2nd WSEAS Int. Conf. on CIRCUITS, SYSTEMS, SIGNAL and TELECOMMUNICATIONS (CISST'08)Acapulco, Mexico, January 25-27, 2008

Transcription

1 Design of a self-balancing tower crane. J. J. RUBIO AVILA, R. ALCÁNTARA-RAMÍREZ, J. JAIMES-PONCE, AND I. I. SILLER-ALCALÁ. Departamento de Electrónica, Grupo Control de Procesos Universidad Autónoma Metropolitana Av. San Pablo No. 180, Col. Reynosa Tamaulipas, Del. Azcapotzalco, C. P.000, México D.F. MÉXICO sai@correo.azc.uam.mx Abstract: - This paper presents the design of a new concept of tower crane, which was greatly reduced the burden and eliminates the anchor, as will be self-balancing which involves removing the anchor replaced by a sliding counterweight trolley. The paper involves the design of the mechanics and simulations based on its model and a PID control in order to check optimal performance. Key-Words: - PID Control, Crane Control, Modeling, Mechanical Cranes. 1 Introduction Overall a crane is a mechanical system designed to hoist and move loads through a hook suspended from a cable. In the construction industry, where it is needed lift, it is often used cranes that are anchored or subject to a ballast [1] []. In most designs, it aims to have the center of gravity of the system located at the base, and so the center of mass obligate the system to remain in balance, regardless of the magnitude of the load, which is much minor to the total mass of the crane. In the cranes tower, the load lifted must be able to move, an action that is done by a trolley along the boom, reaching the counterweight in the counter boom a fixed distance regard to the tower. This principle of operation limits the weight can be lifted by making it dependent on the distance you want to move in the bloom. This limitation is related to the balance that generates the counterweight, ballast and load. Fig. 1.1 shows the weights that cranes tower can lift according to the length of displacement along the boom As mentioned in [] at present, control cranes are moving from manual operation, which depended on the ability of an operator, to an automatic control, especially when they are very big and move loads at high speeds. Hence, new methods of automation are being developed. For example combinations of classic control laws with modern control laws [3], [4] and [5], also fuzzy logic controllers are used [6], [7], [8] and [9].To control automated cranes can be seen several techniques: The first technique is based on the generation of trajectories [10] and [11] for transporting load from one point to another with minimal sway of the load. That path will depend on the type of crane used, because for some types such as bridge cranes will be relatively easy over the tower crane. These techniques can be used optimal control. The second technique is based on the feedback of the position and angle of oscillation of the load [10]. The third technique is based on divide the controller in two parts, control anti-sway and another control of the position of the load [10]. Each of them designed separately and combined to ensure the performance and stability of the system. Although much research is concentrated on the generation of trajectories, since cranes are being assembled by any anchoring system or excessive ballast, in this work we use the second technique with the application of classical control laws to achieve a self-balancing and proper functioning, as well as devices actuators and sensors for the positioning of counterweight and the joints further. Figure 1 Displacement respect to the load. Design of the crane A tower crane as shown in Fig..3, consists basically [1] by: Page 109 ISBN:

2 A) Mast B) Bloom C)Counter bloom D Counterweight E) Ballast F) Trolley Figure. Overview of a crane parts The operation of the proposed crane is based on the balance of moments as shown in Fig And given by the relationship F1 x D1 = F x D. Specifying the dimensions desired, the experimental tower crane designed is shown in Figure 5, being a good start to apply control laws classical and modern. Noting the technical specifications, in e) indicates that the tower height is 45 cm, choosing this length so that the crane is not very high and has increased stability, it will also rely on a structure as the building, which in our case is going to be a table of 100 cm in height shown in Figure 5, emulating a building. This crane does not have mechanical system of displacement. In f) states that the maximum height of the vertical displacement of the load (m 1 ) should be 130 cm, noting that in Fig 5, it is the sum of the height of the table plus 30 cm in lifting crane, this load is going to be at least 15 cm below the highest point of the bloom. Figure 3. Relationship moments in balance The proposed crane in this paper reduces the ballast and eliminates the anchor, since it will be "auto balancing''. The concept of self-balancing involves eliminating anchoring system, which is replaced by a movable counterweight as shown in Fig. 4. Figure 5. Experimental crane tower on a table Here are just a few pieces for the design of the crane. Figure 4. General Outline of the crane self-balancing.1 Mechanical Design of the crane. To achieve the mechanical design of the tower crane, initially technical specifications are required, both the mechanical and the electrical and electronic components, such as motors, sensors, circuit cards, etc. The general specification are: Crane: A) Type: Tower B) Material: Aluminium and iron C) Length of the boom: 160 cm D) Length of counter boom 60 cm E) The tower height: 45 cm F) Maximum height of load 130 cm displacement: G) Maximum weight of the load: 1000 g H) Speed lifting of the load: 5 cm / sec I) Angle maximum load balancing: 3 J) Rotation angle of the tower: Mast and slewing mechanism of the crane. The mast consists of a group of parts, so that half is fixed to the base, and the other half can be rotated. The parts are displayed in Fig A) lower Mast B) Stand of rotation motor C) Base or slewing stand with swivel bearings D) Pinion Drawing E) Gear Drawing F) higher mast Figure 6. Mast and base The reason they are two sections with almost the same length, it is because at half mast are the mechanical elements of rotation as shown in Fig. 7, gear, (small gear) pinion and motor, which by its dimensions occupy considerable space, and if these traction elements are placed near the junction of the Page 110 ISBN:

3 mast and the bloom, they take away the space to the lifting elements and mass displacement m1, as well as the displacement of counterweight (mass m). Figure 7 Perspective half mast stand motor Figure 8 Gear assembled at the upper mast Figure 11. Internal Supports of the mast and internal screw The second part of the mast is joined to form a single piece gear. As shown in Fig. 5.9, as well as the basis, the gear has a slot where the mast top is assembled. Figure 1. Boom and counter boom of the crane Figure 9. Gear and pinion in detail An important element to give rigidity to the mast is a screw.54 cm (½ in) in diameter and 40 cm long, which is placed in the middle and along the mast coupled with bearings that are shown in Fig.10 and they are assembled by pressure on the internal supports of the mast, in the slewing gear and support of motor rotation, preventing torsion forces affecting the slewing support..13 Trolleys for the movement of the load m 1 and counterweight m. The trolley shown in Fig. 13, consists of a chassis or metal base and four wheels which are to move into two rails. The rails that belong to the boom are longer than those of the counter boom. The trolley will be moved through a steel cable and a pair of sheaves, one of which is coupled to the motor of displacement and the other is coupled to the sensor (encoder) for measuring the distance travelled in one direction or another. Figure 10. Bearings for vertical support.1. Boom and counter boom. In the commercial crane, the boom, counter boom and mast are built with tubular bars and / or angular, forming a lightweight structure and strong at the same time. In the case of the experimental crane has decided to use aluminium bar, because it avoids manufacture every component of the boom and counter boom, satisfying with the characteristics of weight and resistance to be desired. As shown in Fig. 1, taking advantage of the length of aluminium bar, the boom and the counter boom are the in the same bar. Figure 13. a) Bottom of the car, b) A car on rails.1.4 System of horizontal displacement of the masses m 1 and m The displacement system of mass m 1 is constituted by the pieces displayed in Fig.14. Figure 14. Displacement System of mass m1. Page 111 ISBN:

4 Likewise, the displacement system of mass m consists of the pieces displayed in Fig Crane Tower The crane assembled is shown in Figs. 19 and 0 Figure 15. Displacement System of the mass m.1.5 The hoisting mechanism and measuring of load weight (mass m1) The hoisting mechanism of mass m1 consists of the following elements. Figure 19. Front and back of the crane Sheave encoder of hoisting Drum Drum Gear Hoisting Motor Pinion of hoisting motor Sheave of load m1 Figure 16. The hoisting mechanism of mass m1 Figure 0. Mast and additional elements 3. Model of the proposed tower crane In this section is considered the load hoisting (mass m1) and the horizontal displacement of the counterweight (mass m) to maintain balance. Figure 17. Approach system elevation of the mass m1 Elements of measurement of weight are formed basically by: A) Load Cell B) Load sheave of mass m1 C) Sheave support of load The load sheave is fixed to load cell through a support, also the load cell is fixed to trolley as shown in Fig.18. Figure 18. Weight measurement system Figure 1. Balancing moments in the crane, when the distance of the counterweight is adjusted. The Lagrangian is given by: L= KT VT (1) Where L = Lagrangian of the system K T =Total Kinetic energy of the system, and V T = Total potential energy of the system. Considering linear movements, from Fig. 1 is obtained the following equations: x1= r1sinθ 1 () y1= r1cosθ 1 (3) x = r (4) y = h = 0 (5) Therefore Euler Lagrange equation for r1 is given by Page 11 ISBN:

5 L L = τ r1 t r& r 1 1 The model is obtained as: (6) r rr r m m & θ m g τ r1 0 m 0 r && + + = τ r r θ && & θ 1 rr J1+ mr1 mgtanθ τ θ1 1 l1cosθ1 l1 l1cosθ1 && r1 1 l1cos θ1 0 l1 1 (7) 4. Analysis and simulation results with the control laws selected In order to tuning the controller, constants were chosen to obtain a over damped response, these parameters are in the Table 1. It is important to mention that parameters provide a better response because avoid overshoots in the movement response of the two masses m1 and m. These overshoots can generate considerable forces due to inertia of the masses, causing an imbalance in the moments and therefore the inevitable collapse of the crane. Figure 4. The position amplification of the counterweight (mass m) The oscillation of the mass m1 is shown in Fig. 5, with an initial angle of 3 (0,054 rad), hoisting the mass m1 from 0.8 [m] to 0.4 [m] and in Fig. 6 is hoisted from 0.8 [m] to 0. [m], clearly observed that the frequency of oscillation is increased by reducing the value of r1, as previously mentioned. Kpr 1 Kdr 1 Kir 1 Kpr Kdr Kir m 1 (Kg) m Kg) r 1 J Figure 5. Angle oscillation of the burden (angle q1) Table 1 Parameters simulation PID control 4.1 PID control with sway of the mass m1. The Oscillation Angle = 3 = 0,054 rad is considered. In Fig. can be seen that by lifting the load from an initial value of 0.8 [m] to 0. [m] an permanent error very small is presented, which can be reduced by increasing gain Kp, in order to avoid overshoot it is necessary to increase the constant Kv. In the same way, the displacement of the mass m shown in Fig. 3, the parameters are chosen to provide a over damped response, in order to keeping the balance of the crane. In Fig. 4, it can be seen as rd has an oscillation due to the compensation being made by the Control law, by the forces generated due to the oscillation of mass m1; r tries to follow rd, which is not shown in Fig. 3. Figure 6. Angle oscillation of the burden (angle q1) 4. PID control with anti-sway of mass m1. The control anti-sway of load is very important [1], [7], [3] and [13], as for example for other cranes, the control sway allows transportation of load in the shortest time, however, excessive oscillation in a tower crane, can be a cause of the imbalance and hence the collapse of the system. Kpr 1 Kdr 1 Kir 1 Kpr Kd r K r Kpθ 1 Kdθ 1 Kiθ 1 M 1 (Kg) m Kg) r 1 J Table. Parameters simulation PID control with anti-sway Figure. Response of r1 (length of the cable that holds the load) The responses obtained by applying PID control are shown in Figs. 7 and 8, which avoid overshoots. Figure 3. Position of the counterweight (mass m) Figure 7. Performance of r1 (cable that holds the load) Page 113 ISBN:

6 Figure 8. Position counterweight (m) Figure 9. Amplification of the counterweight position m Figure 30. Oscillation Angle of the load q1 In Fig. 30 an oscillation damped is shown because a control law is applied in order to get angle θ1 = 0. This is achieved by moving the trolley with m1 along the boom, being this third degree of freedom. In the simulation with oscillation of m1 the trolley remains fixed, and therefore there is no control over the angle θ1. Comparing the Figs. 9 where position m is amplified, with its angle θ1 corresponding, rd presents a small oscillation not uniform, which is related in magnitude with the damping of its angle θ1, taking a fixed value once the angle θ1 = Conclusions The dynamic model used and described in Ec. 7 consists of three quations, where each one corresponding to each degree of freedom of the crane. This means that if τ θ1 = 0, there is no control over the angle θ1, then only have control over two degrees of freedom, r1 and r, and as a consequence is free oscillation in the load. If τ θ1 is a control law, then we have a third articulation that will compensate the oscilation of the load (m1), which corresponds to the displacement of the trolley that moves the load along the mast. Therefore the dynamic model is very representative of the proposed tower crane on different forms of control, which was checked with the simulation. In the simulation of each control law and with different values of the parameters, it is found that the dynamic model is correct and covers the most important features of a mechanical crane to ensure when it is built it could be made a good control, in addition it can be ensure that with a modern control law it may be controlled much better. The path has been followed for the development of the crane self-balancing, it has been in the first place modelling and then its simulation, considering that from these steps it can be defined with great accuracy factors that determine a good behaviour of the system to design and build. References: [1] Joaquín Costa Centena, Diseño de una grúa automontable de N y m de flecha. Escola Tècnica Superior d Enginyeria Industrial de Barcelona. Tesis para obtener el título de Ingeniero Industrial. []Mazin Z. Othman. A New Approach for Controlling Overhead Traveling Crane Using Rough Controller - INTERNATIONAL JOURNAL OF INTELLIGENT TECHNOLOGY VOLUME 1 NUMBER ISSN [3] Rigoberto Toxqui Toxqui. Control con antioscilación para una Grúa en tres dimensiones en tiempo real. CINVESTAV. Tesis para obtener el grado de Doctor en Ciencias en la especialidad de Control Automático. Agosto del 006. [4] Rigoberto Toxqui, Wen Yu, Xiaoou Li. PD Control of Overhead Crane with Velocity Estimation and Uncertainties Compensation. Proceedings of the 6th World Congress on Control and Automation, June 1-3, 006, Dalian, China. [5]J. de Jesus Rubio, J. Jaimes P. y R. Alcántara R., Sliding Mode Control for a New Crane System, paper aceptado (# IS - 09) para ser presentado en forma oral en la sesión Sliding mode control de la 13th IEEE International Conference on Methods and Models in Automation and Robotics, Szczecin, Poland, August 007. [6]Nally M. J. and M. B. Tarbia, Design of a Fuzzy Logic Controller for Swing-Damped Transport of an Overhead Crane Payload, in Proceedings of the ASME Dynamic Systems and Control Division, DSC Vol. 58, [7] Mahfouf M., Kee C.H., and Linkens D.A., Fuzzy Logic-Based Anti-Sway Control Design for Overhead Cranes, Neural Computing and Applications, Vol. 9, 000. [8] Ho-Hoon Lee and Sung-Kun C. A Fuzzy-Logic Antiswing Controller for Three-Dimensional Overhead Cranes, a, Tulane University, USA, 00. [9] Chunshien Li and Chun-Yi Lee. Fuzzy Motion Control of an Auto-Warehousing Crane System. Page 114 ISBN:

7 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 5, OCTOBER 001. [10] Hanafy M. Omar. Control of Gantry and Tower Cranes. Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering Mechanics. [11] Ho-Hoon Lee. A New Motion-Planning Scheme for Overhead Cranes With High-Speed Hoisting. Journal of Dynamic Systems, Measurement, and Control JUNE 004, Vol. 16. [1] Michael J. Agostini, Student Member, IEEE, Gordon G. Parker, Member, IEEE, Hanspeter Schaub, Kenneth Groom, and Rush D. Robinett, III. Generating Swing-Suppressed Maneuvers for Crane Systems With Rate Saturation. IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 4, JULY 003. [13] Robert H. Overton. Anti-sway Control for Rotating Boom Cranes. United State Patents. Pattent No. 5,961,563. Oct. 5, Page 115 ISBN: