How can you select the best model structure and order for feedforward control?

1 Model structure

The model structure refers to the type and number of inputs, outputs, and parameters that describe the relationship between the disturbance and the output. There are different types of model structures, such as linear, nonlinear, discrete-time, continuous-time, state-space, transfer function, etc. The choice of model structure depends on several factors, such as the complexity of the system, the availability of data, the accuracy and robustness requirements, and the computational resources. Generally, you want to choose a model structure that is simple enough to be identified and estimated, but complex enough to capture the essential dynamics and nonlinearities of the system.

2 Model order

The model order refers to the number of parameters or states that are needed to represent the model structure. For example, a transfer function model has an order equal to the sum of the degrees of the numerator and denominator polynomials. The model order affects the quality and complexity of the model. A higher order model can fit the data better and capture more details, but it can also be more prone to overfitting and instability. A lower order model can be more robust and parsimonious, but it can also be more biased and inaccurate. Therefore, you want to choose a model order that balances the trade-off between fit and complexity.

3 Model selection methods

When selecting the best model structure and order for feedforward control, there are several methods to consider. Trial and error is a simple and intuitive approach, but can be time-consuming and subjective. Alternatively, information criteria such as Akaike information criterion (AIC), Bayesian information criterion (BIC), or final prediction error (FPE) can be used to evaluate and compare models, balancing the fit and complexity of the models while penalizing those with too many parameters. Cross-validation is a more reliable and robust method, but it can be more computationally intensive and data-demanding as it requires splitting data into training and validation sets.

4 Model validation

After you select the best model structure and order for feedforward control, you need to validate the model to check its adequacy and suitability. You can use some techniques, such as the residual analysis, the parameter confidence intervals, the model simulation, and the model sensitivity analysis, to verify that the model meets the assumptions, the parameters are consistent and significant, the model reproduces the data well, and the model is robust to uncertainties and variations. You can also use the model to design and test the feedforward controller, and evaluate its performance and robustness.

Feedforward control is a powerful technique that can improve the performance and stability of a system. However, it requires a good model that captures the relationship between the disturbance and the output. By following the tips and methods in this article, you can select the best model structure and order for feedforward control, and validate the model to ensure its quality and reliability.

5 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?