Fractional-Order Fuzzy PID Controller with Evolutionary Computation for an Effective Synchronized Gantry System

Abstract

Gantry-type dual-axis platforms can be used to move heavy loads or perform precision CNC work. Such gantry systems drive a single axis with two linear motors, and under heavy loads, a high driving force is required. This can generate a pulling force between the drive shafts in the coupling mechanism. In these situations, when a synchronization error becomes too large, mechanisms can become deformed or damaged, leading to damaged equipment, or in industrial settings, an additional power consumption. Effectively and accurately acquiring the synchronized movement of the platform is important to reduce energy consumption and optimize the system. In this study, a fractional-order fuzzy PID controller (FOFPID) using Oustaloup’s recursive filter is used to control a synchronous X–Y gantry-type platform. The optimized controller parameters are obtained by the measurement of control errors in a simulated environment. Four optimization methods are tested and compared: particle swarm optimization, invasive weed optimization, a gray wolf optimizer, and biogeography-based optimization. The systems were tested and compared in order to optimize the control parameters. Each of the four algorithms is simulated on four contour shapes: a circle, bow, heart, and star. The simulations and control scheme of the experiments are implemented using MATLAB, and the reference paths were planned using non-uniform rational B-splines (NURBS). After running the simulations to determine the optimal control parameters, each set of acquired control parameters is also tested and compared in the experiments and the results are recorded. Both the simulations and experiments show good results, and the tracking of the X–Y platform showed improved performance. Two performance indices are used to determine and validate the relative performance of the models and results.

Integrated Design and Control of a Sustainable Stormwater Treatment System

“…This work discusses the combination of a fuzzy PID controller with obtaining gains using the PSO method applied to an induction motor. Very similar cases can be seen in [31][32][33][34].…”

“…In Figure 5, you can see what is described. The profits obtained are as follows: P = 61.3731892931105, I = 2.425D = 59.298 Some works that talk about genetic processes and algorithms include [31][32][33][34]. where Equation ( 12) can be represented in frequency as follows:…”

“…In Figure 5, you can see what is described. The profits obtained are as follows: 𝑃 61.3731892931105, 𝐼 2.425 𝐷 59.298 Some works that talk about genetic processes and algorithms include [31][32][33][34]. In general, the genetic algorithm (GA) starts with several solutions randomly to generate new answers until reaching the most optimal solution after placing the weights and setting the limits ([0.1, 01, 01] and [100, 100, 100]).…”