Editing Model predictive control (section)

=== Principles of MPC ===

Model predictive control is a multivariable control algorithm that uses:
* an internal dynamic model of the process
* a cost function ''J'' over the receding horizon
* an optimization algorithm minimizing the cost function ''J'' using the control input ''u''

An example of a quadratic cost function for optimization is given by:

:<math>J=\sum_{i=1}^N w_{x_i} (r_i-x_i)^2 + \sum_{i=1}^M w_{u_i} {\Delta u_i}^2</math>
<!-- previous version -- J = weightCV1*(rv1 – cv1) 2 + weightCV2*(rv2 – cv2) 2 +…
+ weightMV1*(Δmv1) 2 + weightMV2*(Δmv2) 2 +… -->

without violating constraints (low/high limits) with

:<math>x_i</math>: <math>i</math><sup>th</sup> controlled variable (e.g. measured temperature)
:<math>r_i</math>: <math>i</math><sup>th</sup> reference variable (e.g. required temperature)
:<math>u_i</math>: <math>i</math><sup>th</sup> manipulated variable (e.g. control valve)
:<math>w_{x_i}</math>: weighting coefficient reflecting the relative importance of <math>x_i</math>
:<math>w_{u_i}</math>: weighting coefficient penalizing relative big changes in <math>u_i</math>
etc.