• Journal of Mechanical Science and Technology
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• 제15권10호
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• pp.1356-1368
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• 2001

In this paper, the model reference adaptive control (MRAC) of a flexible structure is investigated. Any mechanically flexible structure is inherently distributed parameter in nature, so that its dynamics are described by a partial, rather than ordinary, differential equation. The MRAC problem is formulated as an initial value problem of coupled partial and ordinary differential equations in weak form. The well-posedness of the initial value problem is proved. The control law is derived by using the Lyapunov redesign method on an infinite dimensional filbert space. Uniform asymptotic stability of the closed loop system is established, and asymptotic tracking, i. e., convergence of the state-error to zero, is obtained. With an additional persistence of excitation condition for the reference model, parameter-error convergence to zero is also shown. Numerical simulations are provided.

• Journal of Mechanical Science and Technology
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• 제16권8호
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• pp.1053-1063
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• 2002

This paper presents a robust nonlinear controller for a f degree of freedom (DOF) parallel manipulator in the task space coordinates. The proposed control strategy requires information on orientations and translations in the task space unlike the joint space or link space control scheme. Although a 6 DOF sensor may provide such information in a straightforward manner, its cost calls for a more economical alternative. A novel indirect method based on the readily available length information engages as a potential candidate to replace a 6 DOF sensor. The indirect approach generates the necessary information by solving the forward kinematics and subsequently applying alpha-beta-gamma tracker With the 6 DOF signals available, a robust nonlinear task space control (RNTC) scheme is proposed based on the Lyapunov redesign method, whose stability is rigorously proved. The performance of the proposed RNTC with the new estimation scheme is evaluated via experiments. First, the results of the estimator are compared with the rate-gyro signals, which indicates excellent agreement. Then, the RNTC with on-line estimated 6 DOF data is shown to achieve excellent control performance to sinusoidal inputs, which is superior to those of a commonly used proportional-plus-integral-plus-derivative controller with a feedforward friction compensation under joint space coordinates and the nonlinear controller under task space coordinates.