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.
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