MPC控制器

Generals

MPC: regulatory controls using an explicit dynamic model of the response of process variables to changes in manipulated variables.
$obj = min(\sum (y - y_{trajectory})^2)$
basic version uses linear model. Can also be empirical model.
advantages over PID:
- long time constants, substaintial time delays, inverse response, etc;
- multiple variables
- has constraints over process variables
General characteristcs:
- targets (set points) selected by real-time optimization software based on current operating and economic conditions
- minimize square of deviations between predicted future outputs and specific reference trajectory to new targets
- handles MIMO control problems
- can include equality and inequality constraints on controlled and manipulated variables
- solves a nonlinear programming problem at each sampling instant
- disturbance is estimated by comparing the actual controlled variable with the model prediction
- usually implements the first move out of $M$ calculated moves
MPC target trajectories
- Types:
  - Funnel Trajectory
  - Pure dead-band
  - Referecen Trajectory
- Near-term vs. long-term objectives
- Response Target
- Response Speed
Quadratic objective $\sum_{i=0}^p x_i^TQx_i + \sum_{i=0}^{m-1} u_i^TRu_i$