*5.4.2.3 Travel LQR-PI controller*

The control of the travel rate for the 3DOF helicopter system is governed by a GA-LQR based PI controller. The time response of the optimized PI tracking system *A Hybrid Control Approach Based on the Combination of PID Control with LQR Optimal Control DOI: http://dx.doi.org/10.5772/intechopen.94907*

**Figure 13.** *Closed-loop response of the elevation model system.*

In this study, in order to achieve a stable output, a hybrid control system using LQR based PID controller for 3DOF helicopter system is proposed to control the dynamic behaviour of the system. To validate the proposed helicopter stabilization system, the controller is simulated using Matlab programming tool. Three axis, elevation, pitch, travel rate, are considered in the simulation process of the control system. The performance of the helicopter balancing system is evaluated under unit step reference input using rise, settling time overshoot and steady state error parameters for the elevation, pitch and travel angles to simulate the desired

*Control Based on PID Framework - The Mutual Promotion of Control and Identification…*

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

The simulation results show that the controller successed to guide the system output through the desired input trajectory effectively with negligible overshoot,

In this section, an optimized LQR-PD controller based on GA tuning approach is

minifigure of the system response that the LQR-PD controller succeeded to force the pitch angle state of the helicopter system to follow the desired trajectory effectively without overshoot, shorter rise and settling time and zero steady state tracking error.

The control of the travel rate for the 3DOF helicopter system is governed by a GA-LQR based PI controller. The time response of the optimized PI tracking system

designed to control the dynamic model of helicopter pitch angle. Based on the optimized PD parameters stated in **Table 3**, the output response of the proposed helicopter tracking system is illustrated in **Figure 14**. It is obvious from the

parameters listed in **Table 3** for helicopter elevation angle.

short rise and settling time of 0.1 ms and 0.3 ms respectively.

command given by the pilot.

*Open loop response of Helicopter system.*

**Figure 12.**

*5.4.2.2 Pitch LQR-PD controller*

*5.4.2.3 Travel LQR-PI controller*

**36**

*5.4.2.1 Elevation LQR-PID controller*

**Figure 14.** *Closed-loop response of the pitch model system.*

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 tracking error.

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.

for a helicopter system is modeled mathematically and then formulated in state space form to enable utilizing state feedback controller technique. In the proposed helicopter stabilizing scheme, a combination of a conventional PID control with LQR state feedback controller is adopted to stabilize the elevation, pitch and travel axis of the helicopter scheme. The gain parameters of the traditional PID controller are determined from the gain matrix of state feedback LQR controller. In this research, the LQR controller is optimized by using GA tuning technique. The GA optimization method has been adopted to find optimum values for LQR gain matrix elements which are utilized to find best PID gain parameters. The output response of the optimized helicopter control system has been evaluated based on rise time, setting time, overshoot and steady state error parameters. The simulation results have shown the effectiveness of the proposed GA-LQR based PID controller to stabilize the helicopter system at desired values of the elevation and pitch angle and

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

Systems and Control Engineering Department, College of Electronics Engineering,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: ibrahim.mohammed@uoninevah@.edu.iq

travel parameters.

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

**Author details**

**39**

Ibrahim K. Mohammed

Ninevah University, Mosul, Iraq

provided the original work is properly cited.

**Figure 15.** *Closed-loop response of the travel model system.*

**Figure 16.** *Conrol input of 3DOF helicopter control system.*


**Table 4.**

*Values of performance elements s of controllers.*
