## 2 Introduction
### DC Motor Control  
Since the effective control of a DC motor is crucial for the performance of many robotic and automation systems, it is widely studied in the literature. In [27], a fuzzy-based predictive PID controller for controlling the speed of a DC motor is proposed. The mathematical model of a DC motor is derived using corresponding physical laws. Three stages of fuzzy controller, fuzzification, inference and defuzzification are implemented as components of the controller. The fuzzy-based PID controller is combined with the receding horizon controller and it is shown that the performance of the proposed controller is higher than that of the PID controller, fuzzy-based PID controller, and receding horizon controller implemented separately. In [28], a nonlinear PI controller for speed control of a DC motor is proposed. An exponential block placed in front of the PI controller introduces nonlinearity to the control system, improving controller performance. Salp swarm optimization algorithm [29] is used to tune the parameters of the proposed controller. Experiments are conducted on a real DC motor coupled with a real DC generator for disturbance generation and the results are reported. In [30], sliding mode control is used for the performance improvement of a DC servo motor. A closed-loop control system succeeds in achieving first-order system performance and maximum overshoot is reduced. As stated previously, for general automatic control systems, controlling DC motors under low disturbances is a well-studied problem [27; 28; 29; 30]. The challenging scenarios are mainly the ones involving difficult high-amplitude disturbances. The disturbance amplitude should be increased up to the point that the system can theoretically handle it, which may show the limits of the capabilities of the system. This approach is taken in this study, which makes it original and highly different from most of the studies in the literature. This study aims to develop a novel automatic design technique for the automatic control of dynamic systems. Given plant dynamics (parameters of the plant to be controlled), expected references to be provided by the user or a higher intelligence part of the control system and expected external disturbances of the system will be exposed; then, the design of the automatic controller process is automatically carried out by the proposed architecture. A human design engineer should only enter the required information about system and working environment, and the proposed system automatically designs the automatic controller. Proof-of-concept demonstration is performed using a DC motor plant as an example, but the proposed approach can be applied to any automatic control system. The DC motor is a popular electrical actuator used in robotic systems in particular. Its ease of control due to its simplicity makes it preferable in most industrial applications. Robot arms, mobile robots, CNC machines, 3D printers, and many other electromechanical equipment are eligible for DC motor use as actuators. It is worth noting that DC motors are generally used with gearboxes to reduce speed and increase torque. For speed and position sensors, there are many options available, but the optical encoder is among the most popular ones. In Figure 2 below is given a block diagram of a typical DC motor. As shown in Figure 2, the DC motor mainly consists of three parts: electrical, mechanical, and electromagnetic coupling. The electrical part consists of armature resistance and armature inductance. The mechanical part consists of rotor inertia and viscous friction due to bearings. In between, there is an electromagnetic coupling due to back-emf force denoted by \(\mathrm{e_{b}}\). The mathematical model of the DC motor is derived using corresponding physical laws, as shown in the equations below.