IAES International Journal of Robotics and Automation (IJRA) Vol. 11, No. 3, September 2022, pp. 205~212 ISSN: 2722-2586, DOI: 10.11591/ijra.v11i3.pp205-212  205 Journal homepage: http://ijra.iaescore.com Implementation of a complex fractional order proportional- integral-derivative controller for a first order plus dead time system Omar Waleed Abdulwahhab Department of Computer Engineering, University of Baghdad, Baghdad, Iraq Article Info ABSTRACT Article history: Received Feb 11, 2021 Revised Feb 21, 2022 Accepted Mar 3, 2022 This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabilize the system in case 2, the implemented CPID controller stabilizes the system in both cases and achieves better transient response specifications. Keywords: Complex proportional-integral- derivative controller CRONE approximation Linear CRONE approximation Linear phase Real proportional integral derivative controller This is an open access article under the CC BY-SA license. Corresponding Author: Omar Waleed Abdulwahhab Department of Computer Engineering, University of Baghdad Baghdad, Iraq Email: omar.waleed@coeng.uobaghdad.edu.iq 1. INTRODUCTION Fractional calculus is an extension to ordinary calculus by extending the orders of differentiation and integration to noninteger numbers. This mathematical concept was utilized in system modelling and control. In control, several fractional controllers were designed for several types of systems [1], [2]. As a further extension, complex fractional calculus was introduced as an extension to the real fractional calculus, where the orders of differentiation and integration can be complex numbers [3]. In [4], definitions and theorems were presented for complex fractional calculus mathematically. Complex fractional calculus was utilized to introduce models that describe viscoelastic materials [5], to model drug resistance in human immunodeficiency virus (HIV) infection [6], [7], and to present a new mathematical model for the atrial fibrillation [8]. Cois et al. [9] proposed a tool to model and study state-space with complex order. A complex fractional calculus was also applied to solve certain mathematical problems, such as fractional boundary problems [10]. In control theory and applications, fractional calculus has been well utilized to design fractional order controllers. Since the conventional proportional integral derivative (PID) controller dominates other controllers [11], [12], the most common fractional order controller is the fractional order PID controller (also called PI λ D μ controller), proposed by I. Podlubny [13], [14]. It is a generalization of the conventional PID controller, where the integer order derivative and integral actions are replaced by fractional order derivative and integral actions. Some of the recent works that utilize the PI λ D μ controller are presented in [15]–[17].