*3.2. Influence on the System Dynamics*

In RTHS, it is expected that the servo-hydraulic actuator can realize the desired displacement command quickly and precisely. Hence, to give guidance on weighting function selection, the influence of the parameters in the weighting function on the dynamics, namely the settling time, overshoot, and steady-state error, were investigated in this subsection. The control plant, from the controller output *u* to measurement displacement *y*, was taken as

$$P = \frac{20.99}{s + 1.418}.\tag{9}$$

 By several trials, the weighting functions were selected as follows:

$$\mathcal{W}\_{\rm S} = \frac{0.0475s + 170.1}{s + 0.001}, \mathcal{W}\_{\rm T} = \frac{2500 \text{ (s + 250) (s + 14.14)}}{\left(s + 1.571 \times 10^4\right)^2}, \mathcal{W}\_{\rm R} = 0.001. \tag{10}$$

It should be noted that as the control plant is a first-order transfer function, the form of the weighting function *W*T is modified to guarantee that *W*T*P* is a rational function. The step response was obtained and is shown in Figure 4. It is seen that the controlled system could respond to the reference command quickly, and there was no steady-state error, indicating a perfect tracking performance.

**Figure 4.** Step response of the *H*∞-controlled system.
