Process Control/Direct Synthesis

[katy1995]

Homework Statement

Hi everyone, I am so stuck in this one homework problem. Any help is greatly appreciated
The question asks to use direct synthesis to design a controller for the transfer function below. The desire closed loop time constant is 1

Homework Equations

(-s+1)*e^(-s)/(5*s+1)^2

The Attempt at a Solution

So I set (y/yd) = e^(-s)/(s+1). However, when I plugged in the equation Kc = (y/yd)/((1-(y/yd)), I cannot simplify the equation to the form of a PID controller (Kc*(1+1/tau_i*s+tau_d*s)). I am guessing that my (y/yd) is wrong but I do not know how to fix. We learned about FOPDT or SOPDT in class but third order transfer function

 

[KataKoniK]

is not covered.

Hi there,

I can see why you are having trouble simplifying the equation to the form of a PID controller. The transfer function given is a third order function, which means it will require a more complex controller than a standard PID controller. In this case, you will need to use a PID controller with a third derivative term, also known as a PID3 controller.

To design this controller using direct synthesis, you will need to first determine the desired closed loop time constant, which in this case is 1. Then, you will need to use the direct synthesis method to calculate the controller gain, integral time constant, and derivative time constant.

To do this, you will need to follow these steps:

1. Set the desired closed loop time constant as 1.
2. Use the direct synthesis method to determine the controller gain, integral time constant, and derivative time constant.
3. Plug in these values into the PID3 controller equation: Kc*(1+1/tau_i*s+tau_d*s+tau_dd*s^3).
4. Simplify the equation and compare it to the given transfer function to ensure they match.

I hope this helps. Let me know if you need any further assistance. Good luck with your homework!