ABSTRACT 

The present thesis studies the multirate sampling systems, it works with specific model 
blocks of input and outputs BMIO Albertos [1], and this model turns a multirate system into 
a single rate system with metaperiod by means of lifting inputs and outputs forming blocks. 
There are studies of different controllers developed for this type of model and discussed the 
causes that originate the intersampling ripple that produce these controllers and the possible 
forms of eliminating it. 

In the first approximation that the controllers have a ripple at the output of the system due to 
the fact that the actions of control varies along the metaperiod, even in stationary conditions, 
this actions provoke that the outputs of the system change along the metaperiod. At first 
instance the controller works with a deadbeat that applies compensators, this makes the 
control actions equal along for the metaperiod eliminating in this way the intersampling 
ripple. These compensators are integrated at the controller design stage, and developed a way 
to calculate the matrixes of the controller that includes these compensators, this means, that 
the rows related to each input of the matrixes used to obtain the control actions are equal. 
The matrix form allows the analysis of the controller behavior and facilitates the 
development of controllers for MIMO systems. 

A second alternative to face the ripple problem using a controller based on the pole 
assignment which works with the model at high frequency but obtains the control matrixes 
doing the calculations at low frequency and repeating these results in high frequency, the 
control actions results are equal, this alternative method to work assures the stability of the 
new controlled system and the elimination of the ripple, but the drawback is an offset in the 
output. Developing two ways to eliminate this offset one for SISO systems and other for 
MIMO systems based on the stationary state gain modification for a feedback system. 

The alternative for an Optimal Control Design for the last controller is to calculate the 
matrixes at low frequency, applying these results at high frequency, obtaining a stable and 
ripple free controller. 

The incorporation of filters makes a transition between the original control matrixes and the 
new ones developed in this work, taking advantage of a better transitory response for the first 
ones and the elimination of the ripple in stationary state for the second ones. 


Finally a Toolbox CACSD (Computer Aided Control System Design) for 
MATLAB/SIMULINK is developed that helps in the design, application and study of the 
controllers treated here.