How do you deal with constraints, disturbances, and model mismatch in MPC and advanced algorithms?

1 What are constraints, disturbances, and model mismatch?

Constraints are the physical or operational limits that restrict the range of values that the inputs, outputs, or states of a process can take. For example, you may have constraints on the temperature, pressure, or flow rate of a reactor, or on the power consumption or speed of a motor. Disturbances are the external factors that affect the process behavior, but are not controlled by the inputs. For example, you may have disturbances from the feed composition, ambient temperature, or measurement noise. Model mismatch is the difference between the actual process dynamics and the mathematical model used by the MPC or advanced algorithm. For example, you may have model mismatch due to nonlinearities, time delays, or parameter uncertainties.

2 Why are they important for MPC and advanced algorithms?

Constraints, disturbances, and model mismatch are important for MPC and advanced algorithms because they affect the feasibility, optimality, and stability of the control solution. If the constraints are violated, the process may operate in unsafe or inefficient conditions, or even damage the equipment. If the disturbances are not accounted for, the control performance may degrade or oscillate. If the model mismatch is significant, the control solution may be inaccurate or inconsistent with the process behavior.

3 How do you deal with constraints in MPC and advanced algorithms?

One of the main advantages of MPC and advanced algorithms is that they can explicitly handle constraints in the optimization problem, allowing them to find the optimal input sequence that satisfies constraints over a prediction horizon while minimizing a cost function. However, dealing with constraints can be challenging, such as ensuring feasibility, avoiding infeasibility, and handling conflicting or changing constraints. To address these issues, you can use slack variables or soft constraints to relax the hard constraints and penalize the violations, active set methods or interior point methods to efficiently solve the constrained optimization problem, feasibility enforcement or constraint tightening to ensure the solution is feasible for the actual process, or priority ranking or weighting to resolve trade-offs between competing or changing constraints.

4 How do you deal with disturbances in MPC and advanced algorithms?

MPC and advanced algorithms can incorporate disturbances in the optimization problem, predicting the effects of disturbances on the process outputs and states, and adjusting the inputs to compensate or reject them. To do this effectively, you need to consider estimating, forecasting, and filtering the disturbances, as well as choosing the right disturbance model and horizon. Various techniques can be used to achieve this, such as state estimation or observers to estimate current state and disturbance values from measurements, time series analysis or machine learning to forecast future disturbance values from historical data or trends, Kalman filters or moving average filters to smooth noise or outliers in disturbance measurements or forecasts, and stochastic MPC or robust MPC to account for uncertainty or variability in the disturbance model or horizon.

5 How do you deal with model mismatch in MPC and advanced algorithms?

A common assumption of MPC and advanced algorithms is that they use a perfect or accurate model of the process dynamics. However, in reality, there is always some degree of model mismatch due to various sources of errors or uncertainties, such as simplifications, approximations, linearizations, discretizations, or parameter variations. This can lead to suboptimal or unstable control performance, or even divergence or instability of the optimization problem. To address this issue, you can employ techniques like model identification or calibration to update the model parameters or structure based on the process data or experiments. Additionally, adaptive MPC or online MPC can be used to adjust the model or the control solution in real time based on feedback and measurements. Nonlinear MPC and hybrid MPC are also available for capturing nonlinearities and mode changes in the process dynamics. Lastly, robust MPC and tube MPC can be employed to account for bounded or worst-case model mismatch.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?