I'm in need of help finding a third-order or higher system in which I can derive a transfer function. We have a class project in which we need to find a real-life example of the system that equates to a 3rd order system or higher.
The problem that I have is that I do not know what a third-order system looks like in real life. I can find a lot of examples of 2nd order systems (acceleration, velocity, and displacement). But no 3rd order! Help!
Step 1: Find a system of interest to you, discuss why this system is of specific interest to you and why this is a good topic for the class project;
Step 2: Model the system in three forms: differential equations, transfer function, and state-space representation. Note if the system is nonlinear, please linearize it first;
Step 3: Find and plot system output under step input and another input of your choice. Discuss the physical implications;
Step 4: Study the system stability, discuss the physical meaning of instability in your case;
Step 5: Assume a negative unity feedback system, two possible controllers:
$\ C_1(s)=k_0 $
$\ C_2s= k_p + k_ds+k_i \frac 1s $
• Design the two controllers, so that the system is stable.
• With all your designed control parameter values, what are the feedback system’s output under step input and another input of your choice?
• What are the steady-state errors under the four cases (2 controllers, 2 inputs)?