Extended second order sliding mode control for mismatched uncertain systems with only output measurable

Abstract

Most existing Second Order Sliding Mode Control (SOSMC) approaches are achieved under assumptions that 1) all of state variables must be accessible; 2) the second derivative of all state variables must exist, even though mathematical model of systems uses the first order equations. In this paper, a new adaptive SOSMC scheme is proposed for mismatched uncertain systems in which these above assumptions are required. In this proposed method, only output variables are used in the sliding surface and controller design. The advantage of no need of all state variables in controller design makes the method more useful and realistic since it can be applied to a wider class of systems. Finally, a vertical take-off and landing aircraft at the nominal airspeed of 135~knots is simulated to demonstrate the advantages and effectiveness of the proposed approach.