Defining and Estimating Partially Known Models (System Identification Toolkit)
Before estimating partially known models, you first must define those models. Using prior knowledge, you choose a model for the plant in a system and set parameter constraints for the model. You then can estimate the model to represent the real-world plant. The LabVIEW System Identification Toolkit provides two VIs you can use to define partially known models—the SI Create Partially Known State-Space Model VI and the SI Create Partially Known Continuous Transfer Function Model VI.
Use the SI Create Partially Known State-Space Model VI to define partially known continuous or discrete state-space models.
You can use the SI Create Partially Known State-Space Model VI, for example, to define a state-space model that represents an RLC circuit consisting of a resistor R, an inductor L, and a capacitor C. Using prior knowledge, you describe the relationship of R, L, and C with the following equations:
D = 0
You also can use prior knowledge to define the initial guesses and upper and lower limits of R, L, and C. The SI Create Partially Known State-Space Model VI uses variables rather than numerical values to construct a symbolic model. As the following figure shows, you use variable names, such as R, L, and C, in the symbolic A, symbolic B, symbolic C, and symbolic D inputs to define the RLC circuit. Then you specify values for R, L, and C in the variables input.
Use the SI Create Partially Known Continuous Transfer Function Model VI to define partially known continuous transfer function models. The following equation represents a continuous transfer function model.
| where | Kp is the transfer function gain |
| Tdis the delay | |
| Tp is the first-order time constant | |
| w is the natural frequency | |
| r is the damping ratio | |
| s represents the time |
You can apply the prior knowledge you have about the parameters K, Td, Tp, w, and r to the static gain, delay(s), Tp(s), natural freq (rad/s), and damping ratio inputs, respectively, of the SI Create Partially Known Continuous Transfer Function Model VI by defining the initial guesses and upper and lower limits.
With the System Identification Toolkit and a partially known model, you can set constraints on each parameter of a state-space or continuous transfer function model in two ways—with an upper and lower limit or with an initial guess.