How can I control the current in an RL circuit using state space modeling?

[nbsundaram]

Hi.. This is sundaram, I'm trying to learn state space modeling, I'm trying to model the simple RL series circuit, to control/read the current flowing through inductor.

I could find the way to monitor the voltage across inductor. as below

x'=(u - Rx)*(1/L)
y=(u - Rx)

where:
x => i (current), x' => di/dt
R=> resistance & L=> inductance
u is the applied voltage
y=> the voltage across inductor


can anyone help me in framing the state space equation to control I

Thanks in advance..!
Sundaram..

 

[meBigGuy]

I'm too lazy to figure out and rewrite your variables.

Rewrite it with I, V, and R and subscripts.

I'm not sure what you mean by state space, but maybe it will be clear when you rewrite the equations.

 

[weavertri]

hello sundaram...
you did right... let me call the current that is flowing through the inductor i_L = x₁
using kirchhoff voltage law you got

x₁' = u/L - (R/L)*X₁

to "control" your current you just need to use y = x₁

in MATLAB you can use
A = [-R/L]
B = [u/L]
C = [1]
D = 0
sys = ss(A,B,C,D)
step(sys)
it will show you the step response of your system using the current as output. :D