Jinkun Liu

A robust observer design for a flexible manipulator based on a PDE model

This paper proposes a robust observer for a flexible single-link manipulator based on the partial differential equation (PDE) dynamic model. Unlike observers for the PDE model introduced by previous researchers, this observer is designed to estimate the distributed spatiotemporally varying states with unknown boundary disturbance and spatially distributed disturbance. The asymptotic stability of the proposed observer is proved by theoretical analysis and demonstrated by simulation results.

Active vibration control of a nonlinear three-dimensional Euler–Bernoulli beam

In this paper, boundary control is designed to suppress the vibration of a nonlinear three-dimensional Euler–Bernoulli beam. Considering the coupling effect between the axial deformation and the transverse displacement, the dynamics of the beam are modeled as a distributed parameter system described by three partial differential equations (PDEs) and 12 ordinary differential equations (ODEs). Firstly, model-based boundary control is designed based on a mathematical model of the system. Subsequently, adaptive control is proposed when there are parameter uncertainties in the model. The uniform boundedness and uniform ultimate boundedness are proved under the proposed control laws. Finally, numerical simulations illustrate the effectiveness of the results.

Boundary control for a flexible manipulator with a robust state observer

In this paper, a boundary controller for a flexible manipulator is proposed based on a partial differential equation (PDE) robust observer. In the previous work we have proposed a PDE robust observer to estimate the infinite dimensional states of the flexible manipulator with unknown boundary disturbance and spatially distributed disturbance. On the basis of the proposed robust state observer, a boundary controller is designed to achieve the stability control, regulate the joint position and suppress elastic vibration in this paper. The stabilities of the proposed observer and the boundary controller are validated by theoretical analysis. Numerical simulations are provided to demonstrate the effectiveness of the closed-loop system.

Adaptive neural network control of an arm-string system with actuator fault based on a PDE model

In this paper, an adaptive boundary controller for an undersea detection robot system with actuator failure, unknown disturbance and boundary deflection constraint is proposed. Using Hamilton’s principle, a partial differential equation (PDE) model is established for the detection system, which consists of a rigid arm, a flexible string and a sensor. Considering the actuator failure, a fault-tolerant scheme is proposed to tackle it. To handle the unknown disturbance, we employ radial basis function (RBF) neural networks (NNs) to neutralize the boundary uncertain nonlinear disturbance. The proposed adaptive controller includes a proportional–derivative (PD) feedback structure, a fault-tolerant strategy and a NN control scheme. By choosing an appropriate Lyapunov-Krasovskii function and applying LaSalle’s Invariance Principle, the asymptotic stability of the closed-loop system is rigorously proven. Simulation results validate the proposed controller.