2. Parameter *b* in *W*S

When designing the weightings in Equation (10), the desired system band was 20 Hz and *b* was 1.35. To analyze the influence of the parameter *b* on weighting function *W*S, the other parameters in the weightings were kept unchanged. By changing *b* from 0 to 1.5, the dynamics were calculated by the step response, which is shown in Figure 6. It is seen in Figure 6 that when parameter *b* was less than 0.1, with the increase in parameter *b*, the settling time decreased rapidly, while the overshoot almost remained unchanged. When parameter *b* was larger than 0.1, with the increase in parameter *b*, the settling time decreased very slowly, while the overshoot increased quickly. The steady-state error almost remained unchanged. It is seen in Equation (6) and Figure 3 that with the increase in *b*, the system bandwidth widened, resulting in the response speed accelerating and the overshoot increasing. Hence, it is recommended that a larger *b* should be used if one expects a faster response speed.

**Figure 6.** Effect of parameter *b* on *W*S. (**a**) Settling time; (**b**) overshoot; (**c**) steady-state error.

3. Parameter *c* in *W*S

The parameter *c* was changed from 0 to 1.5 to investigate its influence, while the other parameters in the weightings were kept unchanged. The dynamics were calculated by the step response, which is shown in Figure 7. It is seen that with the increase in parameter *c*, the settling time and the overshoot almost remained unchanged, while the steady-state error increased. Hence, it is recommended that the parameter *c* should be small enough to eliminate the steady-state error, which is very important to RTHS.

**Figure 7.** Effect of parameter *c* on *W*S. (**a**) Settling time; (**b**) overshoot; (**c**) steady-state error.
