Thesis (MScEng)--University of Stellenbosch, 2000.ENGLISH ABSTRACT: A unified method is proposed to treat saturation in both Multi-Input-Multi-Output MIMO
and Single-Input-Single-Output controllers. This method offers superior performance over
existing MIM 0 anti-saturation schemes.
The anti-saturation problem is posed as a linear programming problem. A practical and
efficient implementation of the algorithm is developed by transforming the problem into its
dual linear programming form. The problem, in dual form, is then solved using the dual
simplex method rather than the primal simplex method. The nature of the problem when
expressed in dual form and the properties of the dual simplex method are harmonised to
guarantee an initial basic feasible solution and an optimal bounded final solution in a finite,
predictable and minimal number of iterations.
The resultant controller never saturates, hence cannot windup. Furthermore the resultant
controller always applies the optimal control effort to the plant to minimise the error signal
input as follows:
• The controller is governed such that while the future free response combined with the
present forced response of the controller results in no saturation limits being exceeded,
now or at some time in the future, the normal linear response of the controller prevails.
• When the future free response combined with the present forced response of the controller
will result in a saturation limit being reached, now or at some time in the future,
the present time input signal into the controller is optimally governed to prevent the
saturation limit from being exceeded at any future time.AFRIKAANSE OPSOMMING: 'n Metode word voorgestel waarmee versadiging in enkel-inset enkel-uitset en meer-inset meeruitset
(MIMU) stelsels beheer kan word. Die metode presteer beter as ander huidige teenversadiging-
maatreels vir (MIMU) beheerders.
Die teen-versadigings-probleem word as 'n lineere programmeringsprobleem herformuleer. 'n
Praktiese en effektiewe implementering van die algoritme word verkry deur die probleem na
die duale vorm te transformeer. Die probleem, in duale vorm, word opgelos met die duale
simplex metode, in plaas van die direkte metode. Die eienskappe van hierdie formulering is 'n
gewaarborgde, aanvanklike, bereikbare oplossing en 'n optimale, begrensde, finale oplossing in
'n eindige, voorspelbare en minimum aantal stappe.
Die uiteindelike beheerder versadig nooit nie, en wen gevolglik nie op nie. Die beheerder wend
altyd die optimale aanleg-inset aan om die foutsein te minimeer soos volg:
• Wanneer die nul-inset gedrag saam met die huidige inset-gedrag geen beperkings nou
of in die toekoms saloorskry nie, word geen beperkende aksie geneem nie, en tree die
beheerder dus lineer op.
• Sodra die toekomstige nul-inset gedrag saam met die huidige inset-gedrag, nou of later
versadiging sou veroorsaak, word die huidige inset tot die beheerder optimaal begrens
om latere versadiging te voorkom
