Application of singular value decomposition and nonlinear feedback control to a multispace problem

Much has been written to indicate the desirability of process operation at or near an unstable steady state. A new control philosophy has been applied successfully to a first order experimental system to provide stable operation using a nonlinear feedback control device, relay with hysteresis. Based on these encouraging results, the present study undertook to examine application of this control concept to a higher order system, the 2-azobisisobutyronitrile initiated bulk polymerization of styrene in a continuous flow stirred tank reactor.

The tenth order model developed for this polymerization system was studied using singular value decomposition, a mathematical analysis relatively new to the field of engineering applications. This process resulted in a simplification of the model to a lower order through a quantitative approach, improving on the qualitative arguments previously employed. A further application of singular value decomposition indicated specific control loops to be examined for best response to a step input change.

Tsypkin's analysis, used when examining a relay control mechanism, was shown to be the necessary technique for design of the nonlinear control element for higher order systems, as the added complexity led to improper conclusions based on the standard Van Heerden graphical analysis approach. Due to the highly exothermic nature of the free radical polymerization process, control of the reactor temperature by inlet monomer concentration was shown to yield satisfactory process control about the unstable steady state. Period and amplitude of the oscillation as predicted by Tsypkin's analysis compared very well with those resulting from the nonlinear simulation. Several new phenomena not previously observed in the application of this nonlinear scheme are reported. Other results of Tsypkin's analysis of control strategies pointed toward interesting possibilities in the area of pushing (use of large relay drive levels) control theory.