Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

dcgain

Low-frequency (DC) gain of LTI system

Syntax

k = dcgain(sys)

Description

k = dcgain(sys) computes the DC gain k of the LTI model sys.

Continuous Time

The continuous-time DC gain is the transfer function value at the frequency s = 0. For state-space models with matrices (ABCD), this value is

K = D – CA–1B

Discrete Time

The discrete-time DC gain is the transfer function value at z = 1. For state-space models with matrices (ABCD), this value is

K = D + C(I – A)–1B

Examples

collapse all

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 = 

    1.0000   -0.3333
    1.0000   -0.6667

The DC gain for each input-output pair is returned. Kij is the DC gain corresponding to input i and output j.

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 sys.

sys.Kp
ans = 9.0754

Tips

The DC gain is infinite for systems with integrators.

See Also

|

Introduced in R2012a

Was this topic helpful?