1. Process Dynamics and Operations Group (DYN) TU-Dortmund
Tutorial 6
Model Predictive Control
Process Dynamics and Operations Group (DYN)
TU-Dortmund
Elrashid Idris

2. Model Predictive Control
1 - Explain briefly the idea behind a model predictive control (MPC) scheme? 2 2

3. Model Predictive Control
It uses a plant model to predict the plant output(s) over a certain prediction horizon P
It minimizes a quadratic objective function to compute the optimal control moves over the control horizon M.
From the obtained control moves, only the first one is used and the rest is discarded.
At the next time instant, both the horizons are shifted by one time step and the above steps are repeated to obtain a new set of control moves. This is called the receding horizon strategy.
The quadratic objective function is usually of the form: 3

4. Objective function Conventional tracking control Bias correction
where,
N: Number of controlled variables
R: Number of control inputs
P: Prediction horizon
M: Control horizon
Bias correction 4 4

5. subject to constraints
Linear model of the system
Measurements
State constraints
Output constraints
Absolute constraints
Velocity constraints 5 5

6. Model Predictive Control
2 - How is the feedback realized in MPC?
The feedback is realized by using the bias correction term, and
By the re-initialization of the model states and parameters using the measurements and the estimated states and parameters of the real plant. So, if not all of the states are measured a state estimator is needed for better performance of the MPC controller. 6 6

7. Model Predictive Control
3 - In commercial applications, why is the MPC scheme more popular than the classical control methods?
MPC is an optimization-based control scheme. It computes the optimal control moves considering a certain prediction horizon as well as a control horizon.
Constraints on the control inputs, states as well as the plant outputs can be easily incorporated as opposed to the classical control methods. Moreover, other types of constraints can also be considered.
MPC is a non-square multivariable control scheme which means that it can handle multiple inputs and multiple outputs simultaneously as opposed to the classical control methods. 7 7

8. Model Predictive Control
Why MPC is not widely used in industry?
A proof that a new control scheme (MPC) does really improve the productivity of the process. Difficult to proof …
Stability must be guaranteed, i.e. it must be assured that the optimization solver always converges.
The biggest problem is, that the plant operator may not understand the control steps. For them it's more or less a black box. It follows that they will not longer watch the process attentively, errors may not be detected or important alarms ignored. 8 8

9. Model Predictive Control
4 - What is the idea behind real-time optimization (RTO)?
In real-time optimization (RTO), the optimum values of the set-points are re-calculated on a regular basis (e.g. every hour or every day). These repetitive calculations involve solving a constrained, nonlinear steady-state optimization problem with economic objectives. 9 9

10. Model Predictive Control
5 - What is the main assumption considered in multi-stage MPC?
The main assumption considered in multi-stage NMPC is that the uncertainty can be represented by a tree of discrete scenarios. Each branching at a node represents the effect of an unknown uncertain influence (disturbance and model error) together with the chosen control input. The scenario tree usually considers combinations of the maximum, minimum and nominal values of the uncertainty. 10 10

11. Model Predictive Control11 11

12. Model Predictive Control
Questions 12 12