# Partially Known Model Estimation Methods (System Identification Toolkit)

The nonparametric and parametric model estimation methods, also known as black-box estimation methods, assume that systems are unknown. Because these estimation methods do not take prior system knowledge into account, you must use either an algorithm or trial-and-error to vary model parameters until the behavior of the model matches the measured input-output data. Although you can use the estimated parameters to reproduce the response of the system accurately, these parameters might not have any physical meanings.

However, in practice, many systems are partially known because you have information about the underlying dynamics or some of the physical parameters. You can use partially known model estimation methods, also known as grey-box estimation methods, to estimate models when you have this information.

Black-box methods also assume that all model parameters are adjustable. However, in many real-world applications, you cannot adjust all the parameters arbitrarily, because the parameters might have constraints. For example, in some chemical processes, water must flow only in one direction. When estimating the flow rate of water, you know that the flow rate cannot be negative. Thus, the constraint is that the flow rate must be a positive value. You must consider this constraint and any other constraints when you estimate the flow rate of water in this process. Such constraints usually follow one of the following guidelines:

• A parameter must be as close to a value as possible.
• A parameter must be between two values.
• Two or more parameters must correlate to each other.

These constraints reflect the knowledge you have of the physical system. This knowledge can result in a more realistic parameter estimation. Parameter constraints increase the possibility of the System Identification VIs locating the optimal parameters that describe the real-world model. Parameter constraints also improve the accuracy of locating these optimal parameters.

You can set parameter constraints when using grey-box estimation methods, whereas you cannot set parameter constraints when using black-box estimation methods. When using these methods, you can set only the model order that specifies the number of parameters to calculate.