Practical Tuning of Fractional Order Proportional and Integral Controller (I): Tuning Rule Development

2007 ◽  
Author(s):  
Tripti Bhaskaran ◽  
YangQuan Chen ◽  
Dingyu Xue
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
Companion Paper ◽  
First Order ◽  
Tuning Method ◽  
Peak Sensitivity ◽  
Integral Controller ◽  
Gain Optimization ◽  
Practical Nature ◽  
Tuning Rules

This paper presents a new practical tuning method for fractional order proportional and integral controller (FO-PI). The plant to be controlled is mainly FOPDT (first order plus delay time). The tuning is optimum in the sense that the load disturbance rejection is optimized yet with a constraint on the maximum or peak sensitivity. We generalized MIGO (Ms constrained integral gain optimization) based controller tuning method to handle the FO-PI case, called F-MIGO, given the fractional order α. The F-MIGO method is then used to develop tuning rules for the FOPDT class of dynamic systems. The final developed tuning rules only applies the relative dead time, τ of the FOPDT model to determine the best fractional order α and at the same time to determine the best FO-PI gains. Extensive simulation results are included to illustrate the simple yet practical nature of the developed new tuning rules. In Part (II) of this companion paper, interesting experimental results in two experimental platforms are reported using the tuning rule of this paper. The tuning rule development procedure for FO-PI is not only valid for FOPDT but also applicable for other general class of plants as illustrated.

Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
YangQuan Chen ◽  
Tripti Bhaskaran ◽  
Dingyü Xue
Keyword(s):  
Fractional Order ◽  
Dynamic Systems ◽  
Disturbance Rejection ◽  
Dead Time ◽  
Pi Controller ◽  
First Order ◽  
Tuning Method ◽  
Peak Sensitivity ◽  
Practical Nature ◽  
Tuning Rules

This paper presents a new practical tuning method for fractional order proportional and integral (FO-PI) controller. The plant to be controlled is mainly first order plus delay time (FOPDT). The tuning is optimum in the sense that the load disturbance rejection is optimized yet with a constraint on the maximum or peak sensitivity. We generalized Ms constrained integral (MIGO) based controller tuning method to handle the FO-PI case, called F-MIGO, given the fractional order α. The F-MIGO method is then used to develop tuning rules for the FOPDT class of dynamic systems. The final developed tuning rules only apply the relative dead time τ of the FOPDT model to determine the best fractional order α and at the same time to determine the best FO-PI gains. Extensive simulation results are included to illustrate the simple yet practical nature of the developed new tuning rules. The tuning rule development procedure for FO-PI is not only valid for FOPDT but also applicable for other general class of plants.

Tuning Fractional Order Proportional Integral Controllers for Time Delayed Systems With a Fractional Pole

2011 ◽  
Author(s):  
Hadi Malek ◽  
Ying Luo ◽  
YangQuan Chen
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Model Systems ◽  
Delay Model ◽  
Delayed Systems ◽  
First Order ◽  
Tuning Method ◽  
Starting Point ◽  
Reaction Curve ◽  
Pi Controllers

First order plus time delay model is widely used to model systems with S-shaped reaction curve. Its generalized form is the use of a single fractional pole to replace the first order (single-time constant) model, which is believed to better characterize the reaction curve. Using time delayed system model with a fractional pole as the starting point, in this paper, designing fractional order controllers for this class of fractional order systems is investigated. The novelty of this paper is on designing the integer order PID and fractional order PI and [PI] controllers for these class of systems. The simulation and lab experimental results are both included to illustrate the effectiveness of the proposed tuning method. By comparing the results of PID controller, fractional order PI and [PI] controllers, the advantages of the fractional order controller are clearly demonstrated in the case of controlling the single fractional pole plants with constant time delay.

Practical Tuning of Fractional Order Proportional and Integral Controller (II): Experiments

2007 ◽  
Author(s):  
Tripti Bhaskaran ◽  
YangQuan Chen ◽  
Gary Bohannan
Keyword(s):  
Heat Flow ◽  
Fractional Order ◽  
Experimental Results ◽  
The Novel ◽  
Flexible Joint ◽  
Flow Experiment ◽  
Integral Controller ◽  
Tuning Rules

This paper aims to apply the practical tuning procedure for fractional order proportional and integral controller (FO-PI) to two experimental platforms. The first platform is Quanser’s Heat Flow Experiment (HFE) and the second platform is the Quanser’s Rotary Flexible Joint (RFJ) Module. The fractional controllers in both cases have been digitally implemented using Oustaloup’s recursive approximation. The second system however can also be controlled with the Fractroller which uses the novel element Fractor. Practical issues are introduced and discussed and interesting experimental results are reported that could serve as sample applications of the proposed FO-PI tuning rules.

scholarly journals A comparative study of fractional order PIλ/PIλDµ tuning rules for stable first order plus time delay processes

2016 ◽  
Vol 2 ◽  
pp. S136-S152 ◽  
Author(s):  
R. Ranganayakulu ◽  
G. Uday Bhaskar Babu ◽  
A. Seshagiri Rao ◽  
Dipesh Shikchand Patle
Keyword(s):  
Time Delay ◽  
Comparative Study ◽  
Fractional Order ◽  
First Order ◽  
Tuning Rules

The magnitude optimum tuning of the PID controller: Improving load disturbance rejection by extending the controller

2017 ◽  
Vol 40 (5) ◽  
pp. 1669-1680 ◽  
Author(s):  
Jan Cvejn ◽  
Damir Vrančić
Keyword(s):  
Disturbance Rejection ◽  
Pid Controller ◽  
Stability Margin ◽  
Pid Controllers ◽  
First Order ◽  
Fast Tracking ◽  
Tuning Method ◽  
Exogenous Disturbance ◽  
Process Output ◽  
The Stability

The Magnitude Optimum (MO) tuning method for PID controllers, applied on stable and non-oscillating plants, usually gives fast tracking responses and offers very good process output disturbance-rejection performance, even if the process contains significant dead time. On the other hand, when an exogenous disturbance affects the process indirectly, for example, via the plant input, slow disturbance rejection responses may be obtained. The paper proposes a way of removing this problem by means of adding two first-order filters into the control loop, without modifying the controller parameters. The filter parameters are determined so that the disturbance lag is partially compensated and the stability margin properties of the MO tuning are preserved.

scholarly journals Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization—A Guide for Parameters Computation Based on Robustness

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 517
Author(s):  
Blanca Viviana Martínez ◽  
Javier Sanchis ◽  
Sergio García-Nieto ◽  
Miguel Martínez
Keyword(s):  
Multiobjective Optimization ◽  
Disturbance Rejection ◽  
Optimization Design ◽  
Order System ◽  
First Order ◽  
Active Disturbance Rejection ◽  
Disturbance Response ◽  
Tuning Methods ◽  
Different Levels ◽  
Tuning Rules

A set of tuning rules for Linear Active Disturbance Rejection Controller (LADRC) with three different levels of compromise between disturbance rejection and robustness is presented. The tuning rules are the result of a Multiobjective Optimization Design (MOOD) procedure followed by curve fitting and are intended as a tool for designers who seek to implement LADRC by considering the load disturbance response of processes whose behavior is approximated by a general first-order system with delay. The validation of the proposed tuning rules is done through illustrative examples and the control of a nonlinear thermal process. Compared to classical PID (Proportional-Integral-Derivative) and other LADRC tuning methods, the derived functions offer an improvement in either disturbance rejection, robustness or both design objectives.

Kinetics and Mechanism of Hexachloroiridate(IV) Oxidation of Arsenic(III) in Acidic Perchlorate Solutions

1992 ◽  
Vol 57 (7) ◽  
pp. 1451-1458 ◽  
Author(s):  
Refat M. Hassan
Keyword(s):  
Ionic Strength ◽  
Fractional Order ◽  
Activation Parameters ◽  
Order Reaction ◽  
First Order Reaction ◽  
Intermediate Complex ◽  
Constant Ionic Strength ◽  
Kinetics Of Oxidation ◽  
First Order ◽  
Kinetics Of

The kinetics of oxidation of arsenic(III) by hexachloroiridate(IV) at lower acid concentrations and at constant ionic strength of 1.0 mol dm-3 have been investigated spectrophotometrically. A first-order reaction in [IrCl62-] and fractional order with respect to arsenic(III) have been observed. A kinetic evidence for the formation of an intermediate complex between the hydrolyzed arsenic(III) species and the oxidant was presented. The results showed that decreasing the [H+] is accompanied by an appreciable acceleration of the rate of oxidation. The activation parameters have been evaluated and a mechanism consistent with the kinetic results was suggested.

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