# Controls Project: Help needed finding 3rd order system

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;

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)?

• Rest assured, when you try wrapping it with sufficiently prompt control, any system will go right through 3rd-order and straight to multiple poles omygodomygod. Is this a thought experiment, or are you expected to haul physical objects into class? – TimWescott Nov 5 '19 at 0:38

The Temperature Control Lab is a third order system with heater 1 as the system input (controller output) and temperature 2 as the process variable. There are model development and control development modules in MATLAB and Python.

Model Development

• Simulate Step Response
• Convective Heat Transfer
• Radiative Heat Transfer
• Linearize Energy Balance
• First Order Plus Dead Time (Graphical)
• First Order Plus Dead Time (Regression)
• Impulse Response (Analytic Solution)
• State Space Simulation
• Second Order Response
• Higher (Third or Fifth) Order Response

Control Development

• Controller Design
• P-Only Control
• PI Control
• PID Control
• PI Control Tuning
• PID Control Tuning
• PID with Feedforward
• Heater Actuator
• Temperature Sensor
• Block Diagram
• On/Off Control

Here is the schedule for the course I developed with TCLab as the hands-on portion of the class. The topics cover almost all of your required topics.