Software Implementation of Self-Tuning Controllers

Real  control  of  industrial  processes  is  almost  always  burden  with  various  perturbations, disturbances  and  changes  in  process  parameters  or  dynamics  due  to  varying  operational conditions,    plant    properties    themselves,    etc.    Furthermore,    an    acceptable    a    priori mathematical  model  does  not  have  to  be  known.  In  spite  of  it,  such  processes  have  to  be controlled.

A  possible  solution  to  this  task  represents  an  area  of  control  theory  known  as  adaptive control or more specifically usage of self-tuning controllers (Åström & Wittenmark, 1973); (Åström et al., 1977); (Clarke & Gawthrop, 1979); (Åström & Wittenmark, 1989); (Wellstead& Zarrop, 1991); (Isermann et al. 1992); (Hang et al., 1993); (Bobál et al., 1999); (Bobál et al.,2005).  Main  idea  consists  in  modification  of  control  law  according  to  the  changing  plant parameters   obtained   via   recursive   identification.   Their   advantage   is   some   kind   of “intelligent” behaviour, but on the other hand these regulators are quite complex and not easily applicable.This  chapter  deals  mainly  with  software  implementation  of  selected  digital  self-tuning control  algorithms  into  the  Matlab  and  Pascal  environment  for  the  purpose  of  possible industrial  utilization.  The  work  was  motivated  by  co-operation  with  a  manufacturer  of aluminium-based  rolled  products  and  packaging  materials.  His  project  has  supposed primarily  the  application  of  discrete-time  adaptive  compensator  to  control  of  a  metal smelting furnace. Other requirements were the plant model with “a2b3” structure and final implementation   in   Borland   Pascal   (because   of   integration   into   the   existing   system).

However the paper presents not only derived relations applicable to Pascal environment but also   program   for   simulative   purposes   and   testing   created   under   Matlab   and   some preliminary  simulation  results.  In  the  first  stage,  the  applied  methods  have  included  a polynomial    approach    to    discrete-time    control    design    and    recursive    least-squares identification  algorithm  LDDIF,  but  subsequently  also  two  alternative  techniques,  namely control using continuous-time regulator with fixed parameters and use of delta approach in self-tuning  control,  have  been  verified.  Although  all  the  tasks  were  motivated  by  our specific  problem,  the  whole  chapter  tries  to  present  them  in  more  or  less  generally applicable way. The chapter is organized as follows. In Section 2, basic theoretical background of digital self- tuning  controllers  using  polynomial  synthesis  and  applicable  relations  are  provided.  The Section  3  then  contains  the  fundamentals  of  related  recursive  identification  algorithm LDDIF.   Next,   the   Section   4   describes   the   preliminary   software   implementation   and demonstrates  its  facilities  on  an  application-oriented  example.  Furthermore,  design  and utilization  of  fixed  continuous-time  controller  along  with  self-tuning  control  using  delta models as two various alternative approaches are presented in an extensive Section 5. And finally, Section 6 offers some conclusion remarks.The preliminary version of this work has een presented at conferences (Matušů & Prokop,2009), (Matušů et al., 2009).

Discrete-time polynomial synthesis

In  the  first  instance  the  digital  self  tuning  controllers  were  intended  to  be  implemented. Their  very  basic  principle  consists  in  consecutive  identification  of  the  controlled  process using  a  recursive  algorithm  (see  the  following  Section)  and  application  of  obtained  plant parameters  in  computing  the  control  law.  The  control  design  itself  has  been  based  on algebraic  approach  and  pole  placement  (Kučera,  1979);  (Kučera,  1993);  (Wellstead  et  al.,1979); (Åström & Wittenmark, 1980).Despite  the  existence  of  more  complex  control  configurations,  just  the  very  basic  single- input single-output (SISO) control loop with one degree of freedom has been assumed. This classical feedback connection in a discrete-time sense is shown in Fig. 1.


This chapter has been focused mainly on preliminary software implementation of digital self- tuning controllers into the Matlab (for simulative and testing purposes) and Pascal (for real application)  environment.  The  motivation  to  this  task  as  well  as  basic  conditions  and restrictions have been based on technical assignment of a manufacturer of aluminium-based products  related  to  control  of  a  metal  smelting  furnace.  In the  first  instance,  the  applied techniques  have  comprised  a  polynomial  approach  to  discrete-time  control  design  and recursive  least-squares  identification  algorithm  LDDIF.  On  top  of  that,  continuous-time controller with fixed parameters and delta approach in self-tuning control have been utilized. The future work should eventually lead to complete real-time industrial application.

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