  This paper presents the design of multivariable temperature control for a
refrigeration system based on vapor compression employing the internal model
control technique. The refrigeration system is based on the PID18 benchmark,
which is a $2\times 2$ MIMO system. The controlled output variables of the
refrigeration system are the cooling power managed through the outlet
temperature of the evaporator and the superheating degree at the condenser. The
input variables of the system are the valve opening and the compressor speed.
System identification is performed by applying stepped signals to the input
variables, resulting in four transfer functions estimated with a Box-Jenkins
model. From the MIMO system transfer functions, the relative gain array is
calculated to determinate the best variables to be paired. After that,
according to the variables to be paired, the corresponding transfer functions
are reduced to order two to design a PID controller for each output variable
employing the internal model control technique. Then, the controllers are
contrasted employing a set of quantitative performance indexes with the control
results achieved in the PID18 workshop. Obtained results show that the proposed
Internal Model controllers have better performance than most of the proposed
controllers at the PID18.
