ARX Time-Series Model

ARX models are a powerful tool for modeling and analyzing the behavior of dynamic systems. They are widely used in a variety of fields, including control engineering, signal processing, and electrical engineering. ARX models are often used in control engineering, where they are used to design controllers for systems such as robots or manufacturing processes. ARX models are based on the concept of linear time-invariant (LTI) systems, which are systems that can be described by linear differential equations. In an ARX model, the input and output of a system are related by a linear equation.
ARX Model Code: apmonitor.com/dde/index.php/M...
An ARX model is a combination of an autoregressive model (AR) and an exogenous input model (X). It is used to represent the dynamics of a system and is commonly used in control engineering to model and analyze dynamic systems. An autoregressive model is a type of statistical model that represents a time series as a linear combination of its past values and a stochastic process.

[@jonathanuis]

John, a thousand thanks! I love what you are doing. Sharing knowledge in such wonderful manner

[@apm]

Glad you enjoy it!

[@bernagoga]

Your videos are amazing! Thank you for sharing.

[@amel3778]

Thank you for this video. I wanted to ask you a question: in the case where we have data containing a control input u, a disturbance d, and an output y, how can we perform the identification with Gekko?

[@apm]

You can have 2 inputs to the system with [u,d] and one output [y].

[@Tupiniviking_de_osasco]

Your content is amazing! Just one question, is it possible to use such model to implement a control like lqr ?

[@apm]

Yes, there is a lossless conversion between ARX and state space. Once it is in state space one then an LQR can be derived.

[@jinxiangsun9236]

Hello John, can you talk about the Output-only ARX model of MDOF system? Thank you very much.

[@apm]

Here is additional information: www.sciencedirect.com/science/article/pii/S0888327020308256

[@jinxiangsun9236]

@@apm I just read the article you mentioned, but I have no intuitive understanding of the model in it. Fortunately, I have seen your perfect explanation of the ARX model. If possible, I hope you can take this article as a case for another explanation😊😊