A study on parameter tuning of Fractional order PI
λ
-PD
µ
controller
Huijuan Bian
1, a
,Zhidong Qi
1, b
, Liang Shan
1, c
and Boyang Leng
1,d
1
Nanjing University of Science and Technology, Nanjing 210094, china,
a
b06121004@163.com,
b
qizhidong@sina.com,
c
slshan@yahoo.com.cn,810626313@qq.com
Keywords: Fractional order system, Fractional Order PI
λ
-PD
µ
controller, Parameter.
Abstract. Aiming at a kind of special object with fractional characteristics,a new kind of fractional
order PI
λ
-PD
µ
controller is put forward in this paper,In this control system, the forward channel of
system contains a fractional order PI
λ
controller,while the feedback loop adopts PD
µ
controller.The
control structure in this fractional order system can achieve a good performance of the closed loop
control.Moreover,the impacts on system dynamic performance and static performance are compared
when the parameters in the controller are changed.The results show that when these parameters are in
the reasonable range,the system can achieve better control performance.
Introduction
PID control is a kind of control method which is the most widely used in control system. It has
been dominant in the majority of industrial control because of its easy realization,simple structure
and strong robustness.The literature
[1]
puts forward the PI-PD controller structure for the first time,
and it is used on the integer order system without considering the object is the fractional order
model.KAHA applied a PI-PD controller on the object with unstable link and integration element.
which obtained a better control result of the following performance and anti- interference
[2]
.The PID
controller and PI-PD controller whose differential and integration are integer order.,have been
studied widely.
But,with the theory of fractional calculus infiltrating into more and more research field.many
scholars began to study the fractional order control theory. It is proved to be difficult to use
traditional integer order model to describe some complex systems. With fractional characteristic,
Fractional order calculus is an extension of the integer order calculus.As a new mathematical tool,a
fractional order model of the object maybe is more accurately.In order to study fractional order
system,Oustaloup came up with CRONE controller
[3]
, Podlubony
came up with fractional order PI
λ
D
µ
controller
[4]
. Li Wang
raised QFT controller
[5]
.In fact, differential and integration order of the
fractional order controller can be any real numbers.Particularly,when λ=1,µ=1,it is integer order
controller.Therefore,it is necessary to strengthen the study of the fractional order controller for
different parameters.In this paper, firstly,,the structure of PI-PD controller is introduced.In contrast to
integer order controller
[5]
,this paper then puts forward a fractional order controller and applies it on
the fractional order object. Secondly,the impacts on the performance of the system with various
parameters including K
p
, K
i
, T
i
, T
d
, λ, µ of the fractional PI
λ
-PD
µ
controller are studied in
detail.Finally,Finally the simulation is carried out to prove the effectiveness of this fractional order
PI
λ
-PD
µ
controller.
Fractional Order Calculus
Fractional order system which in based on fractional order calculus and the theory of fractional
differential equation is the model system.Fractional order which refers to the order of calculus can be
arbitrary or fraction expanded the description of natural phenomena using integral calculus.Integer
order calculus only decided the partial feature of function.In many aspects,it is much more accurate
to describe the dynamic response of the actual system using the mathematical model of fractional
order calculus.it also can improve the design,characterization and control for dynamic system. the
continuous form of fractional calculus operator is defined as follows:
Advanced Materials Research Vols. 1049-1050 (2014) pp 977-982 Submitted: 26.08.2014
Online available since 2014/Oct/10 at www.scientific.net Accepted: 01.09.2014
© (2014) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.1049-1050.977
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,
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