Associated with the Center for Process Modeling & Control
Synthesis of Controllers for Constrained Systems
All real world control systems must deal with constraints. On the one hand, the range and rate of change of the input or manipulated variables is limited by the physical nature of the actuator (e.g., valve saturation, finite capacities of compressors, pumps, etc.). On the other hand, process state variables or outputs such as pressures, temperatures and compositions may not be allowed to exceed certain bounds arising from equipment limitations, safety considerations or environmental regulations. A number of industrially implementable techniques and a rigorous theory exist for designing controllers -- both linear (PI/PID, H2/Hinfiinty, LQG, LTR) and nonlinear (nonlinear Hinfinity, feedback linearization, gain scheduling). However, none of these popular controller design techniques account for the presence of input and output constraints. The goal of this research effort is to study all aspects of controller analysis and synthesis -- both linear and nonlinear -- for the aforementioned constrained systems. Numerous industrially relevant processes such as the fluidized bed catalytic cracker (FCC) and the hydrocracker are used to test the results of this research.
Robust Model Predictive Control
In the chemical and petroleum processing industry, model predictive control (MPC) or dynamic matrix control (DMC) has been widely accepted as the methodology which explicitly handles process constraints in a systematic manner during regulatory controller design and implementation. However, with the exception of a few recent developments, existing MPC-based controllers are unable to explicitly handle information about plant model mismatch or what is commonly referred to as model uncertainty. In other words, these controllers are not robust to model uncertainty and are known to perform very poorly when implemented on a process which is not exactly described by the model. The goal of this research effort is to formulate the predictive control algorithm with explicit consideration of robustness. In a recent work, we proposed a novel and complete framework for robust MPC based on recent developments in the area of convex optimization using linear matrix inequalities. This framework is the starting point for this research effort. A parallel activity involves extension of the conventional linear MPC algorithm to a class of nonlinear systems which are described by linear parameter varying (LPV) models. An industrial steam generator model is being used to test the results of this research.
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