Two-link Robot Manipulator using Fractional Order PID Controllers Optimized by Evolutionary Algorithms

Abstract

Fractional order (FO) controllers are highly considered with regard to higher performance and robustness of these controllers in FO systems. According to advantages of PID controllers such as suitable performance, low price and simplicity of design, they are widely used in industry. A FOPID controller is used for two-link robot control in this paper. Considering vast use of evolutionary algorithms and numerical optimization, coefficients of the FO controller are optimized using evolutionary algorithms in this paper. An individual FOPID controller is applied in order to control each link. Three evolutionary optimization algorithms including particle swarm optimization (PSO), genetic algorithm and estimation of distribution algorithm, are compared from optimal coefficients determination point of view. Experimental results indicate that FOPID controller is more applicable according to use of actual model for robot and suitable performance of the PSO algorithm. Key words: Evolutionary algorithms, fractional order controller, PID controller, two-link robotAlong with introduction of fractional order (FO) controllers and their higher performance and robustness on FO systems by Podlubny in 1994, FO systems and their control process are significantly considered 1 . Although PID controllers are introduced long time ago, they are widely used in industry because of their advantages such as low price, design simplicity and suitable performance 2, 3 . While three parameters of design including proportional (K p ), integral (K i ), and derivative (K d ) are available in PID controllers, two more parameters exist in FOPID controllers for adjustment. These parameters are integral fractional order and derivative fractional order 4 . In comparison with PID controllers, FOPID controllers have more flexible design that result in more precise adjustment of closed-loop system 5 . FOPID controllers are defined by FO differential equations. It is possible to tune frequency response of the control system by expanding integral and derivative terms of the PID controller to fractional order case. This characteristic result in a more robust design of control system, but it is not easily possible 6 .According to non-linearity, uncertainty, and confusion behaviors of robot arms, they are highly recommended for experimenting designs of control systems. Despite non-linear behavior of robot arm, it is demonstrable that a linear proportional derivative controller can stabilize the system using Lyapanov 7 . But, classic PD controller itself cannot control robot to reach suitable condition. Several papers and wide researches in optimizing performance of the robot manipulator show the importance of this issue. Different adaptive and robust procedures are proposed for robot control that all of them are so complicated in analysis and design [8][9][10][11] . Approaches that have been proposed for robot control are categorized in non-

A Review on Fractional-Order Modelling and Control of Robotic Manipulators

“…However, the trial and error method has often been used to achieve the controller parameters. However, in the case of a two-link planar rigid robotic manipulator, the optimally tuned fractional-order PID and two-degree of freedom fractional-order PID controllers using the cuckoo search algorithm [4], particle swarm optimization [17,19], genetic algorithm [14,46] have performed better than the conventional and two-degree of freedom PID controllers [29,45]. A similar case has also been seen in a three-link planar rigid robotic manipulator, where fractional-order PID tuned using an evaporation rate-based water cycle algorithm has achieved better performance than the PID [56].…”

Intelligent Controller for Robot Manipulator

“…Fani and Shahraki [13] suggested an individual FOPID controller is applied in order to control each link. Three evolutionary optimization algorithms included particle swarm optimization (PSO), genetic algorithm and estimation of distribution algorithm, are compared from optimal coefficients determination point of view.…”

Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform

“…Fractional modeling and control of an industrial selective compliant assembly robot arm was described in [ 13 ]. A fractional order PID controller was used for two-link robot control in [ 14 ]. A fractional order model of an inverted pendulum system based on simulated and experimental data was presented in [ 15 ].…”