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Abstract: The tracking-differentiator algorithm is adopted in the position and speed detection system and suspension system of maglev train to solve the practical ...
Proceedings of the 34th Chinese Control Conference July 28-30, 2015, Hangzhou, China

On Realization of Signal Processing Based on Tracking-Differentiator for Maglev Train DOU Fengshan, WANG Zhiqiang, HE Hongli, LONG Zhiqiang School of M echanics Engineering and Automation, National University of Defense Technology , Changsha 410073 E-mail: [email protected] Abstract: The tracking-differentiator algorithm is adopted in the position and speed detection system and suspension system of maglev train to solve the practical problems of signal processing. The realization of signal processing based on tracking-differentiator in Field Programmable Gate Array (FPGA) is studied. In this paper, the tracking- differentiator algorithm is described with Very-High-Speed Integrated Circuit Hardware Description Language (VHDL) and the calculation process is introduced. M eanwhile, the tracking-differentiator algorithm is simulated in M ATLAB-M odelsim, and tested in the experiment. The simulation and experiment results illustrate that it is feasible to achieve the signal processing based on tracking-differentiator in FPGA. Key Words: M aglev Train, Signal Processing, Tracking-Differentiator, FPGA Realization



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capabilities, and powerful re-configurability as well as

Introduction

scalability. In this paper, the signal processing based on

In the system of hybrid maglev train based on

tracking-differentiator is realized in the signal processing

synchronous traction of long stator, the suspension is

platform of FPGA with VHDL.

achieved by electromagnetic suction, and the operation is

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controlled by synchronous traction of long stator on the

VHDL Description

ground. In the position and speed detection system, the

A discrete second-order nonlinear tracking- differentiator

output signal will be abnormal when the relative position

based on boundary characteristic curves is proposed in

detection sensors pass through the joint of stator, which will

literature [4], which can quickly track the input signal, and has

increase the difficulty of position and speed detection, and

no flatter and overshoot. Meanwhile, the algorithm is more

[1, 2, 3]

concise compared to the tracking-differentiator proposed by

affect the regular operation

. In the suspension system,

Han Jingqing.

the accelerometer is adopted in the gap sensor, and the noise jamming will be occurred for the presence of electromagnetic

This type of differentiator is easy to be realized in FPGA for

interference and the effect of error transmission in the

its no radical sign, logarithm, power in the calculation process,

process of signal transmission, which will affect the control

which are difficult to be achieved in hardware. The discrete form of tracking-differentiator is:

performance of the system seriously.

­ ° x1 (k  1) x1(k )  hx2 (k ) ® ° ¯ x2 (k  1) x2(k )  hu (k ) ( u d r )

Numerous studies show that tracking-differentiator can not only extract differential signal accurately, but also has a strong filter capability. It is widely applied to the field of Wherein

maglev train, and there have done a thorough research on the application of tracking- differentiator in the position and

(1)

x1 , x2 are the state variables, u is the control

h is the discrete step, r is the value range of u , and u is the function of x1 , x2 , h , r , which can be

function,

speed detection system as well as suspension system of maglev train in literatures [4, 5, 6]. It is necessary to have a research on the realization of signal processing based on tracking-differentiator to make

written as:

u

fxie( x1 , x2 , r , h)

(2)

signal processing algorithms be applied to the system of maglev train actually. FPGA has been widely used in the field

The control function can be selected through the method

of digital signal processing for its strong parallel computing

of variable substitution in the case of a given signal v(t ) :

u

*

T his work is supported by National Key T echnology R&D Program of China under Grant 2013BAG19B01

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fxie( x1  v, x2 , r , c0 h)

(3)

Then,

x1 o v x2 | x1c

State S3: Saving the current state. The value of the updated

vc can be realized by adjusting

the parameter r and value of

state is assigned to x1

c0 properly, and the tracking

as a basis for the next iteration to obtain the value of the next

filtering and differential extraction of the input signal will be realized with the output of

and x2 to store the current state, and

time.

x1 , x2 .

Under the control of the clock, the state S1, S2 and S3 cycle. The output signal will be obtained

Discrete tracking-differentiator algorithm is essentially an

with the iterative

calculation by collecting input signal continuously.

iterative process, and there is a context between these iterative formulas. The context on the timing cannot be

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reflected just listing formulas for VHDL is carried out in

Simulation Analysis

parallel computing. In view of the design of Finite State

3.1

Machine (FSM), the calculation process is divided into

MATLAB-Modelsim combines powerful simulation capabilities of Modelsim and rich data processing means of MATLAB, the process of simulation is shown in Fig. 2.

three parts, and every part is defined as a state. Under the control of the clock, the calculation process cycles among

Simulation Process

the three states, as shown in Fig. 1.

Data_generator.m

Generate Given Signal

Input

Read Data

Filter.vhd

Data Processing

Data_out.m

Save Data

Read, Analyse, Dispose Data Filter_test.vht

S1: Calculating controlling function

Fig. 2: M ATLAB-M odelsim simulation process

3.2

Simulation Results

v is

S3: Saving the current state

a given input signal, in which the DC component, sinusoidal component, as well as white noise are included. The simulation results are shown in Fig. 3. It can be observed that the trend of the output and input signal is basically the same, and the noise in the signal is reduced significantly, which illustrates that the filtering algorithm with VHDL is effective.

S2: Updating state variables

Output

Fig. 1: Process of state cycle

In the iteration process, the current state is defined as

x1 , Input

x2 , the previous state is x10 , x20 , the input signal is v ,

clk . The current state is recognized by the rising edge of clk , and the corresponding calculation will the clock signal is

Output

be done according to the value of current state, meanwhile, the value of the next clock cycle will be given. State S1: Calculating control function. The value of the control function

ut is calculated based on the current Fig. 3: Simulation results of analog signal

state x2 . State S2: Updating state variables. according to the previous state

In order to observe the filtering effect better, M file is

x1 is obtained

written to read the input and output signals , which are stored

x10 , x20 . x2 is obtained

in text file, and an M-file program is written to have an

according to the previous state x20 , ut . In order to avoid

analysis on simulation results. Meanwhile, the tracking-

error being occurred in the process of integer division, both

differentiator algorithm is written in MATLAB to deal with the given signal, and then make a comparison with the

2

sides of the first equation multiplied by T , and both sides of

simulation results in Modelsim, which are under the same

the second equation multiplied by T . The desired filtered

excitation signal, as shown in Fig . 4. It can be seen that the

and differential output will be obtained by extracting the value of

filter of VHDL can track the useful component of given signal

x1 and x2 at the end of state updates.

well, and filter out the white noise of the signal. The result is

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slightly different compared with the result calculated in

results show that there is a slight difference in comparison

MATLAB, which is mainly due to the definition of the data

with the simulation results in MATLAB, but overall the error

type. The data type is integer, and it leads to loss of precision

is not great.

after the division. But overall, the relative error is in the range of tolerance.

1 Input Differential in MATLAB Differential in Modelsim

0.8 0.6

2700 Input Output in MATLAB Output in Modelsim

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0.4 amplitude

2600

amplitude

2550 2500

0.2 0 -0.2 -0.4

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-0.6

2400

-0.8

2350 2300

0.01

0.02

0.03 time/s

0.04

0.05

0.06

2250 2200

(a) 0-0.02s simulation results 0.01

0.02

0.03 time/s

0.04

0.05

0.06

Fig. 4 : Time-domain waveform of signal after filtering

Input Differential in MATLAB Differential in Modelsim

-0.3 -0.4

In order to analyze the filtering effect from the frequency domain, there is a frequency spectrum analysis on the input and output signals, the results are shown in Fig. 5. The frequency spectrum of the 0 to 4000Hz is shown in the left side, and the right side is a partially enlarged view of 0 to 100Hz. The results show that the design of the filter can preserve the DC component and the sinusoidal component of given signal well in the range of low frequency, and the attenuation of noise is more visible in the range of high frequency

amplitude

-0.5 -0.6 -0.7 -0.8 -0.9

0.02

0.022

0.024

0.026

0.028 time/s

0.03

0.032

0.034

0.036

(b) Enlarged effect 140

140

Fig. 6: Time-domain waveform of signal after differential

130

spectrum of input signal spectrum of input signal

120

spectrum of input signal spectrum of input signal

120

4

100 amplitude/dB.

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Experiment Analysis

80

100

After the effectiveness of the algorithm is verified in

60

90

simulation, the algorithm is downloaded to signal test board

80

for testing. In order to generate a given waveform and noise

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easily, the input signal is generated inside the FPGA. The

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testing scheme of filter is as follows. First, write the program

40

20

0

0

1000

2000 3000 frequency/Hz

4000

50

0

50 frequency/Hz

of waveform generation, then, generate waveform in FPGA as

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input signal, which outputs through DA of one channel, and the filtered signal outputs through DA of another channel.

Fig. 5: Spectrum analysis after filtering

Meanwhile, acquire the two outputs of DA simultaneously, According to the previous simulation process, the

and observe the waveform of them in the oscilloscope.

simulation of differential is done. And then a comparison with

To observe the filtering effect, a sinusoidal input signal

the results calculated in MATLAB is made, as shown in Fig.

is given, in which irregular noise is included. The

6. A period of the simulation result is shown in Fig . 6 (a), in

experimental results show that the noise signal has been

which the phase of resultant differential output advances

eliminated after the processing of filtering, the sinusoidal

close to 90°, and the amplification to the noise of given signal

signal turns smooth, and the amplitude, frequency of the

is inconspicuous. Fig . 6 (b) is a partially enlarged effect. The

filtered output signal are similar to the input signal,

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filtered signal is around 4ms. The filtering capacity is

channel 1 is the given signal waveform, and channel 2 is the

enhanced as

filtered output waveform.

filtered signal enlarged.

c0 increased, while the phase delay of the

amplitude˄mv˅

amplitude˄mv˅

meanwhile, the phase lag is small, as shown in Fig. 7, which

time(ms)

time(ms)

Fig. 7: Filtering effect of sinusoidal input signal

(a) Filtering result when

c0

=5

To observe the differential effect, a sinusoidal signal is amplitude˄mv˅

given. Since there is no negative voltage output in DA, the DC offset is joined in the differential signal, so that the output signal of the DA will be observed conveniently. AS shown in Fig . 8, the output is sinusoidal, and the phase advances close to 90° compared to the input, and the noise of output is small, which Channel 1 is the given input signal, channel 2 is the

time(ms)

differential output signal. The results show that the designed

(b) Filtering result when c 0 = 10

amplitude˄mv˅

amplitude˄mv˅

differentiator can extract differential signal preferably.

time(ms)

time(ms)

(c) Filtering result when c 0 = 20

Fig. 8: Differential effect with sinusoidal input signal

Fig. 9: Filtering result when c0 at different values

To observe the effect of the filtering factor c0 , a sinusoidal signal with white noise which its amplitude is about 31.2% of

Conclusion In this paper, the realization of the signal processing based

the signal is given. The results are shown in Fig . 9, where c0

on tracking differentiator is studied. The algorithm is

is at different values, and channel 1 is the given signal with

described with VHDL, and the calculation process is

noise, channel 2 is the filtered output signal. When c0 = 5,

introduced. Meanwhile, the tracking-differentiator algorithm is simulated in MATLAB-Modelsim, the simulation results

the amplitude of noise is suppressed to about 50% of the

illustrate that the filtering algorithm with VHDL is effective.

original noise, the phase delay of the filtered signal is small. When

c0

After the effectiveness of the algorithm is verified, the

= 10, the amplitude of noise is further reduced,

experiment is carried out, and the results illustrate that signal

while the phase delay of the filtered signal becomes larger. When

c0

processing based on the tracking-differentiator can be well achieved in FPGA.

= 20, the filtered output is smooth, and the noise in

the signal can be well suppressed, but the phase delay of the

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Acknowledgements This work is supported by the National Key Technology R&D Program of the 12th Five-year Plan, Systematic Study on Engineering Integration of High Speed Maglev Transportation, 2013BAG19B01.

Reference [1]

[2]

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[6]

LI Lu, WU Jun, LUO Hong-hao. Research of Joint –passing of Speed and Position Detection System of M aglev Train [J]. Journal of the China Railway Society, 2009, 31(2), 69-72. DAI Chunhui, XUE Song, LONG Zhiqiang. The Signal Disposal of Position and Speed Detection Sensors Based upon Long Stators for M aglev Train [J] .Chinese Journal of Sensors and Actuators, 2009, 6(22), 822-826. Tang Li. Study and Realization of high-speed M aglev Vehicle Relative Location Sensor [D]. Chengdu: Southwest J1aotong Un1versity, 2006. XIE Yunde. A Discrete Second-Order Nonlinear Tracking-Differentiator Based on Boundary Characteristic Curves [J].Control and Decision, 2014, (6):1120-1124. LI Lu. The Research on Suspension Gap and Relative Position Detecting Technology in High Speed M aglev Train [D]. Changsha: National University of Defense Technology, 2007.

He Ning. Optimal Design and Realization of Relative Position Detection Sensor for High Speed Maglev Train [D].Changsha: National University of Defense Technology, 2012.

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