The crane robust control

Advances in Electrical and Electronic Engineering 52 THE CRANE ROBUST CONTROL Marek Hiár Department of Electrical Drives and Mechatronics, Faculty of Electrical Engineering and Informatics, Technical University Košice, Letná 9, 042 00 Košice, E-mail [email protected] Abstrakt lánok sa zaoberá návrhom riadenia pre kompletnú štruktúru žeriava t.j. maky, mostu a zdvihu žeriava. Najdôležitejšími neznámymi parametrami pre simulácie sú hmotnos bremena a džka závesného lana. Bude použité robustné riadenie pohonu maky a mosta, ktorým zabezpeíme adaptivitu na hmotnos bremena a džku lana. Robustné riadenie bude navrhnuté pre prúdovú reguláciu maky a mosta, k tomu je nutné vedie pásmo neuritých parametrov. Celkové robustné pásmo bude rozdelené na subintervaly a po správnej identifikácii neuritých parametrov budú zvolené najvhodnejšie robustné regulátory. Najdôležitejšou požiadavkou pri pohybe maky a mosta je zakázané kývanie bremena v koncovej polohe. Asynchrónnymi motormi napájanými z frekvenných meniov je navrhnutý pohon maky i mostu žeriava. Zdvih žeriava s pozorovateom hmotnosti bremena použijeme pre kombináciu zdvih, pohon maky a mosta so vzájomným odovzdávaním si parametrov: hmotnos bremena, džka lana a poloha maky a mostu. Regulátory sú navrhnuté metódami stavového riadenia. Výhodne zavedieme pozorovate poruchy, ktorý bude ma za úlohu identifikova hmotnos bremena ako poruchu. Systém bude pracova v oboch režimoch pri prázdnom háku ako aj pri maximálnej záaži: zdvíhanie a spúšanie bremena. Pre pohon zdvihu použijeme trojfázový asynchrónny motor nakrátko napájaný z frekvenného menia. Simulácie sú navrhnuté tak, že najskôr realizujeme zdvih a potom prepínací blok uskutouje súasný pohyb maky a mosta. Pri simuláciách je možné voli ubovonú hmotnos bremena, džku lana, polohy a rýchlosti pohybov maky a mosta. Summary The article is about a control design for complete structure of the crane: crab, bridge and crane uplift. The most important unknown parameters for simulations are burden weight and length of hanging rope. We will use robust control for crab and bridge control to ensure adaptivity for burden weight and rope length. Robust control will be designed for current control of the crab and bridge, necessary is to know the range of unknown parameters. Whole robust will be split to subintervals and after correct identification of unknown parameters the most suitable robust controllers will be chosen. The most important condition at the crab and bridge motion is avoiding from burden swinging in the final position. Crab and bridge drive is designed by asynchronous motor fed from frequency converter. We will use crane uplift with burden weight observer in combination for uplift, crab and bridge drive with cooperation of their parameters: burden weight, rope length and crab and bridge position. Controllers are designed by state control method. We will use preferably a disturbance observer which will identify burden weight as a disturbance. The system will be working in both modes at empty hook as well as at maximum load: burden uplifting and dropping down. For uplift drive we will use an asynchronous motor fed from frequency converter. Simulations are proposed for situation that firstly we do uplift and then switching block realize simultaneous crab and bridge motion. At simulations it is possible to choose different burden weight, rope length, crab and bridge positions and speeds. 1. INTRODUCTION Robust c ontrol has to ensure correct controlling for crane crab, bridge and uplift. Before the whole design it is good to specify which parameters will have to transfer influence between subsystems. The first important, but unknown parameter is burden weight G m , which we will identify by observer in the uplift model. This parameter is transferred for the crab and bridge to know which subinterval of robustness will be necessary for controllers switching to ensure correct position control with zero swinging in the final position. Control system was designed by classical state control primary control structure of all subsystems and their upgrade will be robust design by Ackermann. Ackermann method of calculation needed controllers we will observe the width of the robust area for burden weight at individual lengths of hanging rope. Designing of robust intervals for crab and bridge motion we will ensure covering crane loading limit and so total crane control for burden transport at performing two conditions: robustness against burden weight variations and forbidden burden swinging in the final position of crab and bridge. The uplift drive is a part of the crane crab which moves in perpendicular motion to the crane bridge motion [6, 7]. Fig.1 Model of double cross-beam bridge crane The crane robust control 53 2. SYSTEM FORMULAS We choose followed state parameters: m iw 21 = [A], speed ω == K xx & 3 [rads -1 ], torque current y ix 14 = [A], position K xx = 5 [m], arc circumscribed by burden β = 6 x [m] and burden speed in the arc . 7 β =x [ms -1 ] [5]. Fig.2 Mechanical part of the crane crab and bridge Mechanical crab and bridge model is on the figure 2 where by power from motor K F is driven crane crab (bridge) with own weight K m (for bridge M K m ), whereas burden weight is G m . Index G refers to burden, G F is gravitation power from burden weight. Crab and bridge motion we can describe by formulas [3, 4]: KGKK F d gmxm =− β && , (1) ( ) KGKK F d gmmm −=++ β β && . (2) After modification of formulas (1, 2) and using motion formula (3) of asynchronous motor we can write: zym hc mii L p tp J− + = 12 2 12 3 d d σ ω , (3) β 1 11 121231 c n a iiccax ymK += && , (4) ββ n a xciica K ym 12 .. 312231 −+−= && . (5) For formulas (4, 5) were set up symbols for creation of system for crane crab and bridge: 1 1 1 2 2 1 + = K c m r j p J c , rm j c K = 2 , K c mr j p J c 2 2 3 = , K G m m a= 11 , (6) where l is length of hanging rope, c J total torque of inertia, p number of motor poles, h L main motor induction, coefficient h L L ´ 2 2 σ σ = , z m load torque, r radius of driving wheel and j transmission. Fig.3 Mechanical part of the crane uplift Design for uplift drive is by figure 3: Torque equation for conditions of torque situations for crane uplift is [5]: dt d JMM mZ CZGZmZ ω =− , (7) where mZ M - motor torque, GZ M - burden torque and CZ J - total inertia torque. Firstly we calculate sliding burden speed GZ v to angle motor speed mZ ω : 4 2Z Z mZ GZ D j v ω = . (8) Recalculated burden inertia torque comes from the basic formula 2 2 2 Z G CGZ r m J= where mZ Z G Z v r ω 2 2 = . Potential burden torque at uplift when Z G Z gr m M 21 2 = , then: pZZ ZG GZ j gDm M η 4 2 1 = so burden dropping down: (9) pZ Z ZG GZ j gDm M η 4 2 2 = . (10) Advances in Electrical and Electronic Engineering 54 The final formula for total inertia torque for uplift: CGZCbZ mZ mZ CZ JJ J J++= η , (11) where mZ J - motor inertia torque, CbZ J - drum inertia torque, CGZ J - burden inertia torque. Company KPK Martin offered us real parameters of double cross-beam bridge crane for checking our design control for the crane, bridge and uplift at real crane by figure 4. And more, in cooperation with Department of constructing, transport and logistics, headed by Mr. Juraj Ritók we prepare examination on smaller model by figure 1. Fig.4 Crane of company KPK Martin 3. CONTROL METHOD We decide control system which includes: converter, asynchronous motor and mechanical part. State control describes system with unknown parameters by [1, 2]: ( ) ( ) ( ) zu pepbxpAx ++= & , xc T y= . (12) Feedback parameters i r are calculated by ensuring of poles movement of characteristic polynom of the crane crab and bridge in defined Γ - region by figure 4 with characteristic stability and required damping. Poles region method allows designating control of feedback circuits: xr T u−= , (13) Condition of Γ - stability describes formulas system 14 where unknown parameters are included in polynom ( ) pa . We get by solving formulas system feedback parameters valid for unknown system parameters and so required robustness of the system [1, 2]:       =       − 0 0 )( )(...)(0 )(...)()( 1 1 pa αα ααα no no dd ddd , where: ,1)( = α o d )(2)( 1 ασα =d , [ ] ( ) ααωασαασ 1 22 1 )()()()(2 −+ +−= iii ddd for i = 1, 2, ... n-1. (14) If all poles of characteristic polynom are located in the left part of Γ - region in length ( a − ) from imaginary axis and in sector assigned by damping values γ sin = d is established stability and necessary damping (Fig.5). Robust design needs to know 2 − n feedback parameters. Graphic-calculation method will designate values of the rest two controllers 1 r , 2 r . Then rounds for minimum and maximum variable parameters are calculated and their borders of the intersection show possible area A of choosing robust controllers. Fig. 5 Γ - region definition Robust design of crab and bridge by system 14 determined three subintervals of robust area. Covering areas of minimum and maximum burden weight determines area for choosing controllers. Each area presents covering of total crane loading from 342 kg to 20342 kg of burden weight. We define real burden weight by burden weight identification and switching needed robust controllers. We choose one pair of 36 r , 37 r controllers from robust area A for each subinterval (Fig.6). We observe for crane bridge robust control design whole area A which is located into only one Γ - region s - region Re σ Im ω b - a - R γ The crane robust control 55 area (Fig.7). Choosing of controllers M r 36 , M r 37 ensures covering the whole crane loading at bridge control with different burden weight. Fig.6 Choosing controllers for three subintervals of the crane crab at varying of burden weight Fig.7 Choosing controllers for one subinterval of the crane bridge at varying of burden weight We design by state control crane uplift. We choose PI controllers for current, speed and position control. Preferable disturbance observer will be set which will identify burden weight as a disturbance. By practise reasons designed from KPK Martin we think over for two values of hanging rope: l = 4 or 8 m. At l = 8 m is in progress loading and unloading, burden transport begins after uplifting to l = 4 m. Control is designed by figure 8 and for speed control we can write: ( ) Z ZZ Z Z Z Z ZZZZZZZ Z Z Z Z Z Z w Kv v x x K KdKrKrK r a v v x x 3 33 4 4 3 3 4344344334 4 3 . 3 4 .4 .3 . 0 0 0 000 1 010 000             +                         − −+−− − =               (15) State formula for position PI controller will be: ( ) Z Z Z Z Z Z Z Z ZZZZZ ZZZZZZZZZ ZZ Z Z Z Z Z Z Z w K x v v v x a rKdKK rKdKdKKrK aK j r x v v v x 4 5 3 4 3 5 5 3 3343444 5335435333553 35 2 . 3 . 4 3 .5 .5 . 0 0 0 0 0000 00 1 000 0000               +                                   −− +−−−− − =                   (16) Fig.8 Torque formula for crane uplift Observer: pm zeyyu ∧∧∧ +      −++= hbxAx ^ . , ∧∧ =xc T y ,      −−= ∧∧ yyKz i pm . (16) Total state formula at implementation of difference ∧ −=∆ xxx will be: pmZ Z Z Z pmZ Z iZ Z Z ZZ Z Z z j r e z x K j r eh z x        − +        ∆         − − =          ∆ ∧ ∆ 02 0 2 2 3 2 1 . 3 . . (17) Simulation scheme on the figure 9 represents complete structure of the crane. Switching structure is included in crane control, ensures correct reciprocity of each crane subsystems and does not allows wrong service. Simulation enables from service side to set follows parameters: burden weight at forward and backward motion, rope length during transport and for positioning, reference crab and bridge position at forward and backward motion. Switching structure realizes correct reciprocity of the motions. And more, to the simulation scheme belongs uplift with identified weight and rope length out, crab block and bridge block. Advances in Electrical and Electronic Engineering 56 Fig.9 Simulation scheme of crane from MATLAB Simulink 4. SIMULATION RESULTS Running the simulation immediately starts burden uplift to the reference uplift position (Fig.10, 1’-1, l = 4 m) with burden weight G m = 20342 kg. Simulation allows after finished uplift synchronous crane crab and bridge motion (obr.10, 2’-2). We transfer burden in principle in the position up or down, because controllers were calculated for switching robust area for length of hanging rope l = 4 m and 8 m. However, this complete allows transferring burden in range of rope length from 4 m to 8 m, because system is robust against to variation of rope length in permited tolerance. We consider rope length 4 m for safety because on the other hand problems can become on the trajectory of drives where the burden moves. When crab and bridge are located in reference position with the burden, the burden begins dropping down (Fig.10, 3’-3) and the system waits for burden weight change G m which represents service staff by status change on the hook. If become burden weight change follows uplift (Fig.10, 4’-4). After finished uplift of new weight, crab and bridge move backward or to the specific other position (Fig.10, 5’-5). Again crab and bridge move synchronous and after finishing of their movements follows the burden dropping down (Fig.10, 6’-6), [6, 7]. Fig.10 Reference Z w 5 [m] and real Z x 5 [m] crane uplift at burden transport We can observe on the figures 11 and 12 time sequence with figure 10. In the time about t = 5 s after finishing of uplift begins synchronous crab and bridge motion (at different speed, (Fig.11, 12, 1’-1)). In the crab and bridge reference position (Fig.11, 12, 2’-2) followed burden dropping down and service staff changed burden weight for backward motion (342 kg what means empty hook). Crab and bridge moved to the backward The crane robust control 57 position 5 w = M w 5 = 0 (Fig.11, 12, 3’-3) and in the reference backward position started dropping down of empty hook and system is ready for next uploading by burden for transport. Fig.11 Reference 5 w[m] and real 5 x[m] crane crab position Fig.12 Reference M w 5 [m] and real M x 5 [m] crane bridge position On the figure 13 is sharp identification of real burden weight. Firstly, uplift drive works with maximum burden weight G m = 20342 kg and after unloading system again in minimum time identified empty hook G m = 342 kg. Keeping condition of forbidden swinging in the final position at forward motion and at backward motion is illustrated by figure 14. Burden deviation by crab 6 x [m] and bridge M x 6 [m] have zero value at finishing crab and bridge motions. Their maximum overswingings during crab and bridge motions are different because speed of crab and bridge is different. Rope length has influence also to the maximum overswinging. Fig.13 Real G m[t] and observed G m ∧ [t] burden weight Fig.14 Burden deviation at crane crab 6 x[m] and bridge M x 6 [m] motion 5. CONCLUSION Robust control design ensures sharp burden positioning with different weight at zero swinging in the final position. System is steady resistant against variation of rope length and speed of crane crab and bridge motions. At design of less known, variable systems or systems with variable parameters is very profitably to ensure control by robust design by Ackermann. By identification of burden weight we should in very short time to get information about real burden weight and rope length and these were used for simulations in models of crane crab and bridge. It is good to set up from Advances in Electrical and Electronic Engineering 58 emergency reasons signalization by press-button STOP, pushing by can service staff to disconnect control from object and so disallow state, when service staff after finishing whole cycle in turned on mode would like to manipulate with empty hook. Then system can find out about burden deviation and so will start control for zero deviation what can occur accident to service staff because they are close to the burden and rope in this moment. Article is included in project G-985. REFERENCES [1] Ackermann, J.: Robuste Regelung,Springer Vlg., Berlin 1993. [2] Leonhard,W.: Control of electrical drives,Springer Verlag Berlin, 1997. [3] Zboray, L.: Controlled Drives, ES VŠT Košice, 1990. [4] Zboray, L.: State control of electrical drives, Vienala, Košice, 1995, (Slovak). [5] Hiár, M.: Robust Control Of The Crane Bridge And Crab, EE Magazine For Electrotechnique And Energetics, Slovak Technical University In Bratislava, December 2003, pages 16-18. [6] Ritók, J., Bigoš, P.: Positioning of automate cranes, In: Logistika 2000, Košice 2000, pages 113-116. [7] Ritók, J., Bigoš, P.: Automate crane in logistic system, In: International conference Logistika & Doprava, High Tatras, 2001.