SELF-TUNING ALGORITHM AGAINST MAGNETIC

ACTUATOR WIND-UP FOR MILLING SPINDLE

POSITION REGULATION

Nan-Chyuan Tsai, Rong-Mao Lee and Chun-Chi Lin

Department of Mechanical Engineering, National Cheng Kung University, Tainan City, Taiwan

Keywords: Windup, Active Magnetic Bearing, Saturation of Actuator, PID Controller.

Abstract: An Anti-Windup (AW) compensator is applied to the Embedded Cylindrical-Array Magnetic Actuator

(ECAMA) to sustain the performance of spindle position regulation under actuator saturation. Since

ECAMA is a type of Active Magnetic Bearing (AMB), the maximum supplied coil current and the induced

magnetic force are both limited by their extrema. In this work, an AW compensator is proposed and

employed to compensate the output of PID controller to prevent saturation of ECAMA. By employing

commercial software MATLAB/Simulink and signal processing interface, Module DS1104 by dSPACE, the

efficacy of the AW compensation is practically verified by intensive experiments.

1 INTRODUCTION

Windup is generally referred to the saturation

phenomenon of actuators, i.e., the magnitude or rate

of actuator output is limited by an upper bound.

Consequently, the required control input cannot be

realized by the actuator as long as the magnitude of

control input exceeds the saturation level of the

associated actuator (Astrom and Rundqwist, 1989.

Tarbouriech, Queinnec and Garcia, 2007).

In this work, an Anti-Windup (AW) compensator

is applied to the Embedded Cylindrical-Array

Magnetic Actuator (ECAMA) for milling machines

(Tsai and Lee, 2010) to sustain the performance of

spindle position regulation under actuator windup.

Since the maximum supplied coil current and the

induced magnetic force are both limited by the

extrema of ECAMA, the saturation phenomenon

takes place, once the required control input exceeds

the upper limit of the power amplifier. That is, if the

induced magnetic force reaches its upper limit, the

control law will not be applicable any more and

hence the tremble of spindle becomes drastic.

In this work, an AW compensator is employed to

compensate the output of a PID controller to prevent

windup of ECAMA caused by the electric current

saturation at power amplifier.

2 ANTI-WINDUP (AW)

COMPENSATOR

Generally speaking, there are two approaches which

can be adopted to avoid actuator saturation. The first

approach is to take the actuator limit into the

consideration of controller design directly. However,

the design of controller becomes complicated or

cannot be realized for practical applications. The

alternative approach is to separate the prevention of

windup from the controller design. The controller,

without any constrains on actuator, is firstly

designed to meet the performance requirements.

After the controller has been designed, the AW

compensator is developed to ensure closed-loop

system stability.

The concept of AW compensation is depicted

in Fig. 1 (Tarbouriech and Turner, 2009). The

“Unconstrained Controller” is referred to the

controller with no actuator limit has been designed.

The AW compensator output is either the

constrained or unconstrained control input and

defined as follows:

⎪

⎩

⎪

⎨

⎧

≤≤

min min

maxmin

maxmax

for

uuu

uuuu

uuu

(1)

where

max

and

min

are the upper limit and lower

195

Tsai N., Lee R. and Lin C..

SELF-TUNING ALGORITHM AGAINST MAGNETIC ACTUATOR WIND-UP FOR MILLING SPINDLE POSITION REGULATION.

DOI: 10.5220/0003529801950198

In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 195-198

ISBN: 978-989-8425-74-4

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

limit of control input respectively. Once the required

control input is beyond the upper or lower thresholds,

the AW compensator gets engaged. The

compensation command can be joined to the

feedback signal (

1aw

) or to the output of controller

directly (

2aw

). Such an approach is attractive in

practice because no restriction is imposed upon the

controller design.

3 EMBEDDED

CYLINDRICAL-ARRAY

MAGNETIC ACTUATOR

(ECAMA)

ECAMA is a type of Active Magnetic Bearing

(AMB) and designed for high-speed milling

applications. The proposed ECAMA and the spindle

are depicted in Fig. 2. In addition, a high-speed

motor (>20000 RPM) and a self-sensing module for

spindle position deviation measurement are

equipped at the two ends of spindle. The

configuration of the ECAMA is shown in Fig. 3. It is

mainly composed by the modified concave-type

yokes (Tsai and Hsu, 2007) and the I-shape

electromagnets. The prototype of the I-shape

electromagnets are shown in Fig. 4. Totally 1200

turns of coils are wound around each individual I-

shape silicon steel core.

4 CONTROL STRATEGY FOR

ACTUATOR WINDUP

The unconstrained controller employed in this work

is the PID controller. Owing to the integral action,

the output of controller tends to exceed the upper

limit of power amplifier once a large error exists.

The block diagram of spindle position control

system is shown in Fig. 5. The output of controller is

applied to the coils at ECAMA via power amplifiers.

By tuning the supplied coil current, the spindle

position can be regulated by the induced magnetic

forces. In fact, the AW compensator in Fig. 5 is a

gain. By compensating the input of integral term, the

controller output can be suppressed to be within

unsaturated region. Since the magnetic saturation

against ECAMA is determined by both the supplied

coil current and the area of I-shape silicon steel core,

the actual upper limit of the supplied coil current for

the AW compensator design in this work is

evaluated by experiments. According to the

experimental results (Tsai and Lee, 2010), the upper

and lower ampere-turns limits of coil are found to be

2000 and 0 ampere-turns respectively. Since the coil

wound on each I-shape electromagnet is 1200 turns,

the upper and lower limits of supplied coil current

are 1.67 A and 0 A respectively.

5 EXPERIMENTAL RESULTS

The test rig in our work, including the milling

machine (by How-mau Mchinery CO., LTD, Model

CNC-K3), is depicted in Fig. 6. The original milling

spindle of CNC-K3 is replaced by the proposed

ECAMA. Prior to the experiments, a set of PID

gains which can operate stably under low rotating

speed, i.e., 1000RPM is given. The follow-up

experiments are performed under spindle speed of

6000 RPM. The experimental results in X-axis are

shown in Fig. 7~Fig. 10. Fig. 7 and Fig. 8 are the

outputs of the controller without and with AW

compensation respectively. It is obvious that the

windup phenomenon induces large control outputs,

no matter in positive or negative side. On the

contrary, all the controller outputs are within

,200

which is referred to the supplied coil voltage of

V,20

under AW compensation. The spindle

position deviations in X-axis without and with AW

compensation are shown in Fig. 9 and Fig. 10. The

dotted lines in Fig. 9 and Fig. 10 are referred to the

maximum spindle position deviation which is

limited by the Auxiliary Bearing (AB) (Tsai, Shih

and Lee, 2010) to avoid collision in case

malfunction of ECAMA occurs. The spindle

position deviation under actuator saturation is shown

in Fig. 9. Drastic tremble of spindle and collision is

observed. However, the spindle position deviation,

shown in Fig. 10, is much improved under AW

compensation and no collision between spindle and

ECAMA/AB bearing takes place. In other words, the

efficacy of the AW compensator for actuator

saturation is verified.

6 CONCLUSIONS

The AW (Anti-Windup) compensator is proposed

and applied to ECAMA (Embedded Cylindrical-

Array Magnetic Actuator) to retain the performance

of spindle position regulation under actuator windup.

According to the experimental results, without any

modification of the PID controller, the controller by

aid of AW compensator can still operate well under

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

196

actuator saturation. However, ECAMA is designed

for high-speed milling. Since the cutting force

between the cutter and workpiece sometimes alters

drastically in a very short period of time during the

practical milling process, the response of ECAMA

might not be able to instantly follow up. That is, an

anti-windup compensation against saturation of

supplied current grow rate is therefore required. The

forthcoming research by the authors will be focused

on this issue.

7 FIGURES

Unconstrained

Controller

(Reference)

(Disturbance)

Plant

Anti-Windup

Compensator

aw1

aw2

Figure 1: Schematic Diagram of Anti-Windup

Compensation.

Figure 2: ECAMA and Spindle for Mill Machine.

Modified Concave-type Yoke ( )

Spindle

I-shape Electromagnet ( )

( I-shape Silicon Steel Core

with Coil Wound )

4×

8×

Figure 3: Configuration of ECAMA.

Figure 4: Prototype of I-shape Electromagnets (Bottom

View).

ECAMA

(Position)

Anti-Windup

Compensator

PID Controller

Power

Amp.

Spindle

Dynamics

Figure 5: Block Diagram of Spindle Position Control

System.

Figure 6: Test Rig for AW Compensation.

SELF-TUNING ALGORITHM AGAINST MAGNETIC ACTUATOR WIND-UP FOR MILLING SPINDLE POSITION

REGULATION

197

0.00 1.00 2.00 3.00 4.00 5.00

-400.00

0.00

400.00

800.00

Time (Sec.)

Control Signal for ECAMA in X-axis

Figure 7: Controller Output w/o AW Compensation

(Speed: 6000RPM).

0.00 1.00 2.00 3.00 4.00 5.00

-200.00

-100.00

0.00

100.00

200.00

Time (Sec.)

Control Signal for ECAMA in X-axis

Figure 8: Controller Output with AW Compensation

(Speed: 6000RPM).

0.00 1.00 2.00 3.00 4.00 5.00

-0.80

-0.40

0.00

0.40

0.80

Time (Sec.)

Spindle Position Deviation in X-axis (mm)

0.50

-0.50

Figure 9: Spindle Position Deviation w/o AW

Compensation (Speed: 6000RPM).

Time (Sec.)

Spindle Position Deviation in X-axis (mm)

0.00 1.00 2.00 3.00 4.00 5.00

-0.80

-0.40

0.00

0.40

0.80

0.50

-0.50

Figure 10: Spindle Position Deviation with AW

Compensation (Speed: 6000RPM).

REFERENCES

Astrom, K. J., Rundqwist L., 1989. Integrator Windup and

How to Avoid It. In Proceeding American Control

Conference. Pittsburgh, USA.

Tarbouriech, S., Queinnec I., Garcia, G., 2007. Anti-

Windup Strategy for Systems Subject to Actuator and

Sensor Saturations, Chap. 6 in Advanced Strategies in

Control systems with Input and Output Constrains.

LNCIS, Vol. 346, Springer-Verlag.

Tsai, N.-C., Lee, R.-M., 2010. Regulation of Spindle

Position by Magnetic Actuator Array. International

Journal of Advanced Manufacturing Technology. DOI:

10.1007/s00170-010-2830-0.

Tarbouriech, S., Turner, M., 2009. Anti-Windup Design:

An Overview of Some Recent Advances and Open

Problems. IET Control Theory and Applications, Vol.

3, No. 1, pp. 1-19.

Tsai, N.-C., Hsu, S.-L., 2007. On Sandwiched Magnetic

Bearing Design. Electromegnetics, Vol. 27, No. 6, pp.

371-385.

Tsai, N.-C., Shih, L.-W., Lee, R.-M., 2010.

Counterbalance of Cutting Force for Advanced Milling

Operations. Mechanical Systems and Signal Proce-

ssing, Vol. 24, No. 4, pp. 1191-1208.

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