High-gain adaptive position control

High-gain adaptive position control is proposed for a stiff one-mass system (1MS) and an elastic two-mass system (2MS). The control objective is (load-side) position reference tracking and disturbance rejection (of load torques and friction). Position and speed are available for feedback. Two simple high-gain adaptive position control strategies are presented and applied to a laboratory setup: an adaptive λ-tracking controller and a funnel controller. Both controllers neither estimate nor identify the plant. The λ-tracking controller achieves tracking with prescribed asymptotic accuracy: for given λ > 0 (arbitrary small) the error approaches the interval [−λ, λ] asymptotically. Whereas the funnel controller assures tracking with prescribed transient accuracy: the error and its derivative are bounded by prescribed positive (possibly non-increasing) functions of time. A simple proportional-integral (PI)-like extension for the 1MS, and this extension in combination with a high-pass filter for the 2MS, allow for zero tracking errors in steady-state, respectively. Oscillations in the shaft of the 2MS can be suppressed. Keywords: high-gain adaptive controlposition controlfunnel controlone-mass systemtwo-mass system Acknowledgements The author is indebted to Prof. Achim Ilchmann (Ilmenau University of Technology, Germany) for careful proof-reading the manuscript of this article and for providing a precise list of misprints and suggestions for improvement. Notes Notes 1. This article does not strictly distinguish between dynamic tuning or 'time-varying adjustment' of the controller gain. Both is considered as 'high-gain adaptive' control. 2. For example, and λ1 < δ/2, the case −ψ1(t) + δ/2 ≥ 0 for all t ∈ [t 0, t 1] is possible.