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End-point control of a flexible-link manipulator using stste-dependent Riccati equation technique

Shawky A., Ordys A., Grimble M. J., Petropoulakis L.

Archives of Control Sciences

2002

Vol. 12, no. 3

191-207

The problem of modeling and controlling the tip position of a one-link flrxible manipulator is considered. The paper discusses the control strategy based on the nonlinear state Dependent Ricatti Equation (SDRE) design method in the context of application to robotics and manufacturing systems. Lagrangian Mechanics and the Assumed Mode Method have been used to derive a proposed dynamic model of a single-link flexible manipulator having a revolute joint. The model may be used in general to investigate the motion of the manipulator in the horizontal plane rest-to-rest rotational maneuver. The nonlinear SDRE control law is derived as minimizing a quadratic cost function that penalizes the states and the control input torques. Simulation results are presented for a single-link flexible manipulator to achieve a desired angular rotation of the link while simultaneously suppresing structural vibrations, and the effect of payload on the system response and vibration frequencies is investigated. The results are illustrated by a numerical example.

Dynamic Algorithm for Linear Quadratic Gaussian Predictive Control

Ordys A. W., Hangstrup M. E., Grimble M. J.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 2

227-244

In this paper, the optimal control law is derived for a multi-variable state-space Linear Quadratic Gaussian Predictive Controller (LQGPC). A dynamic performance index is utilized resulting in an optimal steady-state controller. Knowledge of future reference values is incorporated into the controller design and the solution is derived using the method of Lagrange multipliers. It is shown how the well-known GPC controller can be obtained as a special case of the LQGPC controller design. The important advantage of using the LQGPC framework for designing predictive controllers is that, based on stabilizing properties of LQG control, it enables a systematic approach to selection of the design parameters to yield a stable closed-loop system. The system model considered in this paper can be further extended toalso include direct feed-through and knowledge about future external inputs.