Suppression of Base Vibrations and Tracking of the Tip of an Inverted Pendulum Using Sliding Mode Control and Quantitative Feedback Theory

Abstract

This paper presents a robust control method, combining Sliding Mode Control (SMC) and Quantitative Feedback Theory (QFT) to track the tip of an inverted pendulum, subject to base excitation. A Nonlinear inverted pendulum (IP) model is considered to analyze tracking control characteristics through computer simulation in order to demonstrate the effectiveness of the proposed control methodology. The sliding mode control is used to track the trajectory of the tip of the inverted pendulum. However, when the system enters into sliding regime, chattering occurs due to switching delays as well as base vibrations. The chattering is eliminated with the introduction of quantitative feedback theory inside the boundary layer to ensure smooth tracking. Problems with noise amplification, resonances, presence of uncertainties and unmodeled high frequency dynamics can largely be avoided with the use of QFT over other optimization methods. In addition, the QFT design methodology guides design evolution rather than replacing human intervention as would appear to be the case in some control synthesis methodologies.