The multivariable adaptive control theory was applied to a packed bed reactor control system. The control system is 2x2 MIMO (multi-input multi-output) control system; input variables are space time (Δτ) and reactor wall temperature ($\Delta T_w$); output variables are reaction temperature ($\Delta T_i$) at various measuring points of a reactor bed and product yield (ΔY). The reaction is the partial oxidation of $n-C_4H_{10}$ (normal butane) to MA (maleic anhydride), which is highly exothermic.
In case of such reactor control system, there exists a hot spot somewhere in the reactor bed which causes the reactor to be unstable or makes the catalysts deactivated and the system also shows direct transmission behavior in yield response to a step change in space time. Thus the hot spot temperature should be controlled not to exceed maximum allowable limit temperature and the product yield must be regulated not to influence next process stream, inspite of unpredictable changes in input variables or reactor system environments.
There are two important problems which are emphasized in the design of MIMO adaptive control system, one is the selection of temperature sensor location, the other is the direct transmission response of ΔY to Δτ. Each problem was studied separately through $\Delta\tau-\Delta T_i$ and Δτ-ΔY SISO (single-input single-output) applications. And the results were combined to give MIMO adaptive control scheme for a packed bed reactor.
The sensor location $z_i$ was also orthogonal collocation point of a reactor model, and hot spot temperature was calculated through Lagrange Interpolating Polynomial method with $z_1$, $z_2$, $z_3$ and $z_4$ as approximation points. simulation studies showed that the sensor location influenced control system performance seriously and $z_4$ was taken as a good sensor location.
The direct transmission behavior was smoothed by passing ΔY through a low pass filter to produce filtered output $\Delta Y_F$, which resulted good control system performance.
Consequently, the resulting MIMO adaptive control scheme showed good performances at wide operation range. SISO experiments were done with pilot plant scale packed bed reactor, further experiments in MIMO adaptive control system are required to confirm above simulation works.
