Fig 1.
A skater on a remotely controlled swaying bow.
The skater can send remote signals to the servomechanism (the rectangle labeled as Servo) that exerts power P in order to cause a horizontal-angle input deviation of u. The horizontal asymmetry yields the deviation of angle y from the bow symmetry axis—which is then taken as the system output.
Fig 2.
A Flowchart diagram of Algorithm 1.
The flowchart diagram displays the designed DDS algorithm. Its step-by-step formulation is presented in Algorithm 1. The ellipse expresses the starting point, and the oval means the termination point. The rhomb, the trapezium and the square stand for the condition, the output and the execution block, respectively.
Table 1.
Leading pole estimation accuracy benchmark.
Table 2.
Switching delay estimation benchmark.
Fig 3.
Switching delays found by Algorithm 1.
Delay values computed by using pre-warping are indicated by circles and a joint via the solid line; the ones without pre-warping are represented by diamonds and joint by the dashed line. Results are back-grounded stability/instability regions computed by the QPmR with Δτ⋅ = 0.01.
Fig 4.
Details of Fig 3 in selected regions.
Two regions were selected, a moderately detailed one R2 (A) and a very detailed one R3 (B). The stable and unstable areas found by the QPmR for Δτ⋅ = 0.005 and Δτ⋅ = 0.001, respectively, are indicated as well.
Table 3.
Highlighted results of Algorithm 1—Inside region R2.
Fig 5.
Time domain results verification.
The three plots of the system’s step reference time responses for three different delay vectors are displayed. Whereas the nominal setting τ = (0.3,0.1) (A) gives a stable response asymptotically tracing the reference signal, the second option τ = (0.0700747,0.74643) (B) indicates the stability border by steady oscillations, and the last one: τ = (0.04,0.04) (C), gives unstable oscillations with a rising amplitude.