Position Control of Flexible Manipulator Using Nonlinear H∞ with State-Dependent Riccati Equation

Document Type : Original Article

Authors

1 Egyptian Armed Forces.

2 British Energy Senior Lecturer in Control Systems, Industrial Control Centre, Dept of Electronic and Electrical Engineering, University of Strathclyde, 50 George Street, Glasgow, G1 1QE,Scotland, U.K.

3 Professor of Industrial Systems and Director, Industrial Control Centre, Dept of Electronic and Electrical Engineering, University of Strathclyde, 50 George Street, Glasgow, G1 1QE,Scotland,UK.

Abstract

Abstract
The paper is concerned with the control of the tip position of a single-link flexible manipulator. The non-linear
model of the manipulator is derived and tested, assuming the number of model shape functions is two. It is
known that the Assumed Modes Method introduces uncertainty to the model by neglecting higher order
dynamics. There are other sources of uncertainty, such as friction. In addition, the model is non-linear.
Therefore, for the next task, which is the controller design, the H∞ approach is proposed to deal efficiently with
uncertainties, and the non-linear nature of the problem is addressed by the use of State Dependent Riccati
Equation (SDRE) technique. Following the SDRE approach, the state-feedback non-linear control law is
derived which minimizes a quadratic cost function. This solution is then mapped into the H∞ optimization
problem. The resulting control law has been tested with the simulation model of the flexible manipulator and
the results are discussed in the paper.

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