Low-frequency (DC) gain of LTI system
k = dcgain(sys)
k = dcgain(sys)
computes the DC gain
k of the LTI model
The continuous-time DC gain is the transfer function value at the frequency s = 0. For state-space models with matrices (A, B, C, D), this value is
K = D – CA–1B
The discrete-time DC gain is the transfer function value at z = 1. For state-space models with matrices (A, B, C, D), this value is
K = D + C(I – A)–1B
Create the following 2-input 2-output continuous-time transfer function.
H = [1 tf([1 -1],[1 1 3]) ; tf(1,[1 1]) tf([1 2],[1 -3])];
Compute the DC gain of the transfer function. For continuous-time models, the DC gain is the transfer function value at the frequency
s = 0.
K = dcgain(H)
K = 2×2 1.0000 -0.3333 1.0000 -0.6667
The DC gain for each input-output pair is returned.
K(i,j) is the DC gain from input j to output i.
Load the estimation data.
load iddata1 z1
z1 is an
iddata object containing the input-output estimation data.
Estimate a process model from the data. Specify that the model has one pole and a time delay term.
sys = procest(z1,'P1D')
sys = Process model with transfer function: Kp G(s) = ---------- * exp(-Td*s) 1+Tp1*s Kp = 9.0754 Tp1 = 0.25655 Td = 0.068 Parameterization: 'P1D' Number of free coefficients: 3 Use "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using PROCEST on time domain data "z1". Fit to estimation data: 44.85% FPE: 6.02, MSE: 5.901
Compute the DC gain of the model.
K = dcgain(sys)
K = 9.0754
This DC gain value is stored in the
Kp property of
ans = 9.0754
The DC gain is infinite for systems with integrators.