Friction Compensation Saturation for Power Steering Instability
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Solution Overview
Problem
Existing power steering systems face instabilities when using friction models to compensate for friction, leading to suboptimal driver feedback and system performance.
Innovation Solution
A method that involves measuring or estimating speed between parts in a power steering system, using a friction model with a saturation step to ensure the absolute speed value remains below a saturation value defined by the speed, gains, and sampling period, thereby reducing or eliminating instabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a friction model is used to compensate for friction in a power steering system, then the impact of friction on the driver's feeling is reduced, but instabilities appear in the compensation
Solution Approach 1:
The patent applies preliminary anti-action by saturating the speed input to the friction model before it causes instability. The saturation function limits the speed value to prevent the system from entering an unstable regime, thereby counteracting the potential instability before it manifests. This is achieved by comparing the speed with a saturation threshold and capping it at that threshold level.
Solution Approach 2:
The patent changes the parameter of speed input to the friction model by applying saturation. Instead of using the raw speed value directly, the system transforms it through a saturation function that modifies the parameter range. This parameter transformation ensures the speed input remains within stable operating bounds while still providing accurate friction compensation for normal operating conditions.
2Adaptability or versatility
If the friction model processes high speed values, then the model can handle a wider range of operating conditions, but the compensation becomes unstable
Solution Approach 1:
The patent applies dynamics by implementing a dynamic saturation mechanism that adapts to different operating conditions. The saturation threshold is not fixed but is determined based on the current operating state, allowing the system to maintain stability across a wide range of speeds. The saturation function dynamically adjusts the speed input to prevent instability while preserving the full dynamic range needed for various operating conditions.
Solution Approach 2:
The system transforms the speed parameter through saturation to maintain stability. By changing the parameter representation from raw speed to saturated speed, the system can process a wide range of operating conditions without losing stability. The parameter transformation ensures that extreme values are capped while normal values pass through unchanged, maintaining both versatility and stability.
3Measurement precision
If digital implementation is used for friction compensation, then automation and precision are improved, but instabilities appear particularly when the function g(v) takes low values
Solution Approach 1:
The patent applies preliminary anti-action in digital implementation by pre-saturating the speed input before it enters the friction model calculations. This prevents numerical instabilities from arising during digital computation, particularly when g(v) takes low values. The saturation operation is performed as a preliminary step in the digital algorithm to counteract potential instability before it occurs during computation.
Solution Approach 2:
The patent uses a simple saturation function as a computationally inexpensive preprocessing step. This lightweight operation is applied to the speed input before more complex friction model calculations. The saturation function acts as a simple, low-cost protective measure that prevents numerical instability without requiring complex computational resources, making it ideal for real-time digital implementation.
Data Source
AI summary
Method for compensating for a friction between at least two parts, the method being based on a friction model (M), a speed (v) between at least one part and at least one other part of the at least two parts, the speed being measured, or estimated from a measurement, the speed (v) being input data of the model (M), the model (M) being based on an internal state (z) of friction, a time derivative (ż) of the internal state (z) being a function of said internal state and of the speed (v) and of a first gain (σ), the method comprising a step of saturation of the speed v at the input of the friction model, so that an absolute value |v| of the speed (v) remains lower than a saturation value, the saturation value being a function of the speed, of the first gain and of a second gain.