This paper explores optimizing Integral-Retarded (IR) controller strategies for first-order linear time-delayed processes. By employing a model for DC motor dynamics, we incorporate a design approach that considers an unintentional delay within the control loop. The IR controller is optimized using meta-heuristic algorithms, specifically genetic algorithms. The optimization framework integrates multi-objective cost functions, balancing system response speed and control efforts. Experimental verification is carried out on a physical test setup, where the controller’s efficacy is validated against a square wave reference signal. The outcomes demonstrate that the IR controller, optimized for maximum exponential decay and control efficiency, significantly enhances the motor’s velocity tracking and response smoothness.

This note introduces a geometric approach to devising a modified variant of the conventional Proportional Integral (PI) controller, termed "Proportional Delayed Integral" (PδI). By including an artificial delay in the integral term, we demonstrate that the proposed scheme improves the decay rate attained by the classical PI controller. The analysis involves evaluating the spectral abscissa and employing a geometrical method in both (kp, ki)-plane and (h, ki)-plane. Several numerical examples illustrate the effectiveness of our proposal.

This paper presents a new control scheme, named the Proportional Delayed Integral (PδI) controller, for achieving tracking tasks on a tilt-rotor quadrotor. The proposed approach integrates a nonlinear disturbance observer, which effectively mitigates adverse effects stemming from parametric inaccuracies or unknown forces. By enhancing the traditional quadrotor with a tilting mechanism, the operational range is extended, enabling interaction with the surroundings via a robotic arm with one degree of freedom. To ensure precision and adaptability during operations, a comprehensive mathematical model has been meticulously developed, accurately reflecting the unique capabilities of the drone. The synergistic combination of the PδI controller with the nonlinear disturbance observer empowers the tilt-rotor quadrotor to tackle complex tasks with efficiency and reliability. Through rigorous numerical simulations demonstrating the effectiveness of this design, this study lays the foundation for a new era of highly functional and versatile drones, poised to revolutionize various industries and applications.

This paper presents a geometric approach to designing a modified version of the classical PI control called Proportional Delayed Integral (PδI) to obtain the fastest regulation in a type of second-order linear system. Specifically, we first show that by adding an appropriate time delay in the integral component of the PI control, the system achieves a faster response to what can be obtained by using a classical PI control. Then, we outline the conditions under which our delay-based control stabilizes a specific class of second-order systems through an analysis of the spectral abscissa and a graphical approach called D-decomposition. Furthermore, we apply our results to determine the parameters of the fastest regulator.