Retrofitting Fractional-Order Dynamics to an Existing Feedback Control System: From Classical Proportional-Integral (PI) Control to Fractional-Order Proportional-Derivative (FOPD) Control

Abstract

This paper presents a method of retrofitting an external controller into an existing feedback control system governed by a classical proportional-integral (PI) controller to improve the overall dynamics of the entire control system by benefitting from the advantages of fractional-order dynamics in the form of a fractional-order proportional derivative (FOPD) controller. The retrofitting activity requires having access to the input and output signals of the existing control system ideally configured as a unity-feedback system. The difference between the input and output signals is then used as the input to an external controller having a fractional-order element. The design of the external controller is derived from the original values of the PI controller in the existing control system and the parameters of the desired FOPD controller to be used. A numerical example is presented in this paper to demonstrate how straightforward the process is. Discussion on some issues related to its hardware design and implementation is also presented in this paper.

Full text

Retrong Fraconal-Order Dynamics to an Exisng Feedback Control
System: From Classical Proporonal-Integral (PI) Control to Fraconal-Order
Proporonal-Derivave (FOPD) Control
Emmanuel A. Gonzaleza; AlekseiTepljakovb, Concepción A. Monjec, and Ivo Petrášd
Schindler Elevator Corporaona, Department of Computer Systems, Tallinn University of Technology, Tallinn, Estoniab,
Systems Engineering and Automaon Department, Universidad Carlos III de Madrid, Madrid, Spainc, Instute of Control and
Informazaon of Producon Processes, Faculty BERG, Technical University of Košice, Košice, Slovakia d
Corresponding Author Email: emm.gonzalez@delasalle.ph
ABSTRACT

-   
 - -
-
  -
 -

  


Keywords: control theory, control system analysis, fraconal calculus, operaonal ampliers, robust control
1. INTRODUCTION
-   

       
      
    
 -     
     

-
    
   
       
-
     
      
         

    -  
--
     -


      

       
-      
 -    
 - - 


    
    
 -    

       
   --- -
        



        


      
      

     

(1)
International Research Journal on Innovations in Engineering, Science and Technology

IRJIESTRetrong Fraconal-Order Dynamics...
     
     
        
         

      
      
     


       
        
   -  

and



         

       

 
   
         



        
 -     
       





       
     



 


     

   
       
     
     


  

-
     - 
         
        
        
   
     
    -  
-
    
      
       


        

Retrong Process and Architecture
      
       
  

  
        
of

Step 1: 


     
  -   




 
      
       
  
 
 

  

Figure 1. Architecture of an exisng closed-loop system retroed
with an external controller

by acquiring the dierence
between the input and output signals as the input to

Figure 2. Equivalent block diagram of Figure 1 where the
new controller

dened as a funcon of the
external controller

and the exisng classical
controller

(2)
International Research Journal on Innovations in Engineering, Science and Technology

IRJIESTRetrong Fraconal-Order Dynamics...
(3)
(4)
(5)
(6)
(7)
(8)
Step 2:      

      



Step 3:     
       
      
        
   
 
    
        

     
        

 
       
 
        

Proposion: 


 
       

  α  
        
  

   



Proof: -
       
       

   -   
-
A Numerical Example
      
   -    
   - 
  


 
-





        
     
   ω
  
   
  ϕ
  
°,    
       
      
      

-

-


(9)
(10)
(11)
International Research Journal on Innovations in Engineering, Science and Technology

IRJIESTRetrong Fraconal-Order Dynamics...
 
 
   

        
         
       
      
        

Hardware Implementaon of CR (s)
     

-       
        
    
-

CR (s)      

      -

-      
    

       
-
       
      
      
         
-      
-   -   
       

       

    
       
    


  -    
         
      


 -      
  -   
      
        
         
-
       

 



CONCLUSIONS
    
      
   -  
    

        
 


     
       
    
    

        
     

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International Research Journal on Innovations in Engineering, Science and Technology

IRJIESTRetrong Fraconal-Order Dynamics...
5. RECOMMENDATION
          
        

     
       
      


Acknowledgements


        
      
     
--  ---   
      
      
     
       
    
  --    
---
REFERENCES
 
  -   
    Control
Engineering Pracce-
    Design Methods of Fraconal order
Controllers for Industrial Applicaons
    

 
     
IFAC Workshop on Digital Control. Past,
Present and Future of PID Control 
-
   -   λμ
 IEEE Transacons on Automac
Control-
 
  Fraconal Order Systems and Control:
Fundamentals and Applicaons 
    -

         
-  American Control Conference
2009-
 
    
16th Internaonal Carpathian Control
Conference (ICCC)-
 
-  The AUN/SEED-Net Fieldwise
Seminar on Control Engineering  
--
         
      
-    
Internaonal Journal of Pure and
Applied Mathemacs,      
-
 
      
     
   14th Internaonal
Carpathian Control Conference (ICCC)  
-
         
     
   -  
  13th Internaonal Conference on
Control Automaon Robocs & Vision (ICARCV)
--
        
   
-
    ISA Transacons  
-
          
    
     IEEE
Transacons on Control Systems Technology 
-
        
    
 2008 Chinese Control and Decision
Conference-
      -
    
  
2009 American Control Conference
-
 
     
-   Entropy
       
-
International Research Journal on Innovations in Engineering, Science and Technology


    - 
 μ   


--
   μ  
Journal of Computaonal Innovaons and
Engineering Applicaons-

  - - 
-   μ 
 2015 Internaonal Conference on
Humanoid, Nanotechnolo gy, Informaon
Technology, Communicaon and Control,
Environment and Management (HNICEM)  
-
  
       
 -  
  Fraconal Calculus and
Applied Analysis-
IRJIESTRetrong Fraconal-Order Dynamics...
International Research Journal on Innovations in Engineering, Science and Technology