# System Identification in Matlab

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### System identification

In any system, if you want to have control of the system, you need to develop its model. A model is defined as a mathematical representation of the system in a way that the mathematical equation constitutes every parameter of the model. It’s particularly useful if you are to simulate the system. There are two ways that a model can be developed. One is by using physical laws, which is known as modeling from the first principles or secondly from the experimental data or data-based modeling. Most people believe that the first principle of modeling is more useful as compared to data-based modeling, but the two are equally important.  If you are using the second way, then you are using system identification to develop a model.

Therefore we can define system identification as the methodology of creating mathematical models from experimental data. Another definition that we can use is, system identification is the study of modeling dynamic systems. For the second definition, a system is a group of interrelated parts that function towards achieving a certain goal. An example is the human breathing system.  A dynamic system is a system that has a memory i.e., the inputs at a certain time influence the output at that time. In system identification, the model is not created to explain the physical characteristics of the dataset. We need a model that will ensure the stability of the control system in providing the desired results.

The main goal of the system identification is to create an exact approximate model for the system.  If a good model has been created, we can go on and solve the system’s problems such as controlling it and predicting the behavior of the system under different conditions or simulate how the system will react under different changes in environmental conditions.

Because of its advantages in solving systems problems and helping in simulation, system identification has gained a lot of attention from the science community. In fact, it has a wide range of applications, which include.

1. Designing of new cars and planes.
2. Forecasting e.g., weather and stock price forecasting.
3. Simulating
4. Signal processing.
5. Fault detection

There are so many things involved in the creation of a model that it might seem easy, while in real life it’s complicated. Depending on the type of model, we can classify system identification as a linear and nonlinear model identification or parametric and non-parametric model identification.  The process is quite complex and entails a lot of things. We cannot pretend that we will explain all the concepts in system identification in detail. We shall only provide a general idea of what the categories of system identification means. In some instances, the definition will be sufficient. But first, let’s start with the steps used in system identification

### System identification steps.

There are several steps that are used in system identification. The key ingredients for these steps are the data, a set of models that you will select from and a model selection criterion. The steps start with data collection. Data is required in the whole process. How can we develop a mathematical model without data? It’s actually impossible to develop a model without data. All the data processing methods are applied before it’s used for model formulation. Secondly, we formulate the appropriate model for the dataset. The third step is to estimate the parameters in the model. This step is so essential that it’s one of the processes that make us gain confidence in the model. Finally, we end with model validation. If this process fails, we can start all over again from step two- the model formulation.

### Linear and nonlinear identification

Linear identification stems from the fact that the mathematical relationship of the datasets are linear. Linear models are one of the simplest models that one can produce. Nonlinear system identification is the opposite of linear system identification i.e., we formulate a model that is not linear. Developing such a model is more complicated as compared to linear models. Nonlinear models can be used to model both a linear system and a nonlinear system, but in either system, the modeling process is not an easy one.

### Stochastic and deterministic system identification

We can define a stochastic model as a model having random variables.  A stochastic model is characterized by high levels of uncertainty. This model will give you different results if you calculate it separately. Despite giving different results, stochastic models are an important tool in finance and other industries. Deterministic models give the same results even if the process is repeated several times. Here nothing is random. The mathematical properties of the dataset are already known. Any uncertain factors are outside the model.

### The general system identification methods.

There are two types of system identification methods – parametric and non-parametric. For parametric methods, the results are the model parameters, or simply we can say you have to build a mathematical model. They are preferred because of their accuracy in the information. This comes with the price that you have to do a lot of computations. Non-parametric methods are easier to compute as the results are visual representations such as curves and tables. They are usually more appealing and give basic information.

### System identification in Matlab

You can do your system identification assignment using any other software such as C and python. Matlabcan also be used for system identification.  The advantage of using Matlab is that it has a wide scientific base. Universities have incorporated it into their curriculum.  With Matlab, you can load the dataset for analysis and apply a model structure. The system identification toolbox is a Matlab resource for system identification.

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