## 6 Discussion and Conclusions  
This section explores the interpretation and implications of the obtained results. Regarding the optimization aspect, Figure 7 shows that PSO exhibited a very fast convergence rate (majorly within 16 iterations, and completely within 59 iteration). The application of optimization to the controller design helped in improving the control system, through minimizing the response error (as shown in Figures 8, 11, 14 and 17) and the applied torque needed for the system (as shown in Figures 10, 13, 16 and 19). In relation to the robustness attribute, the developed hybrid H\({}_{\infty}\)/SMC control system was able to stabilize the nominal, perturbed by parameter variation, perturbed by external disturbance, and perturbed by measurement-noise system. In all cases, the system responded in the same manner (except for very small differences, as shown in Figures 14 and 17). Concerning performance characteristics, it has been shown in Figure 20 that, in all cases and among all the angles, the error was below 0.152 deg and the average error was 0.053 deg, which is an indication of the system's accuracy. The overshoot in all cases is almost unaffected by the type of uncertainty, as shown in Figure 21. For the first, second, and third angle, the overshoot ranged from 6.035 to 6.472 deg, 9.263 to 10.072 deg, and 11.052 to 11.561 deg, respectively. The least overshoots were in the nominal system case, while the highest were in the perturbed-by-parameter-variation case. Figures 9, 12, 15 and 18 show that the phase plane trajectories of the angular positions and velocities are driven successfully by the developed controller, from the initial condition to a very small neighborhood of the origin, in all cases. Figures 15 and 18 show small fluctuations in the late stage of the trajectory, which come from forcing the states by the controller to reach the origin, in spite of disturbance and noise. From the system's efficiency point of view, the required steady controller effort in all cases ranged from 0.13 to 0.621 N.m in amplitude, owing to the inclusion of the torque in the objective function of optimization. A higher torque was required only at start-up; the average start-up torque for the first actuator is 1.663 N.m and it is 2.158 N.m for the second actuator. This contributes to a more efficient control system. The small chattering caused by the sign function in Equation (47), which is necessary for driving the states, can be attenuated to obtain a smoother control signal, through using boundary-layer or neural networks. As compared to the H\({}_{2}\) control system, the proposed hybrid H\({}_{\infty}\)/SMC system produces fewer overshoots and fewer start-up torques, and smooth states driving in general. The robustness is provided in both control systems with small disparities, as illustrated in the results. So, instead of having unnecessary conservativeness in the system, which degrades the performance with respect to providing robustness against uncertainties, the application of metaheuristic optimization to the controller design for such an under-actuated nonlinear MIMO system is beneficial in enhancing both performance and efficiency of the control system, besides its robustness. Another point to be made is that for this specific electro-mechanical control system-design optimization problem, a swarm size of 10 was suitable, as has been presented in the results. A larger swarm size has to be considered in other optimal designs of engineering problems, especially if more parameters are required to be tuned in the application. Also, the adaptation of the cost function can be considered in future, to further enhance the optimization of the design problem, as proposed and described in [43].