International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 09 | Sep 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 609 Analysis of Fractional PID Controller Parameters on Time Domain Specifications using Nelder-Mead Algorithm & Interior Point Algorithm D. Shanmukha Chandra Kumar 1 , B.T.Krishna 2 1 Student, Dept. of ECE, UCEK, JNTU Kakinada, AP, India 2 Professor, Dept. of ECE, UCEK, JNTU Kakinada, AP, India ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - Fractional PID controller is an extension of classical order PID controller having five parameters rather than three guidelines for the effect of classical PID controller parameters on the time domain analysis are available but for fractional order PID controller there is no guidelines available particularly for the order of integration and order of differentiation. To assist fine tuning ,the effect of the order of differentiation and integration parameters on the time domain specification on various order plants are investigated using nelder mead algorithm and interior point algorithm. The relation between parameters (integration and differentiation) and time domain parameters (rise time, peak time, overshoot, settling time) are observed using nelder mead algorithm and interior point algorithm. The design and simulation is done by using MATLAB and fractional order modeling and control tool box. In general classical PID controller is a kind of feedback control loop mechanism that is widely used in control systems. PID has good stability, In order to improve its stability in control systems several attempts to enhance the classical PID controller, one of them is Fractional order PID controller. Key Words: fractional order PID controller, fractional order calculus, effect of parameters 1. INTRODUCTION In general for classical PID controller guidelines are available for the effect of classical controller parameters on the time domain specifications. However, no guidelines are available for fractional PID controllers, particularly for the order of differentiation (µ) and integration (λ). To assist with fine tuning, the effect of the order of differentiation and integration parameters on the time domain specifications for various plants are investigated. Fractional calculus provides an excellent instrument for the description of memory and hereditary properties of various materials and processes. This is the primary advantage of fractional derivatives in comparison to classical integer order models, where such dynamics not taken into account. The advantages of fractional derivatives become more appealing in the modeling of mechanical, electrical and electro-mechanical properties of real materials, as well as in the description of rheological properties of rocks, and in many other fields. Recent times have wide application of field fractional integrals and derivatives also in the theory of control of dynamical systems, where the controlled system or/and the controller is described by a set of fractional differential equations 2. FRACTIONAL PID CONTROLLER A. FRACTIONAL CALCULUS: The mathematical modeling and simulation of systems and processes, based on the description of their properties in terms of fractional derivatives, naturally leads to differential equations of fractional order the necessity to solve such equations to obtain the response for a particular input. Thought in existence for more than 300 years, the idea of fractional derivatives and integrals has remained quite a strange topic, very hard to explain, due to absence of a specific tool for the solution of fractional order differential equations. Fractional order calculus has gained acceptance in last couple of decades. J.Liouville made the first major study of fractional calculus in 1832. In 1867, A.K.Grunwald worked on the fractional operations. G. F. B. Riemann developed the theory of fractional integration in 1892. Fractional order mathematical phenomena allow us to describe and model a real object more accurately than the classical “integer” methods. Earlier due to lack of available methods, a fractional order system was used to be approximated as an integer order model. But at the present time, there are many available numerical techniques which are used to approximate the fractional order derivatives and integrals. In fractional calculus, the differentiation integration operator, is defined as follows Here α >0 it becomes differentiation if α<0 it becomes integration. B. DEFINITIONS: (Caputo’sdefinition of Fractional Order differentiation). Caputo’s definition is given by