(Control) Derivative filter and discrete model

Thread starter Leo Liu
Start date Nov 15, 2023
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Modeling Simulink

Nov 15, 2023

Leo Liu

Hi I am back :).

I have been doing some Simulink modeling for a project. I modeled it with a discrete system due to the controller rate. I have noticed that for all the discrete system I have tried, adding a derivative filter not only improves the performance (smaller settling time), but it is sometimes also necessary.

The following example involving a discrete PID and a 2nd order discrete transfer function illustrates the behaviour:

Autotune with no derivative filter N:

Autotune with derivative filter N:

I was wondering why such a behaviour would occur. Also, should I model the transfer function as discrete or continuous system for a physical system like F=ma? Any input will be appreciated.

Related to (Control) Derivative filter and discrete model

What is a derivative filter in control systems?

A derivative filter in control systems is a component that approximates the derivative of a signal. It is often used to predict the future behavior of a system by analyzing the rate of change of the system's output. This can help improve the performance of a control system by providing anticipatory actions to counteract changes in the system.

Why is a discrete model important in control systems?

A discrete model is important in control systems because it allows the system to be implemented in digital controllers, which are prevalent in modern control applications. Discrete models enable the use of digital computation and sampling techniques, making it easier to design, analyze, and implement control algorithms on digital hardware.

How do you implement a derivative filter in a discrete model?

To implement a derivative filter in a discrete model, you typically use numerical differentiation techniques such as backward difference, forward difference, or central difference methods. These methods approximate the derivative by calculating the difference between sampled data points over a specified time interval. The choice of method depends on the desired accuracy and stability of the filter.

What are the challenges of using derivative filters in discrete models?

The main challenges of using derivative filters in discrete models include noise amplification and stability issues. Derivatives tend to amplify high-frequency noise in the signal, which can lead to erroneous control actions. Additionally, improper implementation of the derivative filter can lead to instability in the control system. Careful design, such as using low-pass filtering and appropriate sampling rates, is required to mitigate these challenges.

How can you mitigate noise issues in derivative filters for discrete models?

To mitigate noise issues in derivative filters for discrete models, you can use techniques such as low-pass filtering to smooth the input signal before differentiation. Another approach is to design the derivative filter with a built-in noise attenuation mechanism, such as using a higher-order filter or incorporating a regularization term. Additionally, choosing an appropriate sampling rate that balances the trade-off between noise sensitivity and temporal resolution can help reduce the impact of noise.