Adaptive Backstepping Tuning Functions Control Design for Industrial Robot Manipulators

The adaptive backstepping solution to the problem of nonlinear stabilization and tracking in the presence of unknown parameters is a starting point for more elaborate adaptive control designs for feedback systems including robot manipulators [2-4]. One of the improvements to be achieved with the tuning functions design [1] is to reduce the dynamic order of the adaptive controller to its minimum (the number of parameter estimates is equal to the number of unknown parameters). This minimum-order design is advantageous not only for implementation, but also because it guarantees the strongest achievable stability and convergence properties.

 In the tuning functions procedure the parameter update law is designed recursively. At each consecutive step we design a tuning function as a potential update law. In contrast to adaptive backstepping in [2], these intermediate update laws are not implemented. Instead, the controller uses themto compensate for the effect of parameter estimation transients. Only the final tuning function is used as the parameter update law.

 In this paper we presented an adaptive backstepping tuning functions control design for systems in the output feedback form. In the design, different filter structures (K-filter) and identifiers are applied. 

The rest of the paper is structured as follows. A design with tuning functions for a single-link flexible-joint robot manipulator is presented in section II. Experiment design and the performance of the designed real-time control for the flexible-joint robot arm are presented in section III.  We conclude in section IV.