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Model-free controller optimizes antenna azimuth positioning
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Model-free controller optimizes antenna azimuth positioning
1.
International Journal of
Scientific Research and Engineering Development-– Volume 2 Issue 5, Sep – Oct 2019 Available at www.ijsred.com ISSN : 2581-7175 ©IJSRED:All Rights are Reserved Page 384 Model-Free Based on La-Lead Compensator for Antenna Azimuth Position David Monjengue Independent researcher, Maputo , Mozambique Email: bmonjengue@yahoo.com ----------------------------------------************************---------------------------------- Abstract: This research intended to control the positioning of antenna azimuth system with a model-free controller. The model-free controller presented here, has proven to be able to reach comparable performances than advanced techniques controllers. The model-free controller design has a simple structure, its implementation and tuning rule are simple, and does not need any special knowledge about control theories and modelling of the system. It is more efficient than some advanced controllers such as LQR, FLC, QFT, because it can reach similar performances than these controllers, but with less requirements in term of time and effort needed to design the controllers and to tune it, when requested. Keywords —Antenna azimuth, Model-free controller, Proportional integral derivative controllers (PID), Fuzzy Logic Controllers (FLC), Linear Quadratic Regulator (LQR), Quantitative feedback theory (QFT). ----------------------------------------************************---------------------------------- I. INTRODUCTION An antenna is a necessary component of any wireless system [1]. Wireless communication systems have been more and more important in day to day live with the development of digital cellular networks, wireless networking for internet access, wireless sensor networks, point-to-point wireless connectivity, mobile broadcasting systems, navigation satellite systems. The antenna positioning system is required to reduce the pointing error which will enable to receive highest signal strength. Moreover, the increased size of antennas, creates multiple pointing and control challenges [2]. Several techniques were proposed to achieve an optimum control of the azimuth position but such positioning remains a control challenging problem [3]. PID controllers were proposed [4], [3], Fuzzy logic controllers were used and showed better performances than PID [5], hybrid PID-LQR controller [6], and Quantitative feedback theory [7] also showed good performances. Most of the cited methods used a mathematical model of the system to derive the right control strategy to apply on it. In this paper, we explore a different approach; we try to control the positioning of an antenna azimuth without knowing the model of the system. Since the antenna azimuth is well- known and many studies have successfully managed to control it for decades, it is not efficient to still rely on mathematical modelling and advanced control techniques to end with performances that can be easilyobtained with less efforts. Model-free controllers could be very useful for antenna azimuth positioning as they do not depend on the model of the system. Furthermore, the antenna system can be subject to environment changes (wind, dust, etc.) and non-linearities, which are very hard to model in order to design the proper controller. RESEARCH ARTICLE OPEN ACCESS
2.
International Journal of
Scientific Research and Engineering Development ©IJSRED: The purpose of this study is to design a controller that is efficient in term of performances and operability (easy to realize and operate design time requirement should be minimum and the tuning rule should be simple. II. MODEL-FREE CONTROLLER There are already some model-free con present in the literature, for which we can extract two main: - Model-free controller based on local model [8], [9]; - Model-free controller based on Pseudo partial derivative [10]. The above model-free controllers have been implemented with success, but there is no tuning rule proposed in case the need to refine the controller parameters arises. In addition, there are not easy to implement, and may request a lot of expertise to determine the value of the controller parameters. Thus, they do not meet our fixed requirement to be easy to implemented and easy to tune. The proposed model-free controller has a simple structure, it can be implemented easily or hardware. It does not need the mathematical model of the system to be controlled. The below figure (fig.1) represents the principle of the proposed model-free controller, which consist of two parts: - The in-loop part, composes of a Derivative controller, which role is to eliminate the pure integral of the plant, and reduce the disturbances; - The out-loop, compose of a lag compensator, which roles is to transform input signal to a more suitable signal that the in-loop part can use it to achieve the control objectives. Figure 1: Block diagram of the Model-free controller. K.s - + International Journal of Scientific Research and Engineering Development-– Volume 2 Issue 5, Sep Available at www.ijsred.com ©IJSRED: All Rights are Reserved The purpose of this study is to design a Model-free efficient in term of performances and operate). The design time requirement should be minimum and FREE CONTROLLER free controllers present in the literature, for which we can extract free controller based on the Ultra free controller based on Pseudo- free controllers have been h success, but there is no tuning rule proposed in case the need to refine the controller parameters arises. In addition, there are not easy to implement, and may request a lot of expertise to determine the value of the controller not meet our fixed requirement to be easy to implemented and easy to free controller has a simple easily by software or hardware. It does not need the mathematical The below figure (fig.1) represents the principle of free controller, which consists loop part, composes of a Derivative controller, which role is to eliminate the pure integral of the plant, and reduce the loop, compose of a lag-lead compensator, which roles is to transform the to a more suitable signal such use it to achieve the free controller. A. Model free controller Parameters and objective From fig.1, we can see that the controller has three parameters, “K”, the derivative gain, “ These last two are the main controller parameters, used to refine the plant performances. In order to reduce the complexity, a mathematical relation between “a” and “b” was extracted. In this way, only one parameter is needed (we choose arbitrary the parameter “a”), the other parameter, “ case, is drive from a mathematical given relation. B. Stability analysis The system is stable if the plant, represented by is stable and the out-loop compensator is stable as well. 0 C. Error analysis The antenna block diagram is represented in the fig. 2 below [11]. Figure 2: Block diagram of antenna azimuth position before introduce the controller. Let assume that the antenna is represented by the transfer function: ! " " (1) Then, the block diagram of the all system can be represented by the fig.3. Figure 3: Block diagram of the system with the model controller. G(S) K.K.K.K.s - +%& Volume 2 Issue 5, Sep – Oct 2019 www.ijsred.com Page 385 Model free controller Parameters and objective From fig.1, we can see that the controller has three ”, the derivative gain, “a” and “b”. last two are the main controller parameters, used to refine the plant performances. In order to reduce the complexity, a mathematical relation between “a” and “b” was extracted. In this way, only one parameter is needed (we choose arbitrary ”), the other parameter, “b” in this case, is drive from a mathematical given relation. The system is stable if the plant, represented by G(S) loop compensator is stable as ', The antenna block diagram is represented in the fig. : Block diagram of antenna azimuth position represented by the Then, the block diagram of the all system can be : Block diagram of the system with the model-free () * +, - +- %.
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International Journal of
Scientific Research and Engineering Development ©IJSRED: From fig.3, we derive the complete transfer function as: (() - +, +- (() . (2) Applying the final value theorem, we obtain: /0 lim →. (() - +, +- (() . (3) 56 (() +- (() . (4) 789:, (() +- (() <9=<< >+? =@_+??) 68< + B +C= ?C9_+??) >?D)=< 9?E 68< + 56 5>+. (5) The system final value depends on two sub the in-loop closed loop sub-system out-loop sub-system. Let us compute the error F, G %& H /0(6) (5) in (6), G %& H /I . J K J (7) From (7), we can derive the value of b as: LM NOP H 1 (8) If we want to drive the error to zero, we set E=0 from (8), then we can compute the value of NOP H 1 (9) To find “b” we only need to know the closed loop system final value ( /I , “a” is the model parameter that is used to improve the system performance. “a” is a positive real number, initially set to can be increase or decrease. /I is determine by experiment, only by using the system and the in International Journal of Scientific Research and Engineering Development-– Volume 2 Issue 5, Sep Available at www.ijsred.com ©IJSRED: All Rights are Reserved From fig.3, we derive the complete transfer Applying the final value theorem, we obtain: B +C= 5>+ 68< + B +C= The system final value depends on two sub-systems 5>+ and the as: If we want to drive the error to zero, we set E=0 from (8), then we can compute the value of b: we only need to know the closed loop is the model-free parameter that is used to improve the system a positive real number, initially set to a=1, is determine by riment, only by using the system and the in- loop controller and take the stable final value for the desired input. III. SIMULATION The simulations were conducted using the transfer functions for the antenna system as described by Okumus [4], Suresh [7], and Linus [6]. The software used for the simulation was Scilab version 5.5.2. R.RS T.T.UT " TUT After applying the in-loop of the model controller we have: R.RS " T.T.UT TUT A. Model-free controller parameters 1st simulation: K=1, a=1, b=25.79 from (9), with sample time=1ms. Figure 4: Step response of the system with b=25.79. The step response of the system with model controller shows that there is no overshoot, no error and the settling time is Ts=4.14s. Although, the model-free controller achieved a good “overshoot” and “No error”, in the first try with K=1, a=1 (the only parameters to be tuned), its settling time is very low compared to the one obtained by advanced controller (see table 1, below). Volume 2 Issue 5, Sep – Oct 2019 www.ijsred.com Page 386 the stable final value for IMULATIONS The simulations were conducted using the transfer functions for the antenna system as [4], Suresh [7], and Linus [6]. The software used for the simulation was Scilab (10) loop of the model-free (11) free controller parameters 1st simulation: K=1, a=1, b=25.79 from (9), with /I 0.008, : Step response of the system with K=1, a=1, The step response of the system with model-free controller shows that there is no overshoot, no error and the settling time is Ts=4.14s. free controller achieved a good “overshoot” and “No error”, in the first try with K=1, a=1 (the only parameters to be tuned), its settling time is very low compared to the one obtained by advanced controller (see table 1,
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International Journal of
Scientific Research and Engineering Development ©IJSRED: Therefore, there is a need for tuning the controller parameters to meet settling time requirements of advanced controllers. In the second simulation we tried to improve the system response, by increase the value of “ “a”. B - Model-free controller parameters 2nd simulation K=600, a=10, b=0.43 from (9), with 0.959, sample time=0.1ms. Figure 5: Step response of the system with K=600, a=10, b=0.43. The system now, has good performances similar to the performances obtained with advanced controller techniques as shows in the comparative table below: TABLE I:TABLE 1. COMPARATIVE TABLE FOR DIFFERENT CONTROL TECHNIQUES. Parameter Settling time (S) Oversho ot (%) PID Proportional, Integral Derivative 0.8 23.5 LQR Linear Quadratic Regulator 2.4 <4 PID-LQR 1 5 FLC Fuzzy logic Controller 0.125 0 STFLC Self turning FLC 0.05 0 QFT Quantitative Feedback Theory 0.09 2.24 MFC Model-free controller 0.07 0 International Journal of Scientific Research and Engineering Development-– Volume 2 Issue 5, Sep Available at www.ijsred.com ©IJSRED: All Rights are Reserved the controller parameters to meet settling time requirements of the In the second simulation we tried to improve the system response, by increase the value of “K” and free controller parameters 2nd simulation K=600, a=10, b=0.43 from (9), with /I : Step response of the system with K=600, a=10, The system now, has good performances similar to the performances obtained with advanced controller techniques as shows in the comparative DIFFERENT CONTROL Oversho Error (rads) 0 1 0 0 0 0.0033 0 For the system used, the tracking specifications were defined as follow [7]: Y % [ 12%, ] ^ 0.2 _, G``a` From table 1, we can see that the model controller designed here has reached the desired specifications, and its performances are similar to those of STFLC and QFT, without the need to know system parameters or model. It is that the model-free controller required small amount of time for its design and it is easy to tune without the need to know any equation or rules, its performances are very near to the one of advanced techniques for the system used here. IV. CONCLUSIONS We have achieved the design of a simple model free controller easy to use and to implement, however its performances are similar to those of some advanced control technique (LQR, FLC, QFT etc.) for the control of antenna azimuth position. The tuning was reduced to a trivial increase of two parameters “K” and “a”. It only requires to know the system closed-loop final value, which can be known by a prior test. Theoretically, this model controller can be designed in few minutes, thus it will save a lot of time to the control system engineer. It also does not required a particular knowledge of system model, to be able to tune it, making it suitable for industries. The future work will be directed to simulation in laboratory with real system, the studies of the effects of disturbances and the design of an intelligent model controller which may be useful to minimize the effects of disturbances and the non Volume 2 Issue 5, Sep – Oct 2019 www.ijsred.com Page 387 the tracking specifications G``a` ^ 1%. From table 1, we can see that the model-free controller designed here has reached the desired specifications, and its performances are similar to those of STFLC and QFT, without the need to know system parameters or model. It is enlighten free controller required small amount of time for its design and it is easy to tune without the need to know any equation or rules, its performances are very near to the one of advanced techniques for the system used here. We have achieved the design of a simple model- free controller easy to use and to implement, however its performances are similar to those of some advanced control technique (LQR, FLC, QFT etc.) for the control of antenna azimuth position. was reduced to a trivial increase of two parameters “K” and “a”. It only requires to know loop final value, which can be known by a prior test. Theoretically, this model-free controller can be designed in few minutes, thus it lot of time to the control system engineer. It also does not required a particular to be able to tune it, making it suitable for industries. The future work will be directed to simulation in laboratory with real ies of the effects of disturbances and the design of an intelligent model-free controller which may be useful to minimize the bances and the non-linearities.
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International Journal of
Scientific Research and Engineering Development-– Volume 2 Issue 5, Sep – Oct 2019 Available at www.ijsred.com ISSN : 2581-7175 ©IJSRED: All Rights are Reserved Page 388 REFERENCES [1] K. M. LUK, “The Importance of the New Developments in Antennas for Wireless Communications”, Proceedings of the IEEE, Vol. 99, No. 12, December 2011, DOI: 10.1109/JPROC.2011.2167430, p2082-2084. [2] W. Gawronski, "Control and pointing challenges of antennas and telescopes," Proceedings of the 2005, American Control Conference, 2005, Portland, OR, USA, 2005, pp. 3758-3769 vol. 6, doi: 10.1109/ACC.2005.1470558. [3] A. Uthmanand S.Sudin, “Antenna Azimuth Position Control System using PID Controller & State-Feedback Controller Approach”, International Journal of Electrical and Computer Engineering (IJECE) Vol. 8, No. 3, June 2018, pp. 1539-1550 ISSN: 2088-8708, DOI: 10.11591/ijece.v8i3.pp1539-1550. [4] H.İ. Okumus, E. Sahin and O. Akyazi, “Antenna Azimuth Position Control with Fuzzy Logic and Self-Tuning Fuzzy Logic Controllers”, in Electrical and Electronics Engineering (ELECO), Nov. 8th International Conference IEEE, pp. 477-481, 2013. [5] L. Xuan, J. Estrada and J. Digiacomandrea, “Antenna Azimuth Position Control System Analysis and Controller Implementation”, term project, 2009. [6] L. A. Aloo, P. K. Kihato and S. I. Kamau, “Servomotor-based Antenna Positioning Control System Design using Hybrid PID-LQR Controller”, European International Journal of Science and Technology Vol. 5 No. 2 March, 2016. [7] S. Suresh, R. Binoy, “Antenna azimuth position control using Quantitative feedback theory (QFT)”, International Conference on Information Communication and Embedded Systems, ICICES 2014, doi: 10.1109/ICICES.2014.7034112. [8] P. A. Gédouin, E.Delaleau, J. M.Bourgeot, C. Join, S. A. Chirani,andS. Calloch, “Experimental comparison of classical PID and model-free control: position control of a shape memory alloy active spring.” Control Engineering Practice, Elsevier, 2011, 19 (5), pp.433-441. [9] M.Fliess, C. Join, M. Bekcheva, A.Moradi andH.Mounier. “A simple but energy efficient HVAC control synthesis for data centers. 3rd International Conference on Control, Automation and Diagnosis, ICCAD’19, Jul 2019, Grenoble, France. ffhal-02125159f. [10] W. Mingmei, C.Qiming, C.Yinman, and W.Yingfei. “Model-Free Adaptive Control Method for Nuclear Steam Generator Water Level”. 2010 International Conference on Intelligent Computation Technology and Automation. DOI 10.1109/ICICTA.2010.131. [11] Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons.
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