*5.4.2.1 Elevation LQR-PID controller*

This section deals with the simulation of LQR based PID controller used to control the position of helicopter elevation model. The parameters of the hybrid controller are tuned using GA optimization method. **Figure 13** presents a tracking control curve of the demand input based on the PID controller using optimized gain parameters listed in **Table 3** for helicopter elevation angle.

The simulation results show that the controller successed to guide the system output through the desired input trajectory effectively with negligible overshoot, short rise and settling time of 0.1 ms and 0.3 ms respectively.

> using optimum gain parameters which are listed in **Table 3**. is shown in **Figure 15**. It can be noted from the miniplot of the system response that the optimised hybrid LQR-PI controller enabled the system output state to track the desired input trajectory without overshoot, and shorter rise and settling time with minimal steady state

> *A Hybrid Control Approach Based on the Combination of PID Control with LQR Optimal Control*

The control inputs supplied to the propellers motors of the proposed 3DOF helicopter system are shown in **Figure 16**. Consequently, it can say that the control performance of optimised GA-LQR based PID, PD and PI controllers for helicopter elevation, pitch and travel axis model respectively was acceptable through tracking the system output states for the reference input efficiently. Based on the minifigures of **Figures 13** and **14** and **Figure 15**, the performance parameters of PID, PD and PI controller for helicopter elevation, pitch and travel axis are listed in **Table 4**. From the response data of the controlled helicopter system in **Table 4** it can be said that the hybrid controllers were able to provide robust and good tracking performance

in both the transient and steady state responses.

tracking error.

**37**

**Figure 14.**

**Figure 13.**

*Closed-loop response of the elevation model system.*

*DOI: http://dx.doi.org/10.5772/intechopen.94907*

*Closed-loop response of the pitch model system.*
