First order low pass filter (LPF) learning

Introduction: Voltage-based chain observers are of interest because of their clear physical concept and simplicity of use. However, the voltage chain observer contains a pure integral term, and the initial phase and DC bias of the product term can affect the integration result. Therefore, there are many improvements to the traditional voltage-based chain observer, and this article focuses on the use of a first-order low-pass filter to replace the pure integral link.

I. Introduction to low-pass filters

The filter is used as a frequency selection device and is an important concept in signal processing. Currently there are three main types of filters, namely low-pass filters, high-pass filters and band-pass filters, which can of course also be divided into two categories of active and passive filtering according to the working principle of the circuit.

1.1 Definition

The inductor blocks the passage of high-frequency signals while allowing low-frequency signals to pass through, while the capacitor has the opposite characteristic. A filter that allows signals to pass through an inductor or a filter that connects to ground through a capacitor has less attenuation for low frequency signals than for high frequency signals and is called a low pass filter.

1.2 Principle

The principle of using capacitors to pass high frequencies and block low frequencies, and inductors to pass low frequencies and block high frequencies. For the high frequencies that need to be cut off, the capacitor is used to absorb and the inductor to block it from passing through. For the low frequencies that need to be released, the capacitor is used to let it through with a high resistance and the inductor with a low resistance. The simplest low-pass filter consists of an inductor and a capacitor, as shown below.

Figure 1 RC passive low-pass filter

Figure 2 Amplitude-frequency characteristic curve of RC passive filter

II. Low-pass filter replacing pure integration

The expression for a voltage-based magnetic chain observer is

The transfer function of the low-pass filter is

2.1 Implementation of the low-pass filter

2.2 Simulation verification

Figure 3 Error caused by variable integration term at 150r/min

From Figure 3, it can be found that the variable motor parameter stator resistance causes the error caused by the product term, and the pure integral term causes the DC bias and phase error. Replacing the pure integral term with a low-pass filter improves the DC bias and initial value problems to some extent. However, with the LPF, there are still errors in magnitude and phase when comparing the observed values with the actual values.

III. Summary

When there are deviations in the motor parameters Rs, the conventional voltage-based chain observer (pure integration) suffers from DC bias and initial phase problems, resulting in large observer errors, especially in the low speed region. There are various ways to improve the existing voltage-based chain observer, and it is simpler to replace the pure integral link with other links, commonly low-pass filters, high-pass filters and compensation algorithms.

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