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# 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

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