Design and implementation of an optimal quadratic controller with minimum order observer

This paper addresses a critical need in the literature for research focused on the real-world implementation of combined optimal control strategies and minimum order observers. Despite the recognized advantages of these methods, there is a notable absence of studies that apply both techniques in tandem to naturally unstable and nonlinear systems. To address this research gap, this paper presents a detailed exploration of control systems, focusing on the design and implementation of an optimal control strategy based on the Linear Quadratic Regulator method, coupled with a minimum order observer. The methodology is systematically outlined, providing a versatile blueprint that can be utilized for a variety of high order systems. This paper also highlights the common challenge of reconciling theoretical results with real-world implementation, thereby emphasizing the complexity of transitioning control strategies from theory to practice. While the actual system's behavior exhibits some deviations from the simulation due to inherent non-linearities, the established objectives were still successfully met, demonstrating satisfactory results. This highlights the practical applicability of the control design, despite the inherent complexities of real-world systems. This paper concludes by suggesting further exploration of optimal controllers and state observers in different types of systems, thus contributing to fill the gap within the literature underlining the use of these strategies in real-world systems.