Automatic Frequency Calibration Using Fuzzy Logic Controller

A way of frequency calibration using jizqv logic controller (FLC) is presented in this paper. Generally, atomic clocks tend to drzfr due to temperature, aging, or some emironmental eflects. It is sure that one cannot compensate for the drift with a fuced amount of control quantity. As a controller, it has the task to adaptively catch up with the vurzation. Our approach takes advantage of FLC to determine the control quantiv. Three procedures are employed in our approach. Firstly the performance of the device being calibrated is observed continuously. Then the FLC uses the performance data to generate the control quantity, Finally the FLC calibrates the device using the computed control quantrw. The FLC can calibrate the device at any time since the performance of the device is continuousIy being monitored In the experiment, we use F M S (Frequency Measurement and Analysis System) as the performance evaluation equipment and the FLC is realized by a PC. In the experiment, a cesium-beam oscillator is chosen as the target. The result validates the eflectiveness of our approach. An oscillator with fiequency ofset of --1.4 x 1 01'3 can be improved to approximate& 1.0 x 1 0-l4 aafr one week of calibration. INTRODUCTION Due to temperature, aging, or some environmental effects, atomic clocks generally tend to drift in an unknown way. This ends up with a difficulty in characterizing the clock. For example, it is not possible to compensate for the drift with a fixed amount of control quantity during frequency calibration [I]. A fizzy logic controller (FLC) has been 1 deemed to be suitable for use in a time-varying, nonlinear, or hard-to-defined system 121. In this paper, we use FLC 1 to adaptively determine the control quantity to compensate for the drift. Three procedures are employed in our approach. First, the performance of the device being calibrated is continuously being monitored. Note that this requires a reference frequency with accuracy much better than that of the device being calibrated. Second, the performance data are connected to the FLC. Upon receiving data fkom the performance evaluation equipment, the FLC calculates the control quantity according to some fuzzy rules. Finally, the FLC calibrates the device through the command compliant to some particular form. The FLC can calibrate the Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE DEC 1998 2. REPORT TYPE 3. DATES COVERED 00-00-1998 to 00-00-1998 4. TITLE AND SUBTITLE Automatic Frequency Calibration Using Fuzzy Logic Controller 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) National Standard Time & Frequency Lab.,Telecom Labs. of Chunghwa Telecom Co., Ltd,12, Lane 55 1, Min-Tsu Road Sec. 5, Yang-Mei, Taoyuan,Taiwan 326, ROC, 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES See also ADA415578. 30th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting, Reston, VA, 1-3 Dec 1998 14. ABSTRACT see report 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as Report (SAR) 18. NUMBER OF PAGES 6 19a. NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 device according to some predefined criteria. For example, it can be done at a regular interval or on an on-demand basis. The performance evaluation equipment used in this work is the FMAS (Frequency Measurement and Analysis System), measurement equipment developed by NIST (National Institute of Standards and Technology). The FLC is realized by a commercial PC. Fig. 1 shows the system configuration. The reference frequency used is the master clock in our laboratory. The accuracy of the reference frequency is better than 5 x lo-" and hence is sufficient for calibrating most commercial oscillators. Let y,e,_,d,, denote the fiequency offset of the reference frequency relative to the ideal frequency; i.e., Y , , ~ , ~ ~ ~ = (f,, f,,,I)lAj;dral . Similarly, the frequency offset of the user's clock relative to the reference frequency is y,_, = (fun f,,) 1 f,, and that of the user's clock relative to the ideal clock is y = ( fu.w f, dtal ) I JhO, . Having these relations, the frequency offset of the user's clock relative to the ideal clock can be expressed ;is Hence, if fm, G f;, , then y M. r_, can be approximated by It is obvious from (2) that y E y I provided y ,_,, 0 , and the phase offset at the beginning of each observation interval is assumed to be zero. Note that this is tantamount to balancing the phase offset with an action of single step made at the beginning of each observation interval. Also, we use bold lines to indicate the residual frequency offsets in the corresponding observation interval. It is intuitively seen that the phase offset resulting from the frequency offset of yn_, > 0 (i.e., Aen_, as shown in the figure) can be balanced by imposing a phase offset with direction opposite to the former; i.e.,(on =-Aen_, . However, as mentioned in the last section, oscillators tend to drift in an unknown way. It is therefore not possible to keep residual frequency offset to a minimum with such a fixed amount of control quantity. If the residual is equal to zero (i.e., yn = 0) after the above action is done, then the control quantity is deemed to be temporarily correct. In this case, the controller has the task to keep the same control quantity in the next observation interval; i.e., (on+l = (on as shown in Fig. 2a. If the residual has a positive slope, i.e., yn > 0, then the controller has the task to increase the controller quantity; i.e., l v n + , l > lqn) as shown in Fig. 2b. On the contrary, if the residual has a negative slope, i.e., y,, < 0 , the controller has the task to decrease the control quantity; i.e., l p n + l l < /(on 1 as shown in Fig. 2c. The variation of phase error is generally nonlinear. The one shown in Fig. 2a is but a hypothetical case. It cannot be an easy job to have a proper control quantity for atomic clocks. To overcome this difficulty, the FLC is used to evaluate the control quantity before applying it to the device being calibrated. In this work, the control quantity is made to be adaptive in the way where Aq, is the updating term and is determined by the FLC. The initial value of qp can be chosen arbitrarily. Fig. 3 shows the basic structure of an FLC. It consists of the following four units: 1) fuzzidcation unit, 2) fuzzy reasoning unit, 3) fuzzy rule base and fuzzy data base unit, and 4) defuzzification unit. Two variables are used as the input to the fuzzy rule base. One is the frequency offset read from the FMAS (i.e., y,,). The other is the difference of the frequency offsets between two adjacent observation intervals (i.e., Ayn = yn yV_, ). Table 1 gives the fuzzy rule base used in this work. The ranges for the two input variables and the output are divided into five parts. They consist of the following fuzzy sets: NB (Negative Big), NS (Negative Small), ZE (ZEro), PS (Positive Small), and PB (Positive Big). The membership functions chosen for these fuzzy sets are of a triangular form. Fig. 4 shows the membership functions stored in the fuzzy data base. Additionally, the fuzzy reasoning method chosen is the Max-Min method, and the mean of maximum (i.e., modified centroidal) is used as the method of defuzzification [2]. EXPERIMENT RESULTS In our experiment, a cesium-beam oscillator is chosen as the device being, calibrated. The frequency offset of a cesium lies between y,, E [-I x lo-'', 1 x lo-" ] and therefore Ay? E [-2 x lo -" , 2 x Taking these ranges into account, the membership functions shown in Fig. 4 are scaled by 1 0-l3 and 2 x lo-" respectively for yn and Ayn . The range for the output is the same as y, . The oscillator originally has frequency offset of 1.4 x 10-l3 . The result shows that the frequency offset can be improved to 1.0 x 10-l4 after about one week. Fig. 5 shows the variation of the frequency offset.