Rotary Inverted Pendulum stabilization with time delays using BAT optimization

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1 ITSI Transactions on Electrical and Electronics Enineerin (ITSI-TEEE) Rotary Inverted Pendulu stabilization with tie s usin BAT optiization Srikanth avirayani, Gundavarapu V Naesh uar Assistant Professor, GVPCE(A),Visakhapatna Associate Professor,GITA University, Visakhapatna Abstract The influence of tie on a rotary inverted pendulu stabilization was encountered with the help of a BAT alorith for stabilization. The loudness and pulse rate paraeters used in a typical BAT alorith when varied ave useful insihts into the functionality of the effectiveness of the alorith when the converence of the syste was considered for a iven fitness of peak overshoot. The tradeoff between settlin tie and peak overshoot has been studied and the tie of coputation was seen as a paraeter contributin to the success of the alorith. Index Ters stability, aloriths,, paraeter optiization, position control I. INTRODUCTION The desin and realization of the rotational Inverted pendulu(rip) control syste structure dates back to the classical Indian rope trick where a rope is ade to stand in thin air. The control of this odel involves the successful stabilization of the pendulu syste about its unstable equilibriu position. This syste is a non linear syste siilar to the inverted pendulu ounted on a cart which has becoe a benchark under-actuated syste that has been widely used in any control laboratories to find the effectiveness of different control approaches in a anner analoous to the control of any real systes. Rotary Inverted Pendulu(RIP) is a typical underactuated non-linear plant which has potential applications in the field of entertainent, defense, aerospace, echatronic systes and other industrial applications which use various levels of anipulators. RIP as a syste can be used for understandin and actin as an aid for control education. A typical rotary inverted pendulu has a rotary head and also a pendulu at the end which is free to oscillate about its axes fro the unstable equilibriu position to the stable equilibriu position. Typically the arraneent has a otor driven control for such a syste usin which the stability can be achieved. Researchers akkapati et al [] have discussed about Usin Pade approxiation for the dead tie of a sinle input sinle output plant where the output trackin proble for the approxiated non-iniu phase syste can be reforulated as a state trackin proble. Several authors have developed prototypes for the rotary inverted pendulu and also have developed toolboxes usin which the characteristics of the plant such as ass of the rotary ar, lenth of the ar and the specifications of the otors that can be controlled ar. Various types of controllers such as LQR, LQG, H-Infinity, alan filter based observer desin have been applied by researchers. Active re-search has happened on other versions of the rotary in-verted pendulu systes such as the double inverted pendulu and double inverted pendulu systes. The use of optiization techniques such as eta-heuristic ethods to optiize the cost of usin a particular controller has been predoinant in the control of coplex systes. Natural inspired aloriths such as BAT, Firefly, Particle swars have been exhaustively used keepin in view the varied advantaes of tie of coputation, resource utilization and speed of converence. In this paper, the effect of tie contained in the rotary inverted pendulu is iniized usin full state feedback controller based on BAT optiization. The tie caused in the sinal transitted to the otor that control the input of the rotary inverted pendulu and also a transport to the sinal iven to the pendulu are considered in Srikanth et al. [4]. On successful iniization of the loudness paraeter the desined values are used as the poles of the syste that can be applied to the linearized plant which is in the proxiity of the unstable equilibriu position. The dynaics of such a syste have been further odified by introduction of a tie paraeter which chanes the state atrices and a new set of state a-trices are evolved. These evolved states are further stabilized with the help of BAT optiization and the results are copared with that of the syste without tie. It was observed that in ters of settlin tie, peak overshoots, peak tie, there is wide spread advantae of introducin the tie. The proposed controller has iven satisfactory perforance even under the influence of tie when copared with a syste without tie II. SYSTE DYNAICS WITH TIE DELAY Below are the typical equations of the plant that needs to be controlled can be represented fro the euler laranian equations with various variables as tabulated in appendix A and with the dynaics of the rotary inverted pendulu can be iven usin equations and. Cos sin cos 3 sin () Cos 4 ( 3 sin ) sin sin cos () Where ISSN (PRINT) : , Volue -3, Issue -4, 5

ITSI Transactions on Electrical and Electronics Enineerin (ITSI-TEEE) Where τ in equation refers to the control input which is applied to the shaft of the ar and i (i=,,, 3, 4) in equations and are

the pendulu and the rotary ar are added a transport la and then the pendulu is tried to be swun up and also stabilized.

2 ITSI Transactions on Electrical and Electronics Enineerin (ITSI-TEEE) Where τ in equation refers to the control input which is applied to the shaft of the ar and i (i=,,, 3, 4) in equations and are positive syste paraeters defined as I l (3) (4) l L (5) l (6) 3 l 4 I l L (7) The fiure below indicates the block diara which represents the condition where the encoders that are connected to both the pendulu and the rotary ar are added a transport la and then the pendulu is tried to be swun up and also stabilized. s s ) x ( ) x (9) x ( x ( ) x x () Where in equation refers to the tie in the control input which is applied to the rotary ar and X denotes the odified output state condition. Now introducin a new state variable λ into the syste, 4 () Tuo Tuo The odified state atrices because of addition of tie paraeter causes a new state to arise which odifies the syste as iven below: Fi.. Typical syste with full state feedback usin BAT and tie in output The dynaics of the plant are odified to accoodate the tie influence on the syste. So, takin the four states that represent as follows a fifth state is added which will influence the syste paraeter and the effect of the state is considered as tie. A transport was incorporated into the syste. The dynaic syste update involves the followin loical process Fi.. Typical DAQ syste [] The tie paraeter which is considered here is at the output easureent which directly affects the syste perforance and is iven at the DAQ. With the help of Pade approxiation, the shift operator can be approxiated by a rational transfer function of first order as ( s / ) ( s / ) e s (8) The tie paraeter would dynaics would involve an additional state defined fro the followin Fi. 3 Encoders Connections of Rotary Inv Pendulu [] The is introduced in the input value received by the data acquisition device fro the coputer of the rotary inverted pendulu. The followin assuption is additionally considered alon with eneric assuptions as in [] a) A sall is considered in transittin the input applied to the pendulu. The plant equations are considered as follows under state space representation as follows: bd / E qd / E Where a J CG / E bg / E A u A 4 / Tuo / Tuo ISSN (PRINT) : , Volue -3, Issue -4, 5 eq b Lr r c 4/ 3L d L E ac b G t R c t A R E B eq R ()

The loudness of the shouts and echos of the bat are taken as the paraeters of the alorith and are used for fine tunin the fitness of a function.

3 Aplitude of Ar vel Aplitude of Pend vel ITSI Transactions on Electrical and Electronics Enineerin (ITSI-TEEE) A b t R E III. BAT ALGORITH BAT alorith is a nature inspired alorith where echolocation behaviour of bats is used as a procedure for obtainin the fitness of the function. The loudness of the shouts and echos of the bat are taken as the paraeters of the alorith and are used for fine tunin the fitness of a function. Aurora [] showed the usae of this alorith extensively in enineerin desin optiization and has iplications on future research. BATS used only sonar data for detection of food, trackin eneies and locatin their surroundin the ipleentation of an alorith that iics the behavior of BAT can be iven as follows usin the below flow chart as shown in fiure 5. Fiure 6 indicates the control loic involved for odelin the systes under the influence of tie. control effort was less. However the dapin involved ore oscillations which indicate that the syste used a systeatic control effort. Fiure 7 indicates the variation was siilar and without tie the response las in coparison. As it can be clearly seen fro fiures 6 to 9 the influence of tie is ainly seen on the settlin tie when copared to the peak overshoot variation. The control effort that oes into the syste ainly as influenced the settlin tie which indicates that the perturbations about the final steady state value are very uch dependent on the nature and kind of input alon with the s that cause the syste to oscillate between the stable and unstable states. % Peak overshoot 8% without tie 6% 4% % Peak overshoot % with tie Fi. 5. Relative Perforance variation with and without tie Settlin Tie without Tie Step response of syste for BAT optiization Without Tie With tie of. secs.5 Fi. 4. Flow chart of BAT alorith IV. RESULTS The perforance of the rotary inverted pendulu in ters of the dynaic response is tested with the BAT alorith where the pendulu velocity and position, ar position and velocity are evaluated. The analysis on the settlin tie and peak overshoots is iven below in fiure 5 where the influence of tie is sinificantly seen in settlin tie with and without tie, however, the influence on the peak overshoot is less due to the tie s. It was observed in fiure 6 the pendulu velocity was very hih whereas the overshoot was less with a tie which indicated the use of tie and the BAT alorith toether have used less enery. Fiure 7 indicates ar velocity and the variation was siilar to that with tie of seconds. In fiure it was observed that without tie aain the peak overshoot was hih which indicates consuption of ore enery for stabilization but with the tie the Tie Fi. 6. Pend velocity variation with and without tie Tie Fi. 7. Ar velocity variation with and without tie ISSN (PRINT) : , Volue -3, Issue -4, Step response of syste for BAT optiization Without Tie With tie of. secs

4 Aplitude of Ar an Aplitude of Pend an ITSI Transactions on Electrical and Electronics Enineerin (ITSI-TEEE) Tie Fi.8. Pend anle variation with and without tie Step response of syste for BAT optiization Fi. 9. Ar anle variation with and without tie V. CONCLUSION Based on the analysis done it could be established that the rotary inverted pendulu control usin a BAT optiization yielded useful insiht for the control in ters of control effort. The desined ethod under the influence of tie could be applied for hiher order systes where the tie s are inherent. It could be also be considered that the effect of tie is to destabilize the syste, however within critical tie boundaries the syste still can be stabilized without ajor concerns. The use of these s in view of unwanted dead tie s that are inherent with lare scale process controls can be analyzed with the help of this dynaic syste as an exaple where we could clearly be convinced that s cause bottle-necks to the process flow loic, however they can also be blessins in disuise. REFERENCES Without Tie With tie of. secs Step response of syste for BAT optiization Without Tie With tie of. secs Tie [] V. P. akkapati,. Reichhartiner and. Horn, (3), The output trackin for dual-inertia syste with dead tie based on stable syste center approach, 3 IEEE ulti-conference on Systes and Control, Conference on Control Applications, Hyderabad, India, pp [] Arora, S.; Sinh, S.,(3), "A conceptual coparison of firefly alorith, bat alorith and cuckoo search," Control Coputin Counication & aterials (ICCCC), 3 International Conference on, vol., no., pp.-4, 3 [3] Ait onar, Coputational Intellience Techniques Principles, Techniques and Applications, Spriner, [4] avirayani Srikanth, G V Naesh uar, (5),"Rotary inverted pendulu control and the ipact of tie on switchin between stable and unstable states with enhanced particle swar optiization",international Journal of Coputer and Counication Syste Enineerin, Volue, Issue 4 [5] Enache, A.-C.; Sarciu, V.,(4) "Anoaly intrusions detec-tion based on support vector achines with bat alorith," 4 8th International Conference Syste Theory, Control and Coputin (ICSTCC) vol., no., pp [6].Srikanth, Dr. G.V.Naesh uar, (4), Desin and Control of Pendulu with Rotary Ar usin Full State Feedback Controller based Particle Swar Optiization for Stabilization of Rotary Inverted Pendulu, Proceedins of 38th National syste conference on real tie systes odelin, Analysis and control, JNTU Hyd, Telanana, India. pp [7] avirayani Srikanth,G V Naesh uar, "Stabilization At Upriht Equilibriu Position of a Double Inverted Pendulu With Unconstrained Bat Optiization", International Journal on copuatational science and appliactions(ijcsa),october 5, Volue 5, Nuber 5 [8] anikanta, G.; Naesh uar, G.V.,(4) "Thyristor Con-trolled Series Capacitor placeent and sizin usin BAT search optiizer to enhance power flow," 4 International Conference on Coputation of Power, Enery, Inforation and Counication (ICCPEIC), vol., no., pp [9] S N Sivananda, S N Deepa, Control Systes Enineerin usin ATLAB,Vikas Publishin house pvt. Ltd., 9 [] Quanser User anuals, ech En, RA Laboratory IIIT,Nuzvid Appendix A: Specifications for RIP Description Value θ Pendulu Anle fro the - vertical θ Ar anle fro the vertical - θ Anular Velocity of - Pendulu ISSN (PRINT) : , Volue -3, Issue -4, 5 3

5 ITSI Transactions on Electrical and Electronics Enineerin (ITSI-TEEE) θ Anular velocity of Ar - p ass of Pendulu.7 k r ass of rotary ar.57 R otor arature resistance.6 Oh B p Equivalent Viscous Dapin Coefficient.4 N..s/rad η Gear box Efficiency.9 η otor electroechanical.69 Efficiency Gravitational constant 9.8 /sec J eq Equivalent oent of inertia w.r.to load.. J otor arature oent of inertia 4.663e-7. J r Rotary ar oent of 9.989e-4 Inertia. L p Pendulu full lenth.3365 otor back-ef constant.77 V.s/rd t otor torque constant.77 N./A l p Distance fro Pivot to.556 t Centre Of Gravity l r Rotary ar distance fro.69 t pivot to center of ass V Aplifier axiu Output 4V Voltae I Aplifier axiu Output 4A Current e Pendulu encoder resolution 496 counts/rev τ Tie to.sec-4s encoders(in-ax) ec S Sensitivity for Tie - T ISSN (PRINT) : , Volue -3, Issue -4, 5 4

Studying Large Scale System Using Decentralized Control

Studying Large Scale System Using Decentralized Control Studyin Lare Scale Syste Usin Decentralized Control MRHOJJAI, SAKRAMINEJAD, MRAZMDIDEH Mechanic Electronic Institute, Junior Collee of asa, IRAN hojatir@ailco, sakrain@ailco, ahdiehlady@yahooco Abstract: