Australian Journal of Basic and Applied Sciences. Optimal Design of Controller for Antenna Control Using ACO Approach

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1 Australan Journal of Basc and Appled Scences, 9(7) August 5, Pages: 9-3 ISSN: Australan Journal of Basc and Appled Scences Journal home page: Optmal Desgn of Controller for Antenna Control Usng ACO Approach Mohammed Ahmed, Ejke Chbuzor Anene,, Jbrn Danlad Jya and Ganyu Aynde Bakare Abubakar Tafawa Balewa Unversty, Electrcal and Electroncs Engneerng Department, Faculty of Engneerng and Engneerng Technology, P. M. B. 48.Bauch. Ngera. Abubakar Tafawa Balewa Unversty, Mechatroncs and Systems Engneerng Department, Faculty of Engneerng and Engneerng Technology, P. M. B. 48.Bauch. Ngera. A R T I C L E I N F O Artcle hstory: Receved 3 June 5 Accepted 5 August 5 Avalable onlne September 5 Keywords: PID controller, parabolc dsh antenna syste backlash, Zegler-Nchols method, ant colony optmzaton algorthm. A B S T R A C T In ths paper the applcaton of Ant Colony Optmzaton Algorthm (ACO) to the desgn of a PID controller for poston control of parabolc dsh antenna system s presented. Parabolc dsh antennas are used for lne-of-sght communcatons, and are sometmes actuated by servomotors. Such arrangements mnmze human errors and energy, are quck and easer for repostonng to another drecton or orgnal poston of the antenna when dsplaced by dsturbances such as wnd, gust, bearng and aerodynamc frctons. A PID controller was desgned for the syste usng the Zegler- Nchols method (); the controller was then redesgned usng Ant Colony Optmzaton (ACO) Algorthm (). The closed loop system wthout controller, wth and were smulated usng SIMULINK/MATLAB a software. The smulaton results revealed that wth the ZN controller the rse tme of system was mproved by %, the peak tme by 79%. And wth the ACO controller, the rse tme was mproved by 43%, the peak tme by 663% and the settlng tme by 4%. The rse tme, peak tme and settlng tmes were best wth the ACO controller; therefore all control schemes performed well but the outperformed the rest. 5 AENSI Publsher All rghts reserved. To Cte Ths Artcle: Mohammed Ahmed, Ejke Chbuzor Anene, Jbrn Danlad Jya and Ganyu Aynde Bakare., Optmal Desgn of Controller for Antenna Control Usng ACO Approach. Aust. J. Basc & Appl. Sc., 9(7): 9-3, 5 INTRODUCTION Parabolc dsh antennas have hgh gan and drectvty at very hgh frequences, these propertes made such systems sutable for use n satellte communcatons, radar systems, rado telescopes and so on ( Natala, ).They operate n pont-to-pont mode, therefore the transmttng and recevng antenna have to be algned or be facng each other. Servomotors can be used to poston the parabolc dsh antennas, such that f the system s perturbed by dsturbances most especally wnd and gust t can be repostoned wth relatve ease. It can be made automatc most especally n crtcal sectors such as banks, mass meda, arports etc. The PID controller has three parameters; the proportonal gan K, the ntegral gan K and the p dervatve gan K d. The performance of the controller depends on the relatve magntudes of these three parameters. Determnaton of the magntudes of the parameters s called tunng of the PID controller. The Zegler-Nchols tunng rule s one of the technques used for tunng the PID controllers (Stanslaw, 8). In the work of Atef (9) a Proportonal Integral and Dervatve PID Controller for a brushless DC motor usng Zegler-Nchols tunng rules was desgned. The result of hs research showed that the system had a faster response wth small overshoot and zero steady state error. Neenu and Poongod (9), n ther paper desgned a poston controller for a DC motor by selecton of a PID parameters usng genetc algorthm. The model of the DC motor was consdered as a thrd order system. The paper compares two methods of tunng the parameters of a PID controller. One of the controllers was desgned by the genetc algorthm; the second was desgned by the Zegler-Nchols method. It was found that the proposed PID parameters adjustment by the genetc algorthm was better than the Zegler Nchols method. They also concluded that the proposed method could be appled to the hgher order system also. Boumedène et al., (9) proposed an ntellgent controller of DC Motor drve was desgned usng partcle swarm optmzaton (PSO) Correspondng Author: Mohammed Ahmed, Abubakar Tafawa Balewa Unversty, Electrcal and Electroncs Engneerng Department, Faculty of Engneerng and Engneerng Technology, P. M. B. 48.Bauch. Ngera. Tel: ; E-mal: nunugoloma@yahoo.com

2 Mohammed Ahmed et al, 5 Australan Journal of Basc and Appled Scences, 9(7) August 5, Pages: 9-3 method for formatve optmal proportonal-ntegraldervatve (PID) controller tunng parameters. The proposed approach have superor feature, ncludng easy mplementaton, stable convergence characterstcs and very good computatonal performances effcency. The DC Motor Schedulng PID-PSO controller was modeled n MATLAB envronment. It was observed that comparng wth fuzzy logc controller usng PSO ntellgent algorthms, the planned method was more profcent n mprovng the speed loop response stablty, the steady state error was reduced, the rsng tme was perfected and the dsturbances do not affect the performances of drvng motor wth no overtakng. Problem Formulaton: The desgn of the PID controller usng ACO can be consdered as optmzaton problem of the cost functon J (w) stated as follows: MnJw () w W N J w k k () N k Where; w = K T p, K,, Kd s the PID controller parameter vector and W s the entre search space. The am s to mnmze the cost functon J (w) by adjustng w. The cost functon can be expressed as the tme-averaged cost functon defned n equaton (); Where k k are the nput or and desred and output or actual responses of the system respectvely, and N s the number of samples used for the calculaton of the cost functon. Concept of Ant Colony Optmzaton (ACO): The ACO s one of the most successful general purpose optmzaton technque among the methods developed through ant behavors and t takes nspraton from the foragng behavor of some speces of ant. The ACO s a swarm ntellgence approach to solvng problems. Swarm ntellgence technques are usually nspred base on the behavor of nsects or other anmals. Ants depost pheromone on the ground n order to mark some favourable path to gude other members of the colony; ths was proved through experments by Deneubourg et al n 99 (Marco, 6). The ACO has the advantage of keepng the best result after teraton (Manezzo et al.,). As mentoned prevously lterature revealed that there are varants of ACO algorthm. The Ant System (AS) was utlzed n ths research was whch the frst ACO algorthm ever proposed (Marco, 6). The pheromone values are updated by all ants that have bult a soluton n the teraton assocated wth nodes m and n. The pheromone n s then updated as; τ n = ( ρ)τ n + Δτ n (3) Where; τ n s the amount of pheromone on a gven edge n ρ s the rate of pheromone evaporaton and Δτ n s the amount of pheromone deposted, typcally gven by g m, n [ f ant g travels on edge n, and d g otherwse ] (4) Where d g s the cost of the gth ant's tour (typcally length or dstance). For the edge selecton; an ant wll move from node m to node n wth probablty P, ; n n n n P m, n m n (5) Where; τ n s the amount of pheromone on edge n α s a parameter to control the nfluence of τ n η n s the desrablty of edge n (a pror knowledge, typcally / d n, where d s the dstance between node m to node n ) β s a parameter to control the nfluence of η n. Implementaton of the ACO Based Poston Controller: The PID controller was desgned for the system usng the Zegler -Nchols method (ZN controller) whch s a classcal method of tunng a PID controller. The controller was then redesgned usng Ant Colony Optmsaton (ACO) Algorthm; ACO based controller (ACO controller). The ACO controller was tuned usng a program wrtten n MATLAB codes. The responses of the system wthout any controller, wth NZ controller and ACO controller were smulated usng SIMULINK/MATLAB a software. The performances of the system wthout controller, wth NZ controller and wth ACO controller were then compared. Fg. s a unty feedback system wth Proportonal, Integral and Dervatve (PID) controller. The nput to the closed loop system s and s the output, whch the poston of the parabolc dsh antenna system whch s the plant. The parabolc dsh antenna system model used by Ahmed et al. () was adopted whch s gven by: 36.8 (6) 3 s 5s 5s

3 Ampltude of Response Mohammed Ahmed et al, 5 Australan Journal of Basc and Appled Scences, 9(7) August 5, Pages: 9-3 Fg. : A Unty Feedback System wth PID Controller. Consder the nput-output relatonshp of the system wth the PID controller as shown n Fg., the system transfer functon becomes; 36.8K d s 36.8K ps 36.8K (7) 4 3 s 5s K d s 36.8K ps 36.8K Smulaton Results and Dscusson: The results were smulated usng SIMULINK/MATLAB a. The parameters of the PID controllers were as shown n table. Fgure shows the unt step responses of the system wthout controller, wth and wth ACO Controller. From the graphs wthout the controller; the rse tme was.79 seconds, the peak tme was.45 seconds, the maxmum overshoot was 4.77% and the settlng tme was.49 seconds. For the system wth ZN controller, the rse tme was.55 seconds, the peak tme was.4 seconds, the maxmum overshoot was 8.88% and settlng tme was.93. And wth the ACO controller; the rse tme was.3 seconds, the peak tme was.5 seconds, the maxmum overshoot was 3.7% and the settlng tme was.76. The results showed that the response had mproved drastcally wth the ACO controllers. And they portray that the ACO controller gves the best response. Fg. shows the responses of system wthout the controller, wth and wth ACO Controller to a trackng sgnal. The sgnal n ths case was the rectangular sgnal. The trackng response represents the ablty of the system to track the nput suppled to t, t s smply a scenaro whereby the poston or drecton of the antenna s changed, so t shows the ablty of the system to respond to the command gven to t. Here also the response of the system wth the ACO controller was most superor because ts response follows the nput sgnal more closely. Fgs. 3, 4 and 5 are graphs of the system wthout controller, wth and wth the ACO Controller respectvely, for dfferent postons of the antenna n 6, 4 and steps. Therefore ths portrays a stuaton whereby the antenna s poston at those postons. It can be seen that from the plots that rrespectve of the poston the system t returns to steady state. Fgs. 6 and 7 are plots of the system when perturbed. The perturbaton represents a stuaton whereby the antenna system s ht by dsturbances whch are manly gust and wnd. The system s perturbed n Fg. 6 when t s n transent state whle the latter when t s at steady state. For all the controllers and both case perturbatons the system reaches steady state, as t can been seen from the graphs the was the fastest to reach steady state, followed the and then wthout the controller. These show that all the controllers are robust. Table : Optmal Controllers Parameter Settngs..4. The Unt Step Response Wthout Controller Tme (seconds) Fg. : Unt Step Response of the System. Summary and Concluson: In ths paper, a PID controller was successfully desgned for the system based on the Ant Colony Optmzaton (ACO) Algorthm. The system was also successfully smulated and tested wthout controller, wth ZN controller and wth ACO controller usng SIMULINK/MATLAB a. The system performance wth the ZN controller were mproved n terms of the rse tme by %, the peak tme by 79% and the settlng tme %, whle the maxmum overshoot was worsen by %. And wth the ACO controller, the rse tme was mproved by 43%, the

4 Ampltude of Response Ampltude of Response Mohammed Ahmed et al, 5 Australan Journal of Basc and Appled Scences, 9(7) August 5, Pages: 9-3 peak tme by 663% and the settlng tme by 4%, whle the maxmum overshoot was worsen by 38%. It was observed that the ACO controller has better performance n terms of the rse tme, peak tme, maxmum overshoot and settlng tmes are superor wth the controllers, wth that of the ACO controller beng the best wth an acceptable overshoot (Katsuhko, ). It performed best n sgnal trackng test, the system reaches steady state when postoned at dfferent postons and all the controllers pass robustness test. Therefore, all control schemes performed well but the outperformed the rest. Therefore, a controller has been desgned successfully usng the Ant Colony Optmzaton algorthm for the closed loop operaton of the parabolc dsh system wth better performance than wthout controller and usng the Zegler-Nchols method..5 Trackng Sgnal Response Trackng Sgnal Wthout Controller Tme (seconds) Fg. 3: Trackng Sgnal Response. 8 7 Dfferent Reference Postons (Wthout Controller) 6 Degrees 4 Degrees Degrees Tme (Seconds) Fg. 4: Unt Step Response for Dfferent Reference Postons wthout controller. 8 7 Dfferent Reference Postons () 6 Degrees 4 Degrees Degrees Tme (Seconds) Fg. 5: Unt Step Response for Dfferent Reference Postons wth. 8 7 Dfferent Reference Postons () 6 Degrees 4 Degrees Degrees Tme (Seconds) Fg. 6: Unt Step Response for Dfferent Reference Postons wth ACO controller..4. Robustness Test Response (Transent) Input Sgnal Wthout Controller Tme (seconds) Fg. 7: Response to Perturbaton/Robustness Test (Transent State).

5 Ampltude of Response 3 Mohammed Ahmed et al, 5 Australan Journal of Basc and Appled Scences, 9(7) August 5, Pages: Robustness Test Response(Steady State) Input Sgnal Wthout Controller Tme (seconds) Fg. 8: Response to Perturbaton/Robustness Test (Steady State). RFERENCES Natala, K.N.,. ECE753 Modern Antennas n Wreless Telecommuncatons, Lecture notes. School of Electrcal and Computer Engneerng, Purdue Unversty. Stanslaw, H.Z., 8. ECE38 Proportonal- Integral-Dervatve (PID), Lecture notes. School of Electrcal and Computer Engneerng, Purdue Unversty. Atef, S.O.A., 9. Proportonal Integral and Dervatve Control of Brushless DC Motor. European Journal of Scentfc Research, 35(): Neenu, T. and P. Poongod, 9. Poston Control of DC Motor Usng Genetc Algorthm Based PID Controller. Proceedngs of the World Congress on Engneerng, : -5. Boumedène, A., G. Brahm and M. Brah 9. Settng Up PID DC Motor Speed Control Alteraton Parameters Usng Partcle Swarm Optmzaton Strategy. Leonardo Journal of Scences, 4: 9-3. Marco, D., B. Mauro and S. Thomas, 6. Ant Colony Optmzaton Artfcal Ants as a Computatonal Intellgence Technque. IEEE Computatonal Intellgence Magazne, 6: Manezzo, V., L. M. Gambardella and F. Lug,. Ant Colony Optmzaton. Ahmed, M., J.D. Jya, E.C. Anene and Y.S. Haruna,. Unty Feedback Poston Control of Parabolc Dsh Antenna Usng Zegler-Nchols and Pole-Placement Methods. Ngeran Journal of Scence and Technology Research. Paper accepted for publcaton. Katsuhko, O.,. Modern Control Engneerng. New Jersey. Prentce Hall Publshers. Agee, T., 99. Stablzaton of Dsh Antennas n Wndy Envronment. M. S. thess, Abubakar Tafawa Balewa Unversty, Bauch, Ngera.