Variable Structure Controller Schemes Based on Work and Energy Principle for SIMO Systems

This paper presents a reasoned methodology for designing variable structure controllers (VSC), also known as sliding mode controllers (SMC), for Single- Input-Multi-output (SIMO) systems. The approach is explicitly based on the assessment of a system total energy, and the realization of a VSC that minimizes that energy. A relationship between controller gains and the slope of the sliding surface is explicitly formulated. The practical implementation of the proposed approach is exemplified on an inverted pendulum system where the system has two independent sliding surfaces representing the two system states. A VSC with hyper sliding surface is also introduced. Since the pendulum system has no dissipative viscous load to absorb energy, a VSC for pure inertial systems is proposed.