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

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Appendix 2.1: Solving Algebraic Equations

Fortunately, the MATLAB fsolve function is easy to use for solving algebraic equations. For a simplified presentation, we use the form

Equation A.1

obtained from Equation (2.66) with a fixed p and u. The most commonly used numerical techniques are related to Newton-Raphson iteration. The “guess” for iteration k + 1 is determined from the value at iteration k, using

Equation A.2

where f[x(k)] is the vector of function evaluations at iteration k, and J(k) is the Jacobian matrix

Equation A.3

The ij element ...

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