Complex Order PIa+jbDc+jd Controller Design for a Fractional Order DC Motor System

Abstract

Fractional order controller DC motor Complex order controller Bode diagram Root locus Industry 4.0 implementation stipulates effective actuator control. In the present work, a complex order PI a+ jb D c+ jd (COPID) controller was designed for a fractional order model of a direct current (DC) motor system. For comparisons, the DC motor system model was also controlled using the conventional proportional integral (PI), proportional integral derivative (PID), proportional resonant (PR) and fractional order PID controllers (FOPID). Time domain results indicated that the PR controller performed exceedingly well for output signal responses, but fared poorly in case of control signal specifications. The PI controller responses suffered from high time domain characteristics for both control and output signals. The PID controller performed moderately in terms of time domain and peak overshoot metrics. The FOPID controller attained the best time domain characteristics, but was unable to effectively limit the control and output signal peak overshoots. It was only the COPID controller, that successfully minimised / eliminated peak overshoots in control and output signals (0.1 % and 0.0 % respectively). Moreover, the COPID controller was also successful in limiting the rise, peak and settling times. In addition, Bode diagram, root locus plot were obtained and system gain parameters were varied to confirm the robustness of the proposed COPID controller. Thus, COPID controller promises to be an effective solution towards accurate and robust actuator control in modern manufacturing.

Complex-order PID controller design for enhanced blood-glucose regulation in Type-I diabetes patients

“…30 As discussed earlier, the CO-PID control procedure has been proposed in the available literature for DC motor’s speed control, inverted pendulum’s balancing control, and surface roughness control in machining applications. 21,22,31 However, the dynamics of the glucose-insulin interactions in human body are quite different than that of the aforementioned electro-mechanical systems. The CO-PID controller, formulated in this section, introduces additional controller parameters that increases the controller’s degrees of freedom and improves its design flexibility, which enables it to effectively track the reference under exogenous disturbances.…”

“…20 The studies have shown that the assignment of complex orders to the aforementioned operators increases the controller’s degrees of freedom, which enhances its resilience against parametric uncertainties especially when the gain and phase characteristics are notable. 21 The complex-order controllers are extensively used to solve practical control engineering problems owing to their aforementioned attributes. 22…”

“…20 The studies have shown that the assignment of complex orders to the aforementioned operators increases the controller's degrees of freedom, which enhances its resilience against parametric uncertainties especially when the gain and phase characteristics are notable. 21 The complex-order controllers are extensively used to solve practical control engineering problems owing to their aforementioned attributes. 22 The main contribution of this article is the systematic formulation and verification of the Complex-Order PID (CO-PID) controller for the normalization and robust regulation of BG levels in TID patients.…”

Robotics in Industry 4.0: A Bibliometric Analysis (2011-2022)

“…Extensive investigations have been carried out to incorporate automated architectures in diverse fields such as bolted joints [1], lean manufacturing [2], bio-fuelled engines [3], flexible robotic arms [4], Covid therapy robots [5], industrial DC motors [6], machining of exotic materials [7]- [18], ball nose end milling [19] and many more [20]- [34]. Many of these investigations included applications of various heuristic algorithms to attain optimal solutions to the automation/control problems [35]- [46]. The following subsections give details of some of the latest literature reviews and bibliometric research investigations in this field.…”

Stability and Dynamics of Complex Order Fractional Difference Equations

“…Time domain, frequency domain and stability analysis of linear systems represented by differential equations with complex order derivative has been carried out [9]. It has found applications such as the design of controller for fractionalorder DC motor system [10], in PID controller and low-pass filter [11]. Such systems have been found to have large stability regions for certain parameters.…”