# Fuzzy Model Predictive Control for Unmanned Helicopter
## 4 System Validation  
In order to evaluate the efficiency of the presented control systems, several test cases were prepared. The rest of the paper aims to demonstrate that the implementation of the Parallel Distributed Compensation approach can lead to achieving more satisfying results than using a single linear MPC controller. The testing platform was built using the FLIGHTLAB software to precisely simulate the dynamics of the ARCHER rotorcraft and the MATLAB/SIMULINK platform to implement the proposed control system. The communication between the two processes is achieved using the TCP internet protocol, where data calculated by FLIGHTLAB and SIMULINK is transferred in predefined buffers. The integration of these two platforms enables conducting detailed simulation tests of the designed control system performance. A scheme describing platform integration is presented in Figure 4.  
During the simulation experiment, the response of the controlled system was computed using a fixed-step fourth-order Runge-Kutta method. The integration step size of the helicopter dynamics model in the FLIGHTLAB environment was set to \(8.333\times 10^{-4}\) s. The sampling frequency of the control signal generated by the automatic flight control system was 50 Hz. No wind effects or any other atmospheric disturbances were considered in any of the test scenarios. The simulation scenarios, comparing two different approaches, are divided as follows:  
* Case 1: The helicopter maintains its initial altitude while changing its forward flight velocity, respectively, by 2, 6, and 10 \(\frac{\mathrm{m}}{\mathrm{s}}\). The total simulation time was 12 s.
* Case 2: The helicopter follows a predefined flight path that includes
* A step change in forward flight velocity \(V_{x}\) at the first second to 6 \(\frac{\mathrm{m}}{\mathrm{s}}\). * At the 5 th second, following the predefined position on the Y-axis of the reference coordinate system while maintaining a forward flight velocity pf \(V_{x}=6\ \frac{\mathrm{m}}{\mathrm{s}}\) and initial altitude of \(Z=-3.43\ \mathrm{m}\). The function describing the predefined trajectory on the Y-axis is presented below (32). This corresponds to the sinusoidal change of position on the Y-axis, where the amplitude is 8.9 m and the oscillation period \(T=9\ \mathrm{s}\). Figure 4: SIMULINK and FLIGHTLAB integration scheme [36]. After 18 s of performing a slalom flight, the rotorcraft returns to forward flight in the initial direction. \[Y^{ref}(t)=8.9\sin(\frac{2\pi}{9}t-\frac{\pi}{9})\ \ [\mathrm{m}] \tag{32}\]  
The total simulation time was 30 s.  
The resulting function, described by Equation (32), was determined in order to check the helicopter's performance for a slalom maneuver defined in the ADS-33-PRF Design Standard Performance Specification, where handling qualities for military rotorcraft are defined [37]. Since ADS-33-PRF refers to large-helicopter dynamics, reference trajectories for testing aerial vehicle performance described in this specification are improper for testing the agility of small unmanned rotorcraft. In order to preserve dynamic similitude for ARCHER's performance testing, the slalom trajectory defined in ADS-33-PRF was scaled in order to keep the same Froude number [38]. The formula for this similitude number is presented below in (33), and for its physical interpretation, it is the ratio between inertia forces and gravitational forces in the airflow. It is assumed that the required distances traveled by the helicopters are scaled by the characteristic linear dimension of the rotorcraft, which in this case are the diameters of the main rotors. \[Fr=\frac{V}{\sqrt{gL}} \tag{33}\]  
where  
* \(V\) is the airflow velocity \([\frac{\mathrm{m}}{\mathrm{s}}]\). * \(g\) is the gravitational acceleration \([\frac{\mathrm{m}}{\mathrm{s}^{2}}]\). * \(L\) is the reference linear dimension \([\mathrm{m}]\).