When you have measured plant data, you can use the System Identification Toolbox™ software to identify a linear plant model. You use the mpc function to create a model predictive controller for the identified plant model.
An identified model has two types of inputs—measured inputs and unmeasured noise inputs. For more information regarding the structure of an identified model, see Input Output Structure of Identified Model.
There are two ways you create an MPC controller using the identified model:
Use only the measured components of the identified model for the controller plant model. This approach is the preferred method for creating an MPC controller for an identified plant model.
Measured inputs of the identified model are treated as the manipulated variables of the model predictive controller.
Measured outputs of the identified plant model are treated as the measured outputs of the plant for the controller.
For an example, see Design Controller for Identified Plant.
Use the noise model of the identified model for the controller plant model. When you have a reliable noise model of the identified plant, you can use this method to create an MPC controller.
The measured components of the identified model are treated just as in the first approach. However, this approach additionally treats the unmeasured noise inputs of the identified model as the unmeasured disturbances to the plant for the controller.
Unmeasured input disturbances influence the default controller design. A plant may yield different noise models for different experiments. If the controller works well during setpoint changes, but eliminates disturbances slowly or exhibits steady-state error, try modifying the unmeasured disturbance model.
For an example, see Design Controller Using Noise Model of Identified Model.
The input/output relationship for an identified model is:
y is the measured output.
u is the measured input.
e is the unmeasured noise input and is Gaussian white noise of a specified variance.
G is the measured transfer function that relates the measured input, u, to the output, y.
H is the noise transfer function that describes the effect of output disturbances.
The noise channel of an identified model, e, is not used in calculating the input size of an identified model. Also, by default, e is not accounted for in traditional model analysis such as simulation, frequency response computation, and pole-zero maps.