Model Predictive control (MPC) models are application control strategies that can be widely accepted and are useful for industrial process applications as a result of their ability to reformulate control problems as optimization problems and show satisfactory performance when meeting operational and safety constraints.
Principle of Operation:
The principle of operation of MPC involves determining the dynamic model of the system to be controlled and determining the physical limits on the system variables. The purpose of the MPC is to determine the input sequence of controls that minimize the performance index or certain cost function (J), based on the desired output path above the predicted horizon §.
From the calculated input sequence, only the first sample is applied to the process. All procedures are repeated in the next instant sample, according to the retroactive horizon strategy.
A continuous version of the approach can be automated with the general predictive control structure:
Components of MPC:
MPC is based on the model and the prediction model is utilized. The algorithm of the MPC is based on the derived model. MPC pays more attention to the function than to the model’s formulation.
To predict future output, the function of a predictive model is based on past information and future input.
Feedback is used to overcome disturbances and to achieve stability in the closed loop. The MPC uses the correction of feedback. The feedback effect is achieved in adaptive MPC through online system model updates and a PID feedback controller used as transparent control is applied.
Prediction:
Predictions are based on the model. Past information and information about the state of the system is used to do this.
The main requirement is that the cost depends on future control and the lowcost value implies good performance in the closed loop.
Constraint Handling:
If constraints are met, an MPC takes systematic account and allows for better performance in compensation and still maintains the robustness of unconstrained control laws for each time step. The handling of restrictions depends on the adopted MPC algorithm.
MPC behaviour:

The MPC controller’s behavior is intrinsically nonlinear as it takes into account state and control constraints. However, if the problem formulation contains no constraints, the controller is linear.

The controller behaves linearly during operation when no constraints are active. In the first case, the control law, could (and should) be calculated offline, whereas in the second case, the optimization procedure must be done each sample.

Using the observation that the MPC control law is piecewise linear in the states, it is possible to calculate, offline, all possible control laws.

The online optimization problem is then transformed into a search problem, where the objective is to find the appropriate partition in the state space, identifying the corresponding control law