A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints

ZHAO Chen; GE Xinsheng

doi:10.21656/1000-0887.390163

Volume 40 Issue 3

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ZHAO Chen, GE Xinsheng. A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints[J]. Applied Mathematics and Mechanics, 2019, 40(3): 302-310. doi: 10.21656/1000-0887.390163

Citation:

ZHAO Chen, GE Xinsheng. A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints[J]. Applied Mathematics and Mechanics, 2019, 40(3): 302-310. doi: 10.21656/1000-0887.390163

Citation:

ZHAO Chen, GE Xinsheng. A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints[J]. Applied Mathematics and Mechanics, 2019, 40(3): 302-310. doi: 10.21656/1000-0887.390163

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A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints

doi: 10.21656/1000-0887.390163

ZHAO Chen¹,
GE Xinsheng²

¹School of Automation, Beijing Information Science and Technology University, Beijing 100192, P.R.China;²School of Mechanical and Electrical Engineering, Beijing Information Science and Technology University, Beijing 100192, P.R.China

Funds: The National Natural Science Foundation of China（11472058；11732005）

Received Date: 2018-06-14
Rev Recd Date: 2018-08-17
Publish Date: 2019-03-01

Abstract

Abstract

The control of underactuated systems was an important field of nonlinear control. The underactuated system refers to a nonlinear system with an input control variable number less than the degree of freedom number. At present, the main methods of dynamics and control research of underactuated nonlinear systems include the linear quadraticform optimal control method and the partial feedback linearization method, and how to make the system stabilize in the equilibrium position is always a difficult point. For the virtual constraint method, the periodic motion of the system is designed with a selected cyclic independent variable. Based on the typical underactuated model crane, the virtual constraint method was adopted to make the system stabilize or oscillate in equilibrium position. First, through establishment of the virtual constraints, the system’s degrees of freedom were reduced. Then, the system state equations were derived according to the partial feedback linearization theory. Finally, the feedback controller was designed with the linear quadraticform regulator. The simulation results show that, the weight can reach a stable state near the vertical position under the feedback control, which reflects the effectiveness of the virtual constraint method for underactuated systems.
- underactuated,
- virtual constraint,
- partial feedback linearization

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References(15)

References

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