Zhi-fu GUO， Zi-fi ZHANG， Hong WANG

(1Shenhua Shendong Coal Group Corporation Limited, Yulin 719315,China) (2School of Mechanical Engineering, China University of Mining & Technology, Beijing 100083,China) (3Taiyuan Institute Co.Ltd. of China Coal Technology and Engineering Group, Taiyuan 030006,China)

Abstract: Based on power spectrum estimation, closed-loop indirect identification method is proposed to deal with system identification of servo-valve controlled even hydraulic actuators, and its identification accuracy has been analyzed using different data lengths, windows, overlaps, segments and sensor resolutions. Firstly, an improved chirp signal is used to stimulate servo-valve controlled even hydraulic actuators. Then, open loop frequency characteristics of actuators are identified by using above method with measured input and output data. Finally, identification accuracy analysis using different signal processing is carried out through numerical simulation. The simulations results show that higher parameter identification accuracy can be obtained by using higher resolution sensor, longer data length, 2 segments and hamming window.

Key words: Power spectrum estimation, System identification, Servo-valve controlled symmetrical hydraulic actuators

1 Introduction

During servo-valve controlled system design procedure, researchers made great efforts on system identification of servo-valve controlled hydraulic system to decrease system uncertainty and improve robustness. Zhao[1] proposed grey box modeling method based on ordinary differential equation identification. Huang and Xie[2-3] developed mean square method and recursive gradient correction method to deal with parameter estimation of unsymmetrical cylinder. Sun and Zhang[4-5] introduced T-S fuzzy model identification and BP neural network to system identification of hydraulic AGC system for cold rolling mill. Literatures[6-9] also mainly focused on structured model identification of hydraulic system, which is convenient for theory analysis and design. Because structured model has given order and structure, it is an approximation of real physical system with certain model error. In order to facilitate practical controller design, controller design software tools have begun to support direct controller design with frequency response data model. As a result, how to acquire frequency response data and exactly model becomes a big problem.

This paper proposed a closed-loop indirect identification method based on power spectrum estimation to deal with frequency response data model identification of open loop servo-valve controlled symmetrical actuators. Quantitative accuracy analysis is also carried out under different sensor resolution, signal data length, window function and data segment.

2 Closed-loop indirect identificationmethod based on power spectrumestimation and its influence factors

2.1 Power spectrum principle

As shown in Figure1, cross correlation function ofX(n) andY(n) is as follows:

RXY(m)=E{X(n)Y(n+m)}=

RX(m)*h(m)

(1)

Its Fourier transform is:

PXY(ω)=PX(ω)H(ω)

(2)

Identification result of transfer functionH(ω) is:

(3)

In order to eliminate effect of noise signal, coherence functionγ2(ω) is adopted and its desired value is 0.8～1.

(4)

2.2 Indirect closed-loop identification

Closed-loop system block diagram is shown in Fig.1.P(s) is system plant,Y(s) is output signal,X(s) is input signal,N(s) is disturbance signal.

Fig.1 Indirect closed-loop identification schematic

The closed-loop output can be written as:

(5)

Transfer function of system plant is:

(6)

Then, the parameters ofP(s) can be identified through open-loop system identification method. Therefore, the estimated open-loop frequency response model is as follows:

(7)

2.3 Improved chirp signal

The improved chirp signal is used as input signalX(s), its mathematical form is as follows:

(8)

fi∈[0.2，0.4，…,40]Hz

Where,Ais amplitude,fiis current signal frequency,niis counter of current frequency,fi-1is last signal frequency,ti-1is shift time fromfi-1tofi,Tis sampling time.

(9)

The frequency of input signal has four period of each current frequency, and it will shift from 0.1 Hz to 40 Hz.

2.4 Accuracy influence factors

During system identification, identification accuracy will be greatly influenced by sensor resolution, signal length, windows function and data segments. Hence, object function of Levy complex number fitting method is used as main index to estimate identification accuracy.

(10)

3 System identification of servo-valvecontrolled symmetrical hydraulic actuators

In order to verify effectiveness of proposed identification method, servo-valve controlled motor is chosen as research object, which is given by

(11)

The improved chirp signal input is shown in Fig.2. Its frequency will shift from 0.2 Hz to 40 Hz, which has 4 period of each current frequency.

System output response under chirp signal input is shown in Fig.3. System will track the input signal well in low frequency zone, but stimulate the resonance in high frequency zone.

Finally, system frequency response data model can be identified with chirp signal input data and output response data by using power spectrum estimation method, which is shown in Fig.4. Magnitude and phase frequency data corresponding to each curve can be directly used for controller design.

Fig.2 Improved chirp signal input

Fig.3 System output under improved chirp signal

Fig.4 Frequency response data model identified by power spectrum estimation

4 Accuracy analyses under different influence factors

During the identification procedure, input data and output data will be discretized, respectively, with 12bit resolution, 16bit resolution and analog infinite resolution. Accuracy analyses is carried out under different signal processing means including 4 period, 8 period and 16 period stimulating signal of each frequent, rectangle window, hanning window, hamming window, and different data segment. The index function is shown in Equation (10).

Accuracy comparison result under different signal length with different sensor resolution are shown in Fig.5, and 12 denotes 12bit resolution sensor, 16 denotes 16bit resolution sensor, and inf denotes analog sensor. Solid line represents error generated with 16 period stimulating signal of each frequent. Dot line represents error generated with 8 period stimulating signal of each frequent. Dash line represents error generated with 4 period stimulating signal of each frequent. From the comparison of these curves, it is clear that smaller identification error can be achieved by higher resolution sensor and longer stimulating signal.

Accuracy comparison result using different window functions with different sensor resolution is shown in Fig.6. Solid line represents error generated by hamming window. Dot line represents error generated by hanning window. Dash line represents error generated by rectangle window. Based on the comparisons of these curves, it is clear that smaller identification error can be achieved by higher resolution sensor using hamming window.

Fig.5 Identification errors resulted from input data length with different sensor resolution

Fig.6 Identification errors resulted from window with different sensor resolution

Accuracy comparison result using different data segment with different sensor resolution is shown in Fig.7. Solid line represents error generated by 1 data segment. Center line with spark represents error generated by 2 data segment. Dash line represents error generated by 4 data segment. Dot line represents error generated by 8 data segment. Center line represents error generated by 16 data segment. Based on the comparisons of these curves, it is clear that smaller identification error can be achieved by higher resolution sensor with 2 data segment.

Fig.7 Identification errors resulted from segments with different sensor resolution

5 Conclusions

This paper proposed a closed-loop indirect identification method based on power spectrum estimation to deal with frequency response data model identification of servo-valve controlled symmetrical actuators. The identification errors have been compared under different sensor resolution, signal data length, window function and data segment. The following conclusions could be safely drawn:

(1) For servo-valve controlled symmetrical actuators, power spectrum estimation method could directly acquire frequency response data model without additional model error as compared to the structured model.

(2) Higher identification error can be obtained with higher resolution sensor, longer stimulating signal through hamming window and 2 data segment.

Acknowledgements

This paper is sponsored by Shanxi Province Youth Technology Research Foundation(No.2015021127).