Simulation of the four control models with and without noise: Model 1 (panel A); Model 2 (panel B); Model 3 (panel C); Model 4 (panel D).
Each panel shows: 1) trajectories in the phase plane (left-upper part without noise, left-lower part with noise); 2) corresponding angular sway sequences (middle-upper part without noise, middle-lower part with noise); 3) power spectral density for the model with noise (right part). In the shaded areas of the phase planes, PD control is switched off. For Models 1 and 2, the following parameters were used: P/mgh = 0.8, D = 270 Nms/rad, σ = 2 Nm. For Models 3 and 4 the parameters in the PD-on regions were as follows: P/mgh = 0.25, D = 10 Nms/rad, σ = 0.2 Nm, and a = −0.4 s−1.