# Modeling a Hydraulically Powered Flight Control Actuation System
## 5 HPFCAS Model Development and Simulations
### Procedures for Actuator Integration with the Model  
Though the boundary conditions were chosen in developing the HPFCAS model, the building blocks were built with the basic equations and the characteristics of the components embedded in all the model blocks. Thus, the block model for the actuator needed the sizing for the principal parameters of the actuator like the stroke length, bore, cylinder length, piston length, and areas of the actuator chambers. These were chosen considering the pressure and the Bernoulli equation's boundary conditions. The maximum pressures that can exhibit pressure forces to drive the actuator and the maximum external force as loading on the actuator were calculated. Hence, the actuator was designed to fit into the system by adjusting the parameters of a double-acting linear actuator block from Simulink libraries and replacing most parameters with the calculated ones. These showed its suitability to be used and integrated with the Simulink and Simscape models. Figure 15 shows some of the calculated actuator simple parameter values.  
The loading, work done, or power relationship of the actuator was calculated for the steady-state flow into the actuator equation as follows [34]:  
\[F_{L}\;\dot{x_{p}}=P_{1}\;Q_{1}-P_{2}\;Q_{2}\delta \tag{3}\]  
Figure 14: The experimental values show the characteristic map for the DPV.  
Figure 15: The designed actuator dimensions and simple properties.  
where \(F_{L}\dot{x_{p}}\) = External load and piston velocity, \(P_{1}-P_{2}\delta\) = Load pressure, and \(Q_{1}-Q_{2}\) = Load flow.  
Combining these with other parameters, the actuator was tested at a steady state. This implies, there is a constant velocity of the actuator piston to observe its steady-state response before being integrated.  
The model in Figure 16 was used for all simulations whether at a steady state of the actuator or at a transient state. However, the equations embedded in the actuator blocks had changes in the parameters. Also, the model was tested without actuator integration to obtain the values for healthy scenarios before the fault injections. Here, a tested flow rate amount of 0.5 L/min and percentage changes in the flow rate for the full opening of the DPV at a constant speed of 400 rpm of the pump were used to run the first simulation in a period of 10 s. This served as the solution process for all other simulations because the initial conditions of the inputs were generated and could simulate any value of mass flow that was not more than 2 L/min for all the changing parameters of the pressure and flow rates. This was simply because the maximum pump speed was 1000 rpm, which was to produce a maximum flow rate of 2 L/min.  
The solution process and Simulink simulation algorithm started with identifying the initial inputs and boundary conditions. The iterative processes continued in each case until both the input designated value and the final value are same where P2 and P3, the unknowns are measured. Table 2 illustrates the solution process for the HPFCAS model.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Inputs** & **Initial Boundary Conditions** & **Descriptions** \\ \hline i (Pressure values) & P1 and P4 & both atmospheric \\ \hline ii (Rpm settings) & 400 & RPM of pump \\ \hline iii (DPV opening) & 100\% & RPM of pump \\ \hline Iv (Pressure values) & P2 and P3 & Unknowns \\ \hline
**Process** & & \\ \hline i (Flow rate values) & 0.5 L/min & Guess mass flow \\ \hline ii (Pressure values) & P3 & Obtained from DPV curve \\ \hline iii (Pressure ratio values) & P3/P2 & Obtained from pump curve \\ \hline iv (Flow rate values) & Flow & Obtained from Bernoulli using stations 1 and 2 \\ \hline v (Flow rate values) & Mass flow & Adjust the flow rate and repeat the process. \\ \hline \hline \end{tabular}
\end{table}
Table 2: The solution process and simulation algorithm.  
Figure 16: The developed Simulink model of the HPFCAS for simulations with actuator integration.