Abstract
This paper studies a new boundary control strategy for a flexible manipulator subject to unknown fast time-varying disturbances. The flexible manipulator essentially is an infinite dimensional continuum. Hence, a continuous function of space and time can be employed to describe the position of such a distributed parameter structure, the motion of which can be described by partial differential equations (PDEs). To cope with fast time-varying external disturbances, a high order disturbance observer is adopted. A control strategy based on such a disturbance observer is proposed for the rest-rest maneuvering of the flexible manipulator. Moreover, a smooth hyperbolic function is included in the controller to satisfy the requirement of input saturation. The stability of the boundary control is analyzed using LaSalle’s invariance principle. Finally, the performance of the presented boundary controller is verified through comparison with that of employing a constant disturbance observer via numerical simulations.
Highlights
At present, flexible manipulators have increasingly wide applications in industrial, agricultural, medical, and aerospace fields
Compared with the ordinary differential equations (ODEs) model, the partial differential equations (PDEs) model can reflect the dynamic characteristic of the flexible structure more accurately; it will increase the difficulty and challenge of controller design
The boundary control issue of the flexible manipulator has been discussed extensively, there are few studies on the control problem of flexible manipulators described via PDEs with input saturation and fast timevarying disturbances
Summary
Flexible manipulators have increasingly wide applications in industrial, agricultural, medical, and aerospace fields. The boundary control issue of the flexible manipulator has been discussed extensively, there are few studies on the control problem of flexible manipulators described via PDEs with input saturation and fast timevarying disturbances. The objectives of this research effort can be summarized as follows: (1) a control law with smooth hyperbolic functions is proposed based on the PDE model, and (2) the use of a higher order disturbance observer to compensate for the fast time-varying disturbances to reduce the disturbance effects.
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