Optimum reference trajectory

In order to control a process, it is necessary first to define the desired control reference or setpoint. The setpoint maybe computed as the optimum reference trajectories (u = u°P ),... 

If a reliable process model is available and can provide solutions in real time, the model can be used to provide the corrected setpoint trajectories for u without decouphng or empirical tuning of controller gains. If a process performance index is defined, then the controller action can be computed directly by inverting the process model. For instance, if it is assumed that the current process states [x(f),y(f)] are known and that it is desired to reach the optimum reference trajectory after tf time units, then Equations 8.18b and 8.35 can be written as... 

Amodel-based closed-loop controller was designed for maximization of polymer production under safe process condition in emulsion copolymerization processes, while keeping the copolymer composition constant [195]. The interesting feature of the proposed controller was the use of a fuzzy model for design of the optimum reference trajectories. 

Equations 8.36a-b and 8.37a-b assume implicitly that the optimum reference trajectories remain constant throughout the time. Although this does allow for removal of process disturbances and significant improvement of the process performance, the fact is that optimum reference trajectories depend on the initial states. As process disturbances modify the state variables (this is why x(t) and x (t) become different), it is certain that the optimum reference trajectory should also respond to unexpected process disturbances. Therefore, if x(f) and x (r) are not coincident, then x (r) should be recalculated in real time. Then, an improved version of the model predictive control scheme can be formulated... 

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