Function: VRFT1_ry


 

C = VRFT1_ry(u,y,Mr,B,W,k,optFilt)


Design a 1 degree of freedom (1 d.o.f.) linear controller so as to match the r(t) to y(t) close-loop transfer function with the model reference Mr (see Figure 1).

Figure 1: 1 degree of freedom control scheme.


Inputs (compulsory)

- u: column vector (Nx1) that contains the INPUT data collected from the plant.

- y: column vector (Nx1) that contains the OUTPUT data collected from the plant. If y is a Nx2 matrix, the two columns contain the output data collected in 2 different experiments (both experiments are made with the same input u(t); the two noise realizations must be uncorrelated).

- Mr: tf-object that represents the discrete transfer function of the reference model. The reference model Mr(z) describes the desired closed loop behaviour from the reference r(t) to the output y(t).

- B: column vector of tf-objects. The linear controller has the following structure: C(z,θ)= B'*θ, where B is a column vector of transfer functions, and θ is the vector of parameters.


Inputs (optional)

- W: tf-object of the weighting function W(z). If this parameter is empty [], the function automatically sets W(z) = 1.

- k: this parameter must be used only if the measured output y is noisy, and a single experiment is available; in this case this parameter sets the order of an ARX(k,k) model used to make an approximate model of the plant. Otherwise this parameter must be empty: [].

- optFilt: if this parameter is set to 'n', the optimal filter is disabled, and the filter L(z) is set to 1. If this parameter is empty ([]) the function uses the optimal VRFT filter.


Outputs

- C: tf-object, which represents the transfer function of the designed controller.