Design of Fractional-Order Lag Network and Fractional-Order PI Controller for a Robotic Manipulator Petar D. Mandi´ c ∗ Paolo Lino ∗∗∗ Guido Maione ∗∗∗ Mihailo P. Lazarevi´ c ∗ Tomislav B. ˇ Sekara ∗∗ ∗ Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade, Serbia (e-mail: pmandic@mas.bg.ac.rs, mlazarevic@mas.bg.ac.rs). ∗∗ School of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade, Serbia (e-mail: tomi@etf.rs). ∗∗∗ Department of Electrical and Information Engineering, Polytechnic University of Bari, Via E. Orabona 4, Bari, Italy (e-mail: paolo.lino@poliba.it, guido.maione@poliba.it). Abstract: Motion control of robotic manipulators is frequently realized by independent control of the DC motors actuating robot joints. Namely, nonlinearities, coupling between actuators and other complex dynamics are neglected if high gear ratios between the actuators and robot joints are considered. This paper proposes a fractional-order lag network or a fractional-order PI controller to control the position of the actuators shafts. The introduced fractional compensators are designed by using the symmetrical optimum principle and by parameters optimization or by frequency-domain loop shaping, respectively. Simulation results and frequency response show effectiveness and robustness of the approach. Keywords: Fractional-order lag compensator, fractional-order PI controller, robust control, frequency response, robotic manipulators, robot control. 1. INTRODUCTION Robotics is a large inter-disciplinary field that is contin- uously growing and finding new applications. It requires knowledge of mechanical and electrical engineering, sys- tems and control theory, and new technology. Research is stimulated by different applications and by the increasing demand in better performance of robotic systems. For example, robotic manipulators are spread in industry but present many issues in motion control because their dy- namics is highly nonlinear, time-varying, and often subject to parametric uncertainty. To achieve a better compromise between performance and robustness, fractional-order con- trol can provide a strategic hand to solve complex issues. Industrial manipulators in automated factories must ex- ecute tasks with high accuracy and repeatability, and should be deployed to allow mass production and quality of products [5]. Although control is complex, manipulators can be controlled in a linear way if their dynamic model is assumed linear because of high gear ratios, gravity com- pensation devices, etc., or is linearized by feedback [26]. Then, nonlinear phenomena as well as dynamic coupling effects from the motion of other joints are neglected. In this way, the robot control problem can be decoupled into independent joint control. So, PID controllers are usually employed for the stabilization of manipulators [17]. In the last decades, application of fractional calculus to control problems has demonstrated several benefits [20; 22; 23; 25; 19]. Namely, fractional-order controllers have at disposal the fractional orders of integration and/or differentiation that can be used as additional degrees of freedom in controller design. In this way, not only performance can be increased, but especially robustness of the control loop is improved. To this aim, the seminal Bode’s idea of the ideal open-loop gain based on a non- integer order integrator is fundamental [1]. Moreover, the compact structure of the controller is based on few parameters (tuning knobs) that allow to achieve similar or better results than integer-order controllers of high order. Literature shows successful applications to robot control [24; 18; 7; 29]. For example, robust path planning in 3- D space is achieved despite UAV mass variations [18]. In details, fractional attractive forces were introduced based on velocity fractional derivative. In this paper, two types of fractional-order controllers of a robot manipulator are compared. A fractional-order lag network (FOLaN) is designed to achieve reference step re- sponse with no overshoot and iso-damping property, such that it is robust to large process gain variations. This prop- erty is very important in position control. Since FOLaN cannot reject disturbances completely, a fractional-order PI (FOPI) controller is designed with that purpose. It makes a compromise between performance and robustness, i.e. it is more sensitive to process gain variations, but disturbance is rejected with zero steady-state error. The two controllers are chosen because they are comparable and give similar results for the same design specifications, Preprints of the 21st IFAC World Congress (Virtual) Berlin, Germany, July 12-17, 2020 Copyright lies with the authors 3735