**4. Simulation results and discussion**

This section represents simulation results and evaluates the performance of the developed control law using MATLAB/Simulink. Three controller strategies are compared in this section, which are the single LQI controller, the switched LQI controller given in Eq. (9), and the fuzzy switching LQI controller given in Eq. (10). The single LQI controller is designed for the data, which is taken at the center of the ADMIRE flight envelope, whereas the switched controller is designed using the flight envelope,

**Figure 5.** *Fuzzy controller rules for overlapping four cells.*

**Figure 6.** *Flight envelope with the four cells.*

which has been divided into four cells as shown in **Figure 6** with the dashed lines showing the boundaries between cells. The feedback gains of the switched controller are computed based on the data of each cell center.

The simulation scenarios were performed to analyze the robust stability and performance of the closed-loop system at flight conditions (Mach = {0.75, 0.9, 0.75} and altitude = {5000, 1500, 4500} m). The pilot command is constricted such that the loadfactor *Nz* stays within the design limits -3 g < *Nz* <9 g over the flight envelope. Loadfactor demand and responses of the closed-loop system with the controllers at flight condition of Mach = 0.75 and Alt = 5000 is illustrated in **Figure 7**. The load-factor response with the single LQI is slower than the switched and fuzzy switching controllers. The switched controller has an oscillatory response during the switching, which is an undesired effect during flight operation. **Figure 8** gives the angle of attack and the Euler pitch rate responses of the closed-loop system with the single LQI, switched, and

*Performance Improvement for Fighter Aircraft Using Fuzzy Switching LQI Controller DOI: http://dx.doi.org/10.5772/intechopen.107032*

**Figure 7.** *Load-factor responses of the closed-loop systems at flight condition Mach = 0.75 and alt = 5000.*

**Figure 8.** *State variables, the angle of attack, and the Euler pitch rate responses at flight condition Mach = 0.75 and alt = 5000.*

the proposed fuzzy switching LQI controllers. One can see from the bottom plot of **Figure 8** that the Euler pitch rate response has an oscillation during switching with the switched controller. However, the proposed fuzzy switching controller has the best transient performance. The corresponding control inputs to the related controllers are given in **Figure 9**. Elevon deflection generates values between 4 deg. and 2 deg. Oscillations are also seen in this elevon deflection and throttle setting, *tss* when the switched controller is used. **Figures 10** and **11** give the indexes of the switched controller and the change in the coefficients of the fuzzy switching controller, respectively. Feedback gains *K*1, *K*<sup>2</sup> and *K*<sup>4</sup> are employed for the switched controller, but all computed controller gains are used with the fuzzy switching controller. **Figure 12** illustrates the trajectory movement in the flight envelope for the different controllers.

In the second scenario, simulation is started at flight condition Mach = 0.9 and Altitude = 1500 m. Load-factor demand and responses of the closed-loop systems are

#### **Figure 9.**

*Control inputs of the single, switched, and fuzzy switching controllers at flight condition Mach = 0.75 and alt = 5000.*

#### **Figure 10.**

*Index of the switched controller gains at flight condition Mach = 0.75 and alt = 5000.*

*Performance Improvement for Fighter Aircraft Using Fuzzy Switching LQI Controller DOI: http://dx.doi.org/10.5772/intechopen.107032*

#### **Figure 12.**

*Altitude responses with the different controllers at flight condition Mach = 0.75 and alt = 5000.*

**Figure 13.** *Load-factor responses of the closed-loop systems at flight condition Mach = 0.9 and altitude = 1500 m.*

given in **Figure 13**. Closed-loop response with the single LQI controller is the slowest amongst the controllers. Load-factor tracking response settles a larger steady-state error than the responses of other controllers. The switched controller has an undesired oscillatory response during the switching instances. **Figure 14** gives the angle of attack and the Euler pitch rate responses of the closed-loop system with the single LQI, switched, and the proposed fuzzy switching LQI controllers. The angle of attack increases at t = 20 sec for a larger demand of load-factor. Input responses of the related controllers are given in **Figure 15**. Throttle setting control input is the largest with the switched controller. The single LQI controller requires 0.288 of the throttle setting in the second scenario. **Figures 16** and **17** display the index of the switched controller and the varying coefficients of the fuzzy switching controller, respectively. All computed feedback gains are employed with the fuzzy switching controller, whereas feedback gains *K*1, *K*2, and *K*<sup>4</sup> are used for the switched controller. **Figure 18** illustrates the trajectory movement in the flight envelope for the different controllers.

#### **Figure 14.**

*State variables, the angle of attack, and the Euler pitch rate responses at flight condition Mach = 0.9 and altitude = 1500 m.*

#### **Figure 15.**

*Control inputs of the single LQI, switched and fuzzy switching controllers at flight condition Mach = 0.9 and altitude = 1500 m.*

**Figure 16.** *Index of the switched controller gains at flight condition Mach = 0.9 and altitude = 1500 m.*

*Performance Improvement for Fighter Aircraft Using Fuzzy Switching LQI Controller DOI: http://dx.doi.org/10.5772/intechopen.107032*

#### **Figure 17.**

*Varying coefficients of the fuzzy switching controller at flight condition Mach = 0.9 and altitude = 1500 m.*

#### **Figure 18.**

*Altitude responses with the different controllers at flight condition Mach = 0.9 and altitude = 1500 m.*

**Figure 19.** *Load-factor responses of the closed-loop systems at flight condition Mach = 0.75 and altitude = 4500 m.*

#### *Advances in Fuzzy Logic Systems*

These simulation results also demonstrate the efficacy of the proposed fuzzy switching controller.

In the third scenario, simulation is started at flight condition Mach = 0.75 and Altitude = 4500 m. Load-factor demand and responses of the closed-loop systems are given in **Figure 19**. It is clearly seen that the switched controller is unable to stabilize the aircraft when the controller switches. Load-factor tracking performance is successful with the fuzzy switching controller. The switched controller drives the closedloop system from stability to instability shown in **Figures 20** and **21**. The index of the switched controller and the varying coefficients of the fuzzy switching controller are given in **Figures 22** and **23**, respectively. **Figure 24** illustrates the trajectory movement in the flight envelope for the different controllers. The fuzzy switching controller improves the load-factor tracking performance and enhances the stability of the aircraft.

**Figure 20.**

*State variables, the angle of attack, and the Euler pitch rate responses at flight condition Mach = 0.75 and altitude = 4500 m.*

#### **Figure 21.**

*Input responses of the single, switched, and fuzzy switching controllers at flight condition Mach = 0.75 and altitude = 4500 m.*

*Performance Improvement for Fighter Aircraft Using Fuzzy Switching LQI Controller DOI: http://dx.doi.org/10.5772/intechopen.107032*

**Figure 23.**

*Varying coefficients of the fuzzy switching controller at flight condition Mach = 0.75 and altitude = 4500 m.*
