Gain scheduling via control signal interpolation: the ball and beam example

This paper presents an approach to gain scheduled controller design based on plant linearizations about equilibria. This method yields controllers that automatically have a desired linearization property and also assume a linear parameter-varying form. The approach eliminates the necessity for measurement of time-derivatives of certain controller inputs as required in related work. A gain scheduled controller involving linear interpolation of the control signal is designed for the well-known ball and beam experiment to illustrate the technique. Nonlinear simulation results indicate satisfactory performance over the specified range of ball position.