Abstract
The design problem of a discrete controller with time delay and acceleration feedback for a single-link flexible manipulator system is addressed in this paper. The dynamical model of a single-link flexible manipulator system is presented by the adoption of the finite element method and Lagrange’s equation. Based on the random-walk process and the discrete reduction method, an augmented discretized delay-free state derivate space equation containing the random noise is established. An acceleration-based Kalman filtering method is developed in order to estimate the system state and external excitation necessary for the controller design. In light of the estimated augmented states, a hybrid controller that combines a feedback control algorithm and a feedforward control algorithm is designed according to optimal control theory and Moore–Penrose theory. Numerical simulation results show that the proposed controller can damp out the vibration response of the flexible manipulator system effectively upon external excitations. Moreover, it is further revealed that the control performance of the presented method can be improved by adding the time delay appropriately.
Highlights
Over the past few decades, manipulators constructed with flexible arms have attracted much more attention because flexible manipulators have the advantages of lighter weight, lower energy consumption, and wider operating range as compared to the traditional rigid manipulators
Various control schemes can be applied to discrete flexible manipulators after the implementation of a series of truncating techniques, such as the finite element method (FEM) [6] or the assumed mode method (AMM) [7]
Where u is an externally driven voltage; cp 2EpAph2p/lp; kv 2EpAphpkv/lp; wp1 and wp2 are the deflections at nodes p1 and p2, respectively; Ep, Ap, and lp are the Young modulus, cross-sectional area, and length of the piezoelectric actuators, respectively; hp is the distance from the controlling point to the neutral axis of the flexible link; and kv is the constant describing the relationship between the control voltage and the deformation of the actuator
Summary
Over the past few decades, manipulators constructed with flexible arms have attracted much more attention because flexible manipulators have the advantages of lighter weight, lower energy consumption, and wider operating range as compared to the traditional rigid manipulators. Due to the complexity of link deformation and the rigid-flexible coupling effect [1], establishing an accurate dynamic model and suppressing the unwanted vibration have become a key research challenge in practical design. A computed torque-time delay approach was presented in Reference [24] to damp out the end point vibration of a single-link flexible manipulator. Saeed et al [25, 26] proposed a time-delayed position-velocity feedback controller to suppress the vibration of the nonlinear system. A time-delayed acceleration feedback controller considering the effects of the external disturbance is applied to a single-link flexible manipulator. An acceleration-based feedback Kalman filtering equation is developed to estimate the system state and external force, which are necessary for the controller design. Numerical simulations are performed to demonstrate the ability of the proposed controller in reducing the vibration response
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