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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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Appendix 16.2: Derivation of the Least Squares Solution for Control Moves

The objective function is

Expanding the objective function, we find

Unconstrained System

The minimization with respect to the control move vector, when there are no constraints, is

and solving for Δuf we find

Equation 16.23

Constrained System

The objective function for a constrained ...

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