sinusoidal trajectory commands with different frequencies and magnitudes were sent and the measured outputs were used to identify the parameters based on an identification algorithm. The following values obtained for the parameters of the model with 95% confidence level. For Y axis: J= (6.89±0.244) ×102 (mm/(s2 .amp))

α=10.2±0.45 (1/s)

For X axis: J= (2.01±0.092) ×103 (mm/(s2 .amp))

α=3.89±0.12 (1/s)

Therefore, the transfer function of each axis is as follows

4

=

6.89 × 10 + 10.2

/

=

2.01 × 10 + 3.89

/

Design of the controllers

(2)

(3)


4.1

Feedback controllers

To fulfill the goals of this research the following requirements placed on the feedback controllers:a)Quick damping out of the response to the step disturbance; b)Zerosteady-state errors in response to both the acceleration and ramp input; c)overshoot less than 20% and natural frequency around 10 Hz regarding the limitations of the amplifiers. Moreover, simple and traditional controllers such as PID controllers were preferred.Since in a basic PID control scheme there is just 1DOF, adjusting the response to a step reference input and step disturbance 39

input is difficult

. Therefore, a two- degree-of-freedom PID controller for each axis was

considered for each axis (Fig.4). To find suitable gains for the controllers, the zero-placement approach described in 39 was applied.

Employing the mentioned design approach resulted in a

PID controller in feedforward path and a derivative in thefeedback path (PIDD). The resulted controllers for each axis, which are indicated as PIDD controllers in this paper, are as follows: For Y axis: 1=

1.035

2 = −1.48

+ 0.0022 + 1.86

(4)

#

For X axis 1=

3.54

+ 0.0077 + 6.35

(5)


2 = −1.93

#

In Fig. 5 the step position and disturbance response of each axis are shown.

Fig.4- Feedback control loop

(a)

(b)

Fig. 5- Step reference input (a)andstepdisturbance response of each axis (b)


4.2

Disturbance observer

Although the designed feedback controllers are able to resist disturbances to some extent, disturbance observers were considered to achieve better disturbance rejection and consequently better precision in the machining process. In this work, Kalman filter was used to observe disturbances and the velocity feedback required for thefeedback loop. Dynamics of the linear motors can be formulated asthe following equation in the state space form37: 0 &( 0 0 1 &' % ') = * + *& + + % ) , + -−1/ 01234 &( 0 − .

(6)

In the above equation,Fload stands for the external loads exerted on the motor such as machining forces and M for the mass of the table.To estimate Fload , it can be considered as a state of the system by rearranging the above equation. In such application, Floadis usually considered as a slowly varying state of the system driven by a white noise process with a specific variance 40. Therefore, it can be modeled as a realization of a random walk process: ( 01234 =5

(7)

In which w is a random process with variance of 67 . The system can be presented in the

following augmented form:


&'( 0 1 8 & ( 9 = -0 − ( 0 0 01234 > = &' +

Motion control of a two-axis linear motor driven stage ...

Motion control of a two-axis linear motor driven stage ...

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