## 4 Quadrotor Control
### Comparisons of Intelligent and Classical Control Performances  
To get the quadrotor to hover at a determined position coordinates, desired signals for positions \([x_{d},y_{d},z_{d}]\) are considered step signals of _1 m_ and desired yaw angle (\(\psi_{d}\)) is fixed to _1 degree_. Table 3 summarizes the PID controllers gains computed online using PSO, CS, and PSO-CS, and offline with the conventional RM for the quadrotor's outputs (\(\phi\), \(\theta\), \(\psi\), \(x\), \(y\), \(z\)). Figures 3-6 show the step responses for the corresponding outputs \([x\), \(y\), \(z\), \(\psi]\) obtained with these methods. Figures 7 and 8 show the various obtained curves for the desired sensor signals as well as the controlled responses. Table 4 gives the obtained quadrotor's responses performances: Settling time (\(T_{s}\)), maximum overshoot (_Mp_), and the errors previously mentioned (ISE, IAE, ITAE, and ITSE). CS results present a considerable overshoot in yaw angle and the errors values of ISE and IAE are around 50% of the desired altitude \(z\), which proves that ISE value weight more significantly the  
Figure 4: Quadrotor’s position \(y\) using Particle Swarm Optimization (PSO), Cuckoo Search (CS), Particle Swarm Optimization-Cuckoo Search (PSO-CS), and Reference Model (RM). Figure 5: Quadrotor’s altitude \(z\) using Particle Swarm Optimization (PSO), Cuckoo Search (CS), Particle Swarm Optimization-Cuckoo Search (PSO-CS), and Reference Model (RM). Figure 6: Quadrotor’s yaw attitude (\(\psi\)) using Particle Swarm Optimization (PSO), Cuckoo Search (CS), Particle Swarm Optimization-Cuckoo Search (PSO-CS), and Reference Model (RM). quality of solutions and more adequate to evaluate the fitness function. However, the PSO approach is suitable and results in better performances. Comparisons of PSO results to those of Genetic Algorithms presented in Reference [16] show that PSO reduces the settling time \(\mathrm{T_{s}}\) from 2.5 s to 0.172 s for yaw angle. For altitude \(z\), the value of \(\mathrm{T_{s}}\) is increased to 1.07 s instead of 0.4 s for GA. These results illustrate that PSO and GA techniques are highly competitive to explore the optimal solution in quadrotor control. In the same project of quadrotor control, the work presented in Reference [32] suggests three intelligent controllers, multilayer neural networks controller based on reference model (RMNN), Neural Networks with PD's controller behavior (CPDNN), and Fuzzy Logic to adjust PID controllers' gains (Fuzzy-PID). The proposed Fuzzy-PID and CPDNN achieves better performances compared to RMNN. Thus, comparing PSO results to those of Fuzzy-PID and CPDNN confirm that PSO is highly competitive to soft computing methods. Figure 7: Quadrotor’s roll attitude (\(\phi\)) using Particle Swarm Optimization (PSO), Cuckoo Search (CS), Particle Swarm Optimization-Cuckoo Search (PSO-CS), and Reference Model (RM). Considering the Figures 3-8 and Table 4, the controllers tuned using PSO-CS have good performances for positions and attitudes. Thus, PSO-CS results are seen concurrent to those obtained using PSO, where responses lead to fast settling times with no overshoot and reduced errors. The desired sensor signal curves in Figures 7 and 8 (desired roll and pitch angles (\(\phi_{d}\) and \(\theta_{d}\))) depend on the outputs of the controllers _PID-x_, _PID-y_, and _PID-z_. It is observed from this figure that these intelligent approaches, and especially PSO and PSO-CS, allow to follow perfectly the sensor signals for roll and pitch (\(\phi_{d}\) and \(\theta_{d}\)), and give controlled responses close to the desired curves. These programs are implemented using Matlab R2016a and performed on a computer with a processor Intel(r) Core(tm) i7-3770 CPU of 3.40 GHz and 8.0 GB of RAM. From the conducted experiments, we can get conclusions that for the same goal, the PSO algorithm spends less CPU time (10 min 45 s) than the PSO-CS algorithm (14 min 12 s) and the CS algorithm (12 min 15 s).