Contributions to non-identifier based adaptive control in mechatronics

Abstract

Funnel-Control (FC)–an adaptive (time-varying) MIMO/SISO control strategy–is re-introduced and its applicability introductory for position control of nonlinear, coupled (rigid) robotic systems and for speed control of nonlinear two-mass flexible servo systems is shown. Additionally Error Reference Control (ERC)–a direct derivative of FC–is established. ERC is specially designed with asymmetric boundaries and auxiliary reference, ensuring that the control error evolves within a prespecified tube (a shrinked funnel region, achieving even better tracking performance). FC and hence ERC are based on the high-gain stabilizability of minimum-phase systems with relative degree one and known sign of the high-frequency gain. Although the plant only needs to be known in structure, both concepts assure prescribed transient behavior without identification and/or parameter estimation. As most industrial applications, also the considered robotic and two-mass flexible servo systems, exhibit relative degrees greater than one, FC and ERC cannot directly be applied. Therefore a special state feedback is introduced, reducing the relative degree and retaining the minimum-phase property. The additional implementation of a nominal PI-like extension guarantees good disturbance rejection and asymptotic tracking of (constant) velocity and position reference trajectories. Simulation results for a 6-DOF Manutec r3 robot underpin and compare the achievable position control performance of one overall MIMO Funnel Controller for all joints and one SISO Funnel Controller for each joint (6 controllers). For nonlinear two-mass flexible servo systems, measurement results demonstrate the achievable load speed control performance of FC and ERC in comparison to optimal LQ state feedback.