*2.3. Sizing Design Parameters*

The fourth step of the flow chart in Figure 2 is sizing the design parameters with given optimization parameters. This is an important process, and its diagram is illustrated in Figure 6. The inputs of the sizing process are the requirements of a control surface, which includes maximum hinge moment (*Tc*), maximum rotation velocity (*ωc*), and deflection angle (*δc*). For a flight control application, the EHA drives the control surface deflection by a level. Therefore, the level length (*R*) is a key parameter that affects the parameters of the EHA actuation system significantly. The maximum force (*F*), maximum speed (*v*), and linear stroke (*s*) can be calculated by (*R*) and (*Tc*), (*ωc*), and (*δc*). When the working pressure (*Ps*) of the EHA system is determined, the relevant parameters of the hydraulic cylinder can also be determined, such as the piston area (*Ap*) and the flow rate. The second key parameter that needs to be determined is the displacement of the hydraulic pump (*Dm*). As shown in Wu et al. [17], the maximum speed of the pump (*ωp*) is limited by the displacement of the hydraulic pump. The torque of the motor (*Tm*) can be obtained by the product *DmPs*. Usually, the maximum current is limited by the servo motor driver, and then the torque constant of the motor (*Ki*) is known. The weight of the EHA can be estimated, based on the scaling law in Wu et al. [17] with the sizing parameters. The parameters also will be transferred to the AMESim model and the dynamic performances can be obtained after running a simulation. In summary, the selected optimization design variables in this paper are (*R*) and (*Dm*), and the optimization targets are weight, energy consumption, rise time, and dynamic stiffness.

**Figure 6.** Diagram of the design process in the EHA parameter optimization.

#### **3. Multi-Objective Optimization of EHA**

In the present study, four objectives are considered for optimization. Therefore, the evaluation model of these four objectives should be integrated into the optimization program. These four objectives include both static and dynamic performances, requiring different evaluation methods which will discussed in the present section.
