Proportional Double Derivative Linear Quadratic Regulator Controller Using Improvised Grey Wolf Optimization Technique to Control Quadcopter

Abstract

A hybrid proportional double derivative and linear quadratic regulator (PD2-LQR) controller is designed for altitude (z) and attitude (roll, pitch, and yaw) control of a quadrotor vehicle. The derivation of a mathematical model of the quadrotor is formulated based on the Newton–Euler approach. An appropriate controller’s parameter must be obtained to obtain a superior control performance. Therefore, we exploit the advantages of the nature-inspired optimization algorithm called Grey Wolf Optimizer (GWO) to search for those optimal values. Hence, an improved version of GWO called IGWO is proposed and used instead of the original one. A comparative study with the conventional controllers, namely proportional derivative (PD), proportional integral derivative (PID), linear quadratic regulator (LQR), proportional linear quadratic regulator (P-LQR), proportional derivative and linear quadratic regulator (PD-LQR), PD2-LQR, and original GWO-based PD2-LQR, was undertaken to show the effectiveness of the proposed approach. An investigation of 20 different quadcopter models using the proposed hybrid controller is presented. Simulation results prove that the IGWO-based PD2-LQR controller can better track the desired reference input with shorter rise time and settling time, lower percentage overshoot, and minimal steady-state error and root mean square error (RMSE).

A Novel Framework of Modelling, Control, and Simulation for Autonomous Quadrotor UAVs Utilizing Arduino Mega

“…The test results show that our approaches proved more effective in a number of aspects such as: (i) A 9 DOF IMU is potentially better than a 6 DOF IMU in the article [16] because it can use sensor fusion (mixing the data from different sensors) in order to improve the quality of the final output (ii) We have added to the model both low feeding rate and high-frequency Gaussian white noise instead of only high feeding rate as in the test of the article [40]. This increased the accuracy of the test results…”

Gain-scheduled linear-quadratic-regulator synthesis for the centre of gravity variations of Boeing 747-100 longitudinal modes

“…Almost all the finding flight responses of quadcopter four motions noticeably improved due to the proposed PD2LQR as an alternative controller. Shauqee et al [17] controlled altitude and attitude responses demonstrated by a quadrotor vehicle. The PD2-LQR was used with an improved grey wolf optimiser (IGWO) to search for an appropriate controller parameter for superior control performance.…”

“…Also, authors [3, 12−20] used the classical LQR to control general aviation A/C, B747-100, quadcopter and rider-less bicycles for real limited scenarios. Some of those [13,[16][17]19] proposed the so-called FI-LQR, R-LQR, P-LQR, PD-LQR, PD2-LQR and IGWO-PD2LQR (Modified LQR versions) to ensure the LQR shortcomings not influencing the performance under unstandardised conditions. Shauqee et al [17] argued that IGWO-PD2LQR showed more pronounced outperformance than the other controllers" responsiveness.…”

“…Some of those [13,[16][17]19] proposed the so-called FI-LQR, R-LQR, P-LQR, PD-LQR, PD2-LQR and IGWO-PD2LQR (Modified LQR versions) to ensure the LQR shortcomings not influencing the performance under unstandardised conditions. Shauqee et al [17] argued that IGWO-PD2LQR showed more pronounced outperformance than the other controllers" responsiveness. Although those obtained responses were based on different 20 models no sufficient guarantee that satisfactory performance might still be accepted over different operating cases as they tested all 20 quadcopters under the same benchmarking conditions.…”

“…In the abundance of literature [14−20], integral square error (ISE), integral time absolute error (ITAE), and integral time square error (ITSE) are widely used to optimise those control laws [32]. However, a refined IAE (RIAE) [17], IAE ∫ ( ) was suggested by accumulating the rise time ( ), percentage overshoot ( ), and steady-state error ( ), merging them with the IAE cost function Equation (6).…”