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)?

  • $\begingroup$ 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? $\endgroup$
    – TimWescott
    Nov 5, 2019 at 0:38

1 Answer 1


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.


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