# What is the difference between Noise, Disturbance, and Uncertainty??

In control engineering, we often hear about these terms: *Noise*, *Disturbance*, and *Uncertainty*. Are these terms have the same meaning? If so, why do we call with different terms? Or if different meanings, what is the impact of these terms in our system? I think some of the above questions quite often come to our brain, especially if you are a control engineering student. So, in this article, I will try to make as clear as possible about these terms.

We start with the **noise**. This term is quite familiar in our ears even if you are not a control engineering student. In control engineering, we need to pay attention to the noise, especially if we are using the controller with a derivative term. For instance, if we used Proportional-Derivative (PD) controller, then we need to add extra work such as designing a low-pass filter to suppress the noise effect on the PD controller. Noise is usually high-frequency that is why we sometimes used a low-pass filter. Noise can come from anywhere in different ways, such as from sensor reading, from connector or cable, environment, and so on. Because of that, you may often hear about these terms: *measurement *noise, *output *noise, and *input *noise. Same as its name, measurement noise can be found in sensor reading and the same for the input and output noise which effect in input and output of our system. If you connected your microphone with a speaker, sometimes, even if you are not speaking in your microphone, there is always some tiny sound from your speaker. It occurred due to noise. Noise also has a different spectrum that you may hear about *white* noise, *pink* noise, or *brown* noise. Nevertheless, we will discuss these kinds of specific noise in other posts. Now, is it possible the noise makes your system to be unstable? The answer is depending on how well you designed your controller. If your controller is very sensitive to a noisy environment, then noise can be destroying your system.

The **uncertainty** or sometimes called variation. According to [1], uncertainty is the error between a real system and a mathematical model. For instance, the car is a highly complex nonlinear system, however, we assumed that the mathematical model of the car is linear for simplicity. This will generate inaccurate behavior between the real car and its mathematical model. Moreover, uncertainty can also come from manufacturing or industries. For illustration, if a car manufacturer has produced a hundred cars, however, all cars do not 100% identically. It is always slightly different between each vehicle. Another example, the mathematical model of the truck trailer without a load will be completely different with a full load. Do you have another example?? Please drop it in a comment. If you control engineering students, then you may have ever heard about *structured* uncertainty and *unstructured* uncertainty. First time heard that, don’t worry :). You will absolutely know that if you learn about *Robust* control. So, for now, don’t think about it too much. If you really want to know about it, drop your comment and I will really pleasure to make an article about it. From my explanation of uncertainty, you can conclude by yourself how significant the uncertainty influences your system.

Based on [1], **disturbance** is a signal that tends to adversely affect the value of the output of a system. If a disturbance is generated within the system, it is called *internal*, while an *external* disturbance is generated outside the system and is an input. This term frequently appears when you are reading a conference paper, journal, magazine, or some paper that specifically talks about the control system. For autonomous vehicles, the disturbance can be road bumps (external), ascending and descending roads (external), wind gusts (external), inaccurate low-level controllers (internal), and so on. In addition, you may also have ever heard about input disturbance and output disturbance. Input disturbance may affect the mathematical model of your plant (system dynamic) because it is added before the plant. For instance, unmodelled actuator dynamics, wind gust, time-varying parameter, and uncertainty. The output disturbance will affect the output signal in your system such as noise in sensor reading. The disturbance can be surely destabilized your system. That is why when you are designing a controller, you need to take into consideration the disturbance such as the magnitude of disturbance. You should remember that your controller should be designed in a certain way to be able to handle a certain disturbance.

The input disturbance is indicated by *d_i* and output disturbance is referred by *d_o*.

**Note:** if you feel something incorrect about my explanation in this article, please drop your opinion in a comment. It is a great pleasure for me to have a nice suggestion from an expert.

Ref:

[1] K. Ogata, *Modern control engineering*. Prentice hall Upper Saddle River, NJ, 2010.

[2] R. Vilanova, V. M. Alfaro, A. Visioli, and M. Barbu, “Considerations on the disturbance attenuation problem for PI/PID controllers for a generic load disturbance dynamics,” in *2017 22nd IEEE International Conference on Emerging Technologies and Factory Automation (ETFA)*, 2017: IEEE, pp. 1–8.