A Linear Parameter Varying Strategy Based Integral Sliding Mode Control Protocol Development and Its Implementation on Ball and Beam Balancer

Abstract

An Integral Sliding Mode (ISM) based robustified Linear Parameter Varying (LPV) control is presented for a laboratory scale ball on a beam balancer system. The inherent input channel nonlinearity and under-actuated coupled dynamics make it a challenging control problem. The ISM control, being famous for reaching phase elimination, operates under the action of a control input which is usually an algebraic sum of a continuous and a discontinuous component. In the design of continuous component, the LPV form is used to linearize the otherwise non linearizable input channel nonlinearity. Hence, an LPV control is designed to cope with the varying dynamics. On the other hand, the discontinuous component diminishes the effect of norm bounded matched disturbances. In addition, the discontinuous control component is made smooth (chattering free) in order to generate a continuous control signal. The stability of the proposed algorithm is presented rigorously in terms of a theorem and is validated experimentally.

Keywords

• Ball and beam balancer
• integral sliding mode control
• linear matrix inequality
• linear parameter varying approach