What are some best practices for tuning the weights and parameters of a model predictive controller?

2 Choose the prediction horizon

The prediction horizon is the number of time steps that the MPC uses to predict the future behavior of the system. The prediction horizon affects the computational complexity and the accuracy of the controller. A longer prediction horizon can capture more information about the system dynamics and the constraints, but it also requires more computation time and memory. A shorter prediction horizon can reduce the computational burden, but it may also result in suboptimal or unstable control actions. Therefore, it is important to choose a prediction horizon that balances the trade-off between complexity and performance. A common way to choose the prediction horizon is to use a rule of thumb based on the system's time constants, such as setting it to four or five times the dominant time constant. Alternatively, some methods can optimize the prediction horizon based on some criteria, such as minimizing the error or maximizing the feasibility of the controller.

3 Select the control horizon

The control horizon is the number of time steps that the MPC uses to optimize the control inputs. The control horizon affects the degree of freedom and the smoothness of the controller. A longer control horizon can provide more flexibility and optimality for the controller, but it may also result in oscillatory or aggressive control actions. A shorter control horizon can limit the control variability and smoothness, but it may also reduce the performance or feasibility of the controller. Therefore, it is important to select a control horizon that balances the trade-off between smoothness and optimality. A common way to select the control horizon is to use a rule of thumb based on the system's dynamics, such as setting it to one or two times the system's order. Alternatively, some methods can adjust the control horizon based on some criteria, such as minimizing the input or maximizing the stability of the controller.

4 Consider the model uncertainty

The model uncertainty is the difference between the actual system behavior and the mathematical model used by the MPC. The model uncertainty can affect the performance and robustness of the controller, especially if it is large or time-varying. Therefore, it is important to consider the model uncertainty when tuning the weights and parameters of a MPC. One way to deal with the model uncertainty is to use a conservative approach, such as increasing the weights of the output or input penalties, or adding some safety margins or buffer zones to the constraints. Another way to deal with the model uncertainty is to use an adaptive approach, such as updating the model parameters or using a disturbance observer or a state estimator to correct the model predictions.

5 Test and validate the controller

The final step in tuning a MPC is to test and validate the controller on the actual system or a realistic simulation. The test and validation process can help to verify the performance and robustness of the controller under different operating conditions and scenarios, such as disturbances, noise, changes in setpoints, or violations of constraints. The test and validation process can also help to identify and correct any errors or issues in the model, the objective function, or the tuning parameters. A common way to test and validate the controller is to use some performance metrics or indicators, such as the root mean square error, the control effort, or the constraint satisfaction. Alternatively, some methods can compare the controller with other controllers or benchmarks, such as a PID controller, a linear quadratic regulator, or an optimal control solution.