Neuro-mimetic dynamic gain-scheduled process control
Abstract
The paradigm of dynamic gain scheduling (DGS) is inspired by a biophysical model of the mammalian baroreceptor reflex. The model uses Hodgkin-Huxley type neuron descriptions, parameter fitting of which is explored using a nonlinear simplex optimization technique. The analysis of the neuronal network model of the reflex revealed that baroreceptors are specialized neurons sensitive not only to pressure but to its rate of change as well. The baroreceptors appear to employ this rate information in scheduling the activity of the next layer of neurons. The dynamic scheduling activity of the network is exploited in a control architecture for a continuous stirred tank reactor (CSTR) with van de Vusse kinetics. A review of gain scheduling theory and applications in process control revealed that dynamic gain scheduling can address the limitation of gain scheduled control to slowly changing scheduling parameters $\xi.$ With this background, the DGS paradigm is explored in the context of nonlinear control theory. The control synthesis is based on algebraic transformations of the composite nonlinear controller obtained using the input-output linearization (IOL) formalism. The controller is reduced to linear form and scheduled in the two-dimensional $\xi$ and $\dot\xi$ space. In this manner, the time-variation of the scheduling parameter is explicitly accounted for. The algorithm is demonstrated on a complex polymerization reactor. Simulation results show satisfactory control during polymer grade changes, disturbance rejection, and noisy measurements. Performance under parametric uncertainty as well as uncertainty with respect to unmodeled dynamics is also evaluated. Structured singular value analysis for nonlinear and time-varying uncertainty facilitated the determination of theoretical stability of the DGS loop. Extension of the DGS algorithm to systems with higher relative degrees and multi-variable processes is demonstrated on an industrial benchmark problem--a solution copolymerization process. Simulations show that the DGS controller is significantly better than a four PI controller system, and even compares favorably to a 3 $\times$ 3 model predictive controller. Finally, a biophysical modeling study for a local cardiac reflex was undertaken for future reverse engineering work.
Degree
Ph.D.
Advisors
Doyle, Purdue University.
Subject Area
Chemical engineering
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