Control of Autonomous Underwater Vehicles using Neural Network Based Robust Control System

Transcription

1 Interntionl Journl of Mechnicl Engineering Control of Autonomous Underwter Vehicles using Neurl Network Bsed Roust Control System İkl ESKİ nd Şhin YILDIRIM * Erciyes University, Fculty of Engineering, Mechtronics Engineering Deprtment, Kyseri, 3839, Turkey, ikl@erciyes.edu.tr, *shiny@erciyes.edu.tr (Corresponding uthor Astrct: - A neurl network sed roust control system design for the yw ngle of utonomous underwter vehicle (AUV is presented in this pper. Two types of control structure were used to control prescried trjectories of n AUV. The results of the simultion showed tht the proposed neurl network sed roust control system hs superior performnce in dpting to lrge rndom disturnces such s wter flow under se. Finlly, the proposed neurl controller improved tht this kind of neurl predictors could e used in rel time pplictions of n AUV. Key-Words: - Neurl network control, roust control, utonomous underwter vehicles, PID controller 1 Introduction Nowdys, AUVs vehicle hve een widely used for underwter investigtions. A mnoeuvring control of n underwter vehicle from the perspective of comined discrete-event nd discrete-time system simultion hs een investigted y Son nd Kim [1]. The proposed simultion model estlished on the sis of discrete-event system specifiction formlism, which ws representtive modelling formlism of discrete-event system simultion. The proposed pproch mde possile to uild simultion-sed expert system which supports the decision mking for the cquisition of the underwter vehicle. Dynmic sttion keeping of n under ctuted fltfish type AUV hs een nlysed nd new method of sttion keeping hs een proposed with n ddition of dedicted thrusters []. Effect of introduction of dditionl thrusters on trcking performnce nlysed nd modulr configurtion suggested reducing its influence on trcking control. Also, comprtive nlysis on power consumption during sttion keeping reserched to prove the effectiveness of the proposed modulr configurtion. An dptive neuro-fuy sliding-mode-sed genetic lgorithm control system for remotely operted vehicle with four degrees of freedom hs een presented y Moghddm nd Bgheri [3]. A set-point controller for utonomous underwter vehicles ws proposed y Hermn [4]. The controller ws expressed in trnsformed equtions of motion with digonl inerti mtrix. The stility of the proposed control lw proved nd the performnce of the developed controller hve een pproved vi simultion on the underwter vehicle. Another investigtion, new control scheme for roust trjectory control hs een presented for the underwter vehicles. The effectiveness of the controller ws verified through simultions nd execution issues were discussed [5]. Adptive control of low speed io-rootic utonomous underwter vehicles in the dive plne using dorsl fins ws considered. An indirect dptive control system hs een developed for depth control using dorsl fins. According to the simultion results, the dptive control system ccomplished precise depth control of the io-rootic utonomous underwter vehicle using dorsl fins in spite of lrge uncertinties in the system prmeters [6]. Autonomous underwter vehicle control rchitectures were reviewed nd sensor dt us sed control rchitecture ws investigted y Kim nd Yuh [7]. A wve drift force ffecting severely the underwter vehicle in shllow wter hs presented y Luo et l. [8]. On the sis of wve force nlysis, three dimension disturnces cused y wvy surge wter mesured nd control system using lest squres multi-order dt fitting polynomil prediction nd fuy compenstion comined with PID controller ws put forwrd. The experimentl results showed tht the control system for disturnce of surge nd wve ws fesile nd effective. ISSN: Volume 1, 16

2 Interntionl Journl of Mechnicl Engineering A chttering-free sliding-mode controller developed for the trjectory control of remotely operted vehicles. Also, new pproch for thrust lloction proposed tht ws sed on minimizing the lrgest individul component of the thrust mnifold [9]. Bess et l., [1] developed n dptive fuy sliding mode controller for remotely operted the underwter vehicles. Their study ws dopted sed on the sliding mode control strtegy nd enhnced y n dptive fuy lgorithm for uncertinty/disturnce compenstion. The performnce of the proposed control structure ws lso pprised using numericl simultions. Nik nd Singh, [] investigted the prolem of suoptiml dive plne control of utonomous underwter vehicles using the stte-dependent Riccti eqution technique. Simultion results presented which show tht effective depth control ws ccomplished in spite of the uncertinties in the system prmeters nd control fin deflection constrints. In other reserch, neuro-fuy controller for utonomous underwter vehicles ws een proposed y Kim nd Yuh [1]. Simultion results showed effectiveness of the neuro-fuy controller for utonomous underwter vehicles. Akkizidis et l., [13] used fuy-like PD controller for n underwter vehicle nd experimentl results were nlyzed nd presented. A switched control lw for stilizing n under ctuted underwter vehicle ws proposed y Snkrnrynn et l. [14]. Simultion results were presented to vlidte the control lw. Lpierre [15] designed nd verified diving-control sed on Lypunov theory nd ckstepping techniques. The results of the control system proved nd simultions developed to demonstrte the performnce of the solutions proposed. Dynmics equtions of utonomous underwter vehicle The motion for n underwter vehicle s generlized six-degree of freedom equtions of is derived under the following ssumptions: The vehicle ehves s rigid ody The erth s rottion is negligile s fr s ccelertion of the mss centre re concerned The vehicle moves t low speed The hydrodynmics prmeters re constnt The equtions of motion for n underwter vehicle cn e represented s [16, 17] M C( D( g( (1 where M is the mtrix of inerti nd dded inerti, C is the mtrix of Coriolis nd centrifugl terms, D is the mtrix of the hydrodynmic dmping terms, g( is the vector of grvity nd uoynt forces, is the resultnt vector of thrusters forces nd moments. J( ( where J( is the kinemtics trnsformtion mtrix T nd ( x,y,z,,,. The liner steering equtions of motion s: 1 13 r 1 3 r 1 r (3 where the components of the mtrix re s follow; 1 u 13 1 u 3 31 Y v(m Yv (I N r (mx (m Y (I N u [(m Y v (Y r v r (m Y v (I N r Y N m(i N r (mx Y r (N r Nv(m Yv (I N r (mx (m Y (I N (I N r (N r v mx (m r (m Y v (I N r (mx Nv (mx Y r 3 1 (m Yv (I N r 33 1 (I (I 13 N (m Y r v (m Y v Y (I r N v v Y Y v (mx N v (Y r (mx N r N r (m Yv N (mx (m Y (I N v r Y N N v r Y The linerized forms for equtions of the AUV motion contining heve nd pitch re s follows: v mx ] mu ISSN: Volume 1, 16

3 Interntionl Journl of Mechnicl Engineering q 1 z 1 3 q z where the components of the mtrix s follows; Mq mx u I M 1 yy yy q W(z zb I M 3 u I yy M M q q s (4 Schemtic representtion of the AUV system with coordintes is shown in Fig.1. The hydrodynmics prmeters nd the AUV prmeters re given in Tle 1. pproprite control ction. The mthemticl expression of the force of the RNF control system is given y; u(t u (t u (t (5 R NN where u R (t is the force of the roust controller nd u NN (t is the force of the neurl controller. The sum of these two forces, control force signl u(t is given. The first prt of control input for the roust controller cn e descried s follows: (t u R de(t ( Rt K P e(t K D *e dt (6 where K P, K D nd R re the proposed control system prmeters nd re empiriclly set to K P = 1, K D =7 nd R=.1. In the following eqution, e(t is the control error; e(t yr (t y(t where y r (t is the reference input signl nd y(t is the system output signl. Neurl Network structure is shown in Fig.. The second prt of control input for the proposed control system is explined in the following su section. Fig.1. Schemtic representtion of the AUV system with coordintes Tle 1. The hydrodynmics prmeters nd the AUV prmeters m 5 kg Mq 3 N.m g 9.81 m/s Mq -3 kgm u m/s Nv 3 N.m -.15 m 1 kg.m x Nv z.3 m Y δ 847 N z B N δ -76 N.m I 14 kg.m Yr 1 Iyy 15 kg.m Yr 1 kg.m Nr 3 N.m Yv 1 N N r -3 kg.m Yv -5 kg 3 Descriptions of Controllers 3.1. Roust Neurl Feedck Control System (RNFCS A designed control system is employed to control the yw ngle of the AUV. The purpose of this proposed control system is to provide the Neurl Controller A neurl controller with Resilient Bckpropgtion Algorithm is one of the populr neurl network structures for control nd prediction. Fundmentlly, two steps re involved when using this control: system identifiction nd control design. The identifiction stge of this control is to trin neurl network to present the forwrd dynmics of the plnt. The neurl network model of the plnt tht needs to e controlled is developed using two su networks for the model pproximtion. The neurl model is s follows: y(t d N[y(t,..., y(t m 1,u(t 1,...,u(t n 1] (8 where y(t is the system output, u(t is the system input nd d is the reltive degree (d. Multilyer neurl networks cn e used to identify the function F. The identifiction model hs the form; ŷ(t d f[y(t,..., y(t m 1,u(t 1,...,u(t n 1] g[y(t,..., y(t m 1,u(t 1,...,u(t n 1].u NN(t (9 where ŷ(t d is the estimte of y(t d. Identifiction is crried out t every instnt t y djusting the prmeters of the neurl network using ISSN: Volume 1, 16

4 Interntionl Journl of Mechnicl Engineering the error e(t ŷ(t y(t. In order for system output, y(t+d, to follow reference trjectory y r (t+d. y(t d f[y(t,..., y(t m 1,u(t 1,...,u(t n 1] g[y(t,..., y(t m 1,u(t 1,...,u(t n 1].u NN(t (1 f nd g re ctivtion functions of the hidden lyer in the first nd second su networks, respectively, s follows: f (t g(t 1 e t 1 ( For ech su network, the liner ctivtion function used the output lyer. The controller output would hve the form of; prmeters without ny controller, in the presence of PID controller nd the proposed RNF control system, respectively. Fig.3.( shows the yw ngle of the AUV for sinusoidl input signl. The response of the AUV unstle ehviour (shown with dshed lines is lso seen in Fig.3.(. Fig.3.( depicts the response of yw ngle of the AUV for sinusoidl input signl using the stndrd PID controller. As seen in the figure, the system response does not show unstle ehviour, ut the desired sinusoidl input signl does not follow. The results show tht the proposed RNF control system hs etter performnce in terms of dpting sinusoidl input signl. yr (t d f[y(t,..., y(t m 1, u(t 1,..., u(t n 1] u(t g[y(t,..., y(t m 1, u(t 1,..., u(t n 1] (1 Using the eqution directly, cuses reliztion prolem, sed on the output t the sme time, y(t. So, insted, the model; y(t d f[y(t,..., y(t m 1,u(t 1,...,u(t n 1] g[y(t,..., y(t m 1,u(t 1,...,u(t n 1].u NN(t 1 Using Eq.(13, the controller; yr (t d f[y(t,..., y(t m 1, u(t 1,..., u(t n 1] u(t 1 g[y(t,..., y(t m 1, u(t 1,..., u(t n 1] (13 (14 The proposed RNF control system rchitecture is shown in Fig.. Fig.. Proposed RNF control system rchitecture Moreover, for comprison purposes, the clssicl PID controller ws used for yw ngle control of the AUV. The PID controller ws initilly tuned using the Ziegler-Nichols method, nd the PID prmeters re found s K p =1., K i =.5 nd K d = Simultion Results This section presents simultion results of the AUV system with neurl network sed controller for yw ngle. Figs.3.(-(c show the response of these Fig.3. Yw ngle of AUV for sinusoidl input signl ( Uncontrolled response PID controller response nd c RNF control system response Fig.4.( represents yw ngle of the AUV for rndom input signl, nd in Fig.4.( response of the AUV is unstle ehviour. The result of the PID controller for yw ngle of the AUV is shown in Fig.4.(. As seen in Fig.4.(, the yw ngle response of the AUV with the PID controller does not trck the desired rndom input signl. Fig.4.(c indictes the result of the RNF control system. This ISSN: Volume 1, 16

5 Interntionl Journl of Mechnicl Engineering grph shows smll overshoot error etween the desired rndom input signl nd the proposed control system. According to simultion results, the proposed control system hs excellent performnce for controlling the AUV prmeters. Fig.4. Yw ngle of AUV for rndom input signl ( Uncontrolled response PID controller response nd c RNF control system response 5 Conclusions A roust control system with neurl network ws designed for yw ngle controlling of the AUV system. Moreover, for comprison, the stndrd PID controller, tuned using Ziegler-Nichols methods, ws lso employed to control the AUV. The results of oth control systems showed tht the use of the proposed roust neurl feedck control system proved to e effective in controlling the AUV nd more roust for the PID controller. The strong performnce of the proposed RNF control system ws cused y the inclusion of oth liner nd nonliner neurons in the network. As depicted from simultion results, the proposed control system cn effectively trck the given trjectory for experimentl pplictions. 6 References [1] Son M.J., Kim T., Mneuvering control simultion of underwter vehicle sed on comined discrete-event nd discrete-time modeling, Expert Systems with Applictions, 39, 1, [] Snthkumr M., Asokn T., Power efficient dynmic sttion keeping control of flt-fish type utonomous underwter vehicle through design modifictions of thruster configurtion, Ocen Engineering, 58, 1, 1. [3] Moghddm J., Bgheri A., An dptive neurofuy sliding mode sed genetic lgorithm control system for under wter remotely operted vehicle, Expert Systems with Applictions, 37, 1, [4] Hermn P., Decoupled PD set-point controller for underwter vehicles, Ocen Engineering, 36, 9, [5] Kumr R.P., Dsgupt A., Kumr C.S., Roust trjectory control of underwter vehicles using time dely control lw, Ocen Engineering, 34, 7, [6] Nrsimhn M., Singh S.N., Adptive optiml control of n utonomous underwter vehicle in the dive plne using dorsl fins, Ocen Engineering, 33, 6, [7] Kim T.W., Yuh J., Development of rel-time control rchitecture for semiutonomous underwter vehicle for intervention missions, Control Engineering Prctice, 1, 4, [8] Luo J., Tng Z., Peng Y., Xie. S., Cheng T., Li Hengyu, Anti-disturnce control for n underwter vehicle in shllow wvy wter, Advnced in Control Engineering nd Informtion Science, Procedi Engineering, 15,, [9] Soylu S., Buckhm B.J., Podhorodeski R.P., A chttering-free sliding-mode controller for underwter vehicles with fult tolernt infinitynorm thrust lloction, Ocen Engineering, 35, 8, [1] Bess W.M., Dutr M.S., Kreuzer E., An dptive fuy sliding mode controller for remotely operted underwter vehicles, Rootics nd Autonomous Systems, 58, 1, ISSN: Volume 1, 16

6 Interntionl Journl of Mechnicl Engineering [] Nik M.S., Singh S. N., Stte-dependent Riccti eqution-sed roust dive plne control of AUV with control constrints, Ocen Engineering, 334, 7, [1] Kim T.W., Yuh J., Appliction of on-line neuro-fuy controller to AUVs, Informtion Sciences, 145,, [13] Akkizidis I.S., Roerts.N., Rido P., Btlle J., Designing fuy-like PD controller for n underwter root, Control Engineering Prctice,, 3, [14] Snkrnrynn V., Mhindrkr A.D., Bnvr R. N., A switched controller for n under ctuted underwter vehicle, Communiction in Nonliner Science nd Numericl Simultion, 13, 8, [15] Lpierre L., Roust diving control of n AUV, Ocen Engineering, 36, 9, [16] Fossen T.I., uidnce nd control of ocen vehicles, 1994, John Wiley, Chichester. [17] Arnd J., Armd M.A., Cruz J.M., Automtion for the mritime industries, 4 PM, Spin. ISSN: Volume 1, 16