Documentation |
Estimate state-space model using a subspace method.
sys = n4sid(data,nx)
sys = n4sid(data,nx,Name,Value)
sys = n4sid(___,opt)
[sys,x0] = n4sid(___)
sys = n4sid(data,nx) estimates an nx order state-space model, sys, using measured input-output data, data.
sys is an idss model representing the system:
$$\begin{array}{l}\dot{x}(t)=Ax(t)+Bu(t)+Ke(t)\\ y(t)=Cx(t)+Du(t)+e(t)\end{array}$$
A,B,C, and D are state-space matrices. K is the disturbance matrix. u(t) is the input, y(t) is the output, x(t) is the vector of nx states and e(t) is the disturbance.
All the entries of the A, B, C and K matrices are free estimation parameters by default. D is fixed to zero by default, meaning that there is no feedthrough, except for static systems (nx=0).
sys = n4sid(data,nx,Name,Value) specifies additional attributes of the state-space structure using one or more Name,Value pair arguments. Use the Form, Feedthrough and DisturbanceModel name-value pair arguments to modify the default behavior of the A, B, C, D, and K matrices.
sys = n4sid(___,opt) specifies estimation options, opt, that configure the initial states, estimation objective, and subspace algorithm related choices to be used for estimation.
[sys,x0] = n4sid(___) also returns the estimated initial state.
sys |
Identified state-space model. sys is an idss model, which encapsulates the identified state-space model. |
x0 |
Initial states computed during the estimator of sys. If data contains multiple experiments, then x0 is an array with each column corresponding to an experiment. |
[1] Ljung, L. System Identification: Theory for the User, Appendix 4A, Second Edition, pp. 132–134. Upper Saddle River, NJ: Prentice Hall PTR, 1999.
[2] van Overschee, P., and B. De Moor. Subspace Identification of Linear Systems: Theory, Implementation, Applications. Springer Publishing: 1996.
[3] Verhaegen, M. "Identification of the deterministic part of MIMO state space models." Automatica, 1994, Vol. 30, pp. 61—74.
[4] Larimore, W.E. "Canonical variate analysis in identification, filtering and adaptive control." Proceedings of the 29th IEEE Conference on Decision and Control, 1990, pp. 596–604.