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Observer-based state feedback control of an intelligent crane Hai Nguyen 1 Duc , 1 Department Nguyen Van 1 Sy and Kwan-Woong 1 Gwak * of Mechanical Engineering, Sejong University * Corresponding author Introduction Then X = ( A − B K ) X + B KX + B Eu * This paper introduced a new mechanism for power-assisted intelligent crane. The system is actuated by suspended cables and it gives the system more flexibility, compactness and is easy to implement than conventional overhead crane that use grinder beam for guiding. The hoist hook block is designed based on double pendulum mechanism with two independent pendulums, one for human operation and another one for connecting payload. This mechanism makes the operator interact with crane more effective in applications that required massive and large payload. * * * Augmented system: X A − B* K = 0 X B K X B E + * * A − LC X 0 * * (7) The eigenvalue of this augmented system: (8) I − A + B K I − A + LC * * * * Eq. (8) shows that K and L can be chosen independently of each other. Modeling Figure 1 represents the simplified model of power-assisted crane system, including hook platform, payload-pendulum, handle-pendulum, payload, cables and hanging rigid body payload. The location of system can be described by T generalized coordinate vector q = x y 1 2 . Variable 10 (kg) Payload mass (m1) 15 (kg) Handle mass (m2) 2 (kg) Payload-pendulum length (l1) 0.5 (m) Handle-pendulum length (l2) 0.35 (m) Base-point 1 coordinate (B1) (-1,1) (m) Base-point 2 coordinate (B2) (1,1) (m) Viscous friction coefficient (d1,d2,d3,d4) (0.4, 0.4, 0.6, 0.2) λ L = −3 −3 −12 −13.5 −10.5 −15 −10.5 −16.5 Physically, that simulation is about the case where the system was commanded to achieve the velocity 0.03 m/s along y-direction from 0.0 m/s while the handle-pendulum was released from 0.1 rad. Fig.2 shows that, system achieved the desired velocity along y-direction, by that way the desired yposition of system can be obtained. Because of the initial condition in handlependulum angle, the system moved along x-direction to gain back the equilibrium position of that pendulum as shown in x-response of Fig. 2. The remaining states are converged to zeros. Fig. 3 shows that the estimated state from the observer converges to the real state from plant. Fig. 1 Simplified model of power-assisted crane The linearized equation of motion was derived as M.q + D.q + C.q + G + B.u = 0 The eigenvalue of augmented system (7) was chosen as λ K = 0 0 −4 −4.5 −3.5 −5 −3.5 −5.5 Value Hoist platform mass (m0) Simulation Results (1) Where: 0 m1l1 m2 l2 m0 + m1 + m2 −1 0 0 m + m + m 0 0 0 1 2 ,B = M= 0 m1l1 0 m1l12 0 2 m2 l2 0 0 m2 l2 0 0 0 0 0 0 0 0 (m + m + m ) g 0 0 1 2 G = 0 ,u = F C= x 0 0 m1l1 g 0 0 0 m2 l2 g 0 0 0 0 d1 0 −1 ,D = 0 0 0 0 0 d2 0 0 0 d3 0 0 0 0 0 d4 Fy Fig.2 The behavior response of system. Reducing the order of Eq. (1): X = A .X + B .u + G * Y = C X * * * (2) Where: I 4 * 0 * I 4 0 0 q A = ,B = ,C = ,G = ,X = . −1 −1 −1 −1 −M C −M D −M B 0 −M G q * Fig. 3 State error and control input of system Controller design The full-order observer was designed for the system (2) without the term G*: X = A .X + B .u * Y = C X The state variables were estimated as: * ˆ * * ˆ * * * ˆ ˆ ˆ X = A X + B u + L(Y − Y ) = A X + B u + L (C X − C X) * * The error dynamics of the observer can be written as: * * ˆ X = X − X = ( A − L.C ) X (3) (4) (5) The error dynamics can be asymptotically stable if we choose appropriate matrix L, then X → 0 as t → Control signal was determined from estimated state as ˆ + Eυ (6) u = −KX Conclusions A double pendulum power-assisted cable system is proposed and the observer based state feedback control is designed and its performance is proved through the simulation. Acknowledgment This research was supported by grants (NRF-2017R1A1015660) from NRF (National Research Foundation of Korea) funded by MEST (Ministry of Education and Science Technology) of Korean government. www.postersession.com www.postersession.com