# Control Systems: 3rd order system project [duplicate]

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!

Project guidelines:

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

• Pneumatic linear rails fromm festo come to mind… Jan 17, 2022 at 9:14
• 3 (connected) water tanks. each will contribute one state (water level in that tank). Or, cascade a second order system and a first order system to get a third order system;
– AJN
Jan 17, 2022 at 11:58
• Newton's second law always gives you two, so anything where a force acts to move an object gets you 2/3 of the way there. Use your imagination for the last one... Jan 17, 2022 at 14:15
• One that pops in my mind is the transfer function of the voltage supplied to a DC motor and the angle of the output. Here, the torque applied to the mass is a function of the current through the circuit. However, as a DC motor is also a coil, the current is equal to the difference of the voltage. This adds (albeit a very large) pole. In mechanical terms, this means the change in angular acceleration (angular jerk) is limited by the voltage you can supply. Jan 18, 2022 at 10:55