Maximizing Allowable Feedback Delay via Sensor Placement for the Acrobot System

The transfer function of a linearized model of the so-called acrobot system, around the upright equilibrium point, is unstable and it has two pairs of poles and a pair of zeros, pairwise symmetric around the origin. A method for strongly stabilizing controller design is considered for this system. The largest allowable feedback delay, by the proposed method, is investigated with respect to the location of the right half plane zero, which in turn depends on the sensor location. The optimal location of the zero is identified for the largest possible delay. The delay margins corresponding to the controllers obtained earlier in the literature are compared with the delay margin resulting from a third order stable controller derived in the paper. Furthermore, the trade-off between delay maximization and sensitivity minimization are discussed with a numerical example. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)