How to tune PID for a Output(t) = k*Input(t) system?

Hi,

Here comes a very simple system: Output(t) = k * Input(t), And a control reference of 1 is to be achieved.

I am adding a feedback PID controller to the system. I have two questions:

1. Is it correct to say that adding a PID controller with P is enough?

2. Is P = 1/k? Since if we make P = 1/k, in theory, the adjustment will be (-1/k*error), then the system will be perfectly compensated.

Answer 1

[Arkadiy Turevskiy]

Plant model does not have an integrator in it, so you need an integral term to achieve zero steady-state error. In other words, if the controller is simply Kp, closed loop transfer function in Kp*K/(1+Kp*K). For Kp=1/K, closed loop transfer function is 1/K*K/(1+1/K*K)=1/2=0.5.

To get zero steady state error you need to add an intergral control. Integral control is all you really need in this case. Hope this helps.