PI Controller for Harmonic Oscillators in Yaw Rate Sensors
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Solution Overview
Problem
Conventional PI controllers are inadequate for controlling oscillators with harmonic reference variables, as they require a constant reference variable and necessitate the use of demodulators and low-pass filters, limiting their applicability in scenarios with harmonic or periodic references.
Innovation Solution
A controller unit incorporating a PI controller with a dead time element, designed to handle harmonic reference variables, which includes a proportional transfer element and an integrating transfer element, and a dead time component to compensate for the system's conjugate complex pole, allowing for phase shifting and improved stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a conventional PI controller is used for controlling an oscillator with harmonic reference variables, then the controller requires a constant reference variable and necessitates the use of demodulators and low-pass filters, but this limits the applicability in scenarios with harmonic or periodic references and reduces the response speed
Solution Approach 1:
The patent transforms the control approach by changing the parameter domain from baseband (constant reference) to harmonic domain (time-varying reference at resonant frequency). The controller operates directly with harmonic reference variables at frequency ω0, eliminating the need for demodulation and low-pass filtering while maintaining control effectiveness.
Solution Approach 2:
The patent extracts and removes the demodulator and low-pass filter components from the control structure. By operating the PI controller directly in the harmonic domain, these intermediate signal processing stages are eliminated, simplifying the overall device while preserving the ability to handle harmonic reference variables.
2Reliability
If a low-pass filter is used to attenuate higher frequency components, then the mixing products at twice the resonant frequency are attenuated, but the bandwidth of the controller is limited and thus its reaction speed to changes in the force amplitude is reduced
Solution Approach 1:
The patent employs periodic action by using a harmonic reference variable at the resonant frequency ω0. The controller processes signals at this specific frequency through synchronized detection, allowing the system to respond quickly to force amplitude changes without requiring broad bandwidth filtering. The periodic nature of the reference enables selective amplification of the resonant frequency components while naturally rejecting other frequencies.
3Measurement precision
If a continuous PI controller with integral component is used, then high steady-state accuracy is achieved for constant reference input, but the controller cannot effectively handle harmonic reference variables
Solution Approach 1:
The patent transforms the static PI controller into a dynamic controller that adapts to harmonic reference variables. By modulating the reference input at the resonant frequency and using synchronous detection, the controller maintains its integral action benefits for accuracy while becoming responsive to time-varying harmonic signals. The controller parameters are optimized for the specific resonant frequency, enabling effective handling of harmonic references.
Data Source
Figure 1A~1B
Figure 1C
Figure 1D
AI summary
The invention relates to a controller unit (220) comprising a PI controller (225, 325) for harmonic reference variables. The transmission function of the PI controller (225, 325) for harmonic reference variables has a conjugate complex pole at a control loop frequency ωr in the s-plane or a pole at e±jω,T in the z-plane, wherein T is the sampling time of a discrete input signal of the PI controller (225, 325) and ωr is greater than 0. The control loop frequency ωr is chosen to be equal to the resonant circuit frequency ω0 of an oscillator (190). The controller parameters are determined for example by pole-zero cancellation. The controller unit (220) enables for example control of harmonic oscillators acting over a wide band in yaw rate sensors (500, 505).