Subsystem backstepping design for controlling a class of nonlinear SISO systems with cascade structure

This paper presents a controller design, referred to as the subsystem backstepping design (SSBD), for a class of nonlinear SISO mechatronic systems that comprise several cascaded subsystems. Compared with the conventional integrator backstepping design (CIBD) that deals with a first-order equation at each design step, the SSBD manages at each design step a subsystem that can be of high order. This both simplifies the design procedure and also makes controller parameters conveniently determined according to dynamic characteristics of each subsystem as in the conventional cascade control design with multiple feedback loops. However, in contrast to the conventional cascade control design, the SSBD does not require the inner feedback loop to respond much faster than the outer feedback loop, while guaranteeing system stability for a class of nonlinear systems. In addition, a variant of the SSBD, called internal model principle-based SSBD (IMP-SSBD), is presented to both further demonstrate the advantages of the SSBD procedure over the CIBD and also achieve robust tracking performance. The effectiveness of the proposed scheme is demonstrated through experimental studies of a harmonic drive system suffering from transmission compliance and periodic disturbances.