(622k) Nonlinear Control of Dynamic Processes Using Models Based On Granular Runge-Kutta Methods

Granular computing have previously been applied to process modeling of dynamic processes using several approaches including fuzzy logic and neural networks. They allow for different levels of granular (coarse to fine) description of a process. As such, different control strategies can be used to arrive at the target, as well as different compensators for disturbance rejection can be implemented based on the local topology of the states. However, these models are predominantly based on discrete-time models and approaches. In this paper, we combine the well-known method of Runge-Kutta with a granular domain description of the states and external inputs to obtain continuous-time process description. This approach allows us to obtain critical nonlinearity of the continuous-time dynamics as well as the multiplicity of steady states of the process.  Moreover, the granular description has the advantage of allowing smooth switches among different control modes via hybrid control methods. One proposed strategy is to use the steady state granular maps for feedforward control, while using the granular dynamic model to design and implement nonlinear feedback strategies. Another approach is to use the granular models for predictive control. The paper focuses on the former appoach. We will include analytical and simulation results based on the proposed approach. The results are very encouraging and point to a generic and effective approach to nonlinear control that also provide a practical generalization of other approaches including gain-scheduled and other hybrid control methods.