Multirate System Frequency Response Identification

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Solution Overview

Problem

In multiplexed-input multirate systems, such as head positioning control systems for magnetic disk devices, existing methods cannot directly identify the frequency response of a controlled object at the sampling period of the control input side due to down-sampling of control output, necessitating an algorithm that considers the unique features of these systems.

Innovation Solution

An identification algorithm using an M-series pseudo white signal and an FIR model is employed, where the sampling period of control output is even multiples of the control input, generating an M-series signal and performing discrete Fourier transform to estimate the impulse response and frequency response of the controlled object.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If usual frequency response identification method is applied, then identification can be performed, but it cannot directly identify frequency response at control input-side sampling period due to down-sampling of control output

Engineering Contradiction:

Improvefrequency response identification accuracyVSAvoidapplicability to multirate system

Core Design Contradiction:

Measurement precisionVSAdaptability or versatility

Solution Approach 1:

The patent changes the sampling period parameter from the control output side to the control input side. By defining the sampling period Ti at the control input side and using the relationship Ti = T/P where T is the control output sampling period, the method enables frequency response identification at the higher-rate input sampling period, resolving the adaptability issue in multirate systems.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent performs preliminary actions by generating a test signal at the control input side before the down-sampling occurs. The test signal is input to the controlled object at the higher-rate sampling period Ti, and the output is captured at the lower-rate sampling period T, allowing the frequency response to be identified at the input rate through the known relationship between the sampling periods.

Inventive Principle:

Principle #10Preliminary action

2Productivity

If high-speed frequency response identification is performed, then identification speed increases, but computational load increases

Engineering Contradiction:

Improveidentification speedVSAvoidcomputational load

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The patent applies local quality by focusing the identification process on specific frequency bands of interest rather than performing a full spectral analysis. The test signal is designed to excite specific frequency ranges, and the frequency response is identified only at these target frequencies, reducing the computational load while maintaining identification speed for the critical frequency bands.

Inventive Principle:

Principle #3Local quality

Solution Approach 2:

The patent uses partial action by capturing output data at intervals that correspond to the lower sampling rate T rather than continuously at the higher rate. By using the relationship between the sampling periods and capturing data at the appropriate intervals, the method achieves high-speed identification without requiring full-rate data processing, thus reducing computational complexity.

Inventive Principle:

Principle #16Partial or excessive action

3Ease of operation

If frequency response is identified at control output sampling period, then down-sampled output can be used, but frequency response at control input sampling period cannot be obtained

Engineering Contradiction:

Improveoperational simplicityVSAvoidfrequency response information

Core Design Contradiction:

Ease of operationVSLoss of information

Solution Approach 1:

The patent introduces the test signal as an intermediary that bridges the input and output sides. The test signal is generated at the control input side, passed through the controlled object, and the output is captured at the control output side. By using the known relationship between the sampling periods Ti and T, the frequency response at the input rate is recovered from the output measurements, preventing information loss.

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

Instead of trying to up-sample the down-sampled output to recover the high-rate frequency response (which would be complex and lossy), the patent inverts the approach by directly measuring at the lower rate and using the mathematical relationship between sampling periods to compute the high-rate frequency response. This inversion simplifies the process while recovering the lost information.

Inventive Principle:

Principle #13The other way round (Inversion)

Data Source

PatentUS9093114B2Method for identifying high-speed frequency response of multirate system and apparatus therefor

Publication Date: 2015.07.28 KK TOSHIBA

AI summary

There is provided with a method of identifying a frequency response of a controlled object at a sampling period of control input in a multiplexed-input multirate system in which a sampling period of control output is even “P” multiples of the sampling period of control input wherein the control object is represented by FIR filter, an M-series signal corresponding to an acquisition data length Mp×P−1 is generated, the Mp indicates a period of the M-series signal, an impulse response value of the controlled object is estimated based on the M-series signal and output data outputted from the controlled object by inputting the M-series signal thereto, and the frequency response of the controlled object is identified by performing a discrete Fourier transform on the impulse response value.