Implicit Euler Method for Engine Air System Simulation
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Solution Overview
Problem
Existing methods for real-time calculation of boost pressure and air mass flow in internal combustion engine air systems, particularly downstream of the control flap, suffer from dynamic inaccuracies and instability, leading to increased computational time and inaccuracies due to the use of explicit Euler methods, which require small time steps and result in noise-infested signals.
Innovation Solution
The method employs an implicit method for quantizing differential equations, allowing stable calculations with larger time steps and improving accuracy by using the currently stored mass in the air system and approximating nonlinear equations with polynomial functions, reducing the need for filtering and enhancing computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the explicit Euler method is used for quantizing differential equations, then the calculation can be performed with simple algorithms, but the dynamic accuracy deteriorates and instability occurs in certain operating ranges
Solution Approach 1:
The patent changes the fundamental parameter of the calculation method from explicit Euler method to implicit Euler method. This parameter change transforms the quantization approach fundamentally, allowing the use of larger time steps while maintaining stability and improving dynamic accuracy. The implicit method uses future state values in the calculation, which provides better numerical stability and accuracy for the differential equations governing the air system.
2Stability of the object's composition
If very small time steps are used to achieve stability, then the stability range is improved, but the computational time requirements increase considerably
Solution Approach 1:
The patent changes the time step parameter from very small values to larger values by switching to the implicit Euler method. This parameter change allows the calculation to remain stable even with larger time steps, thereby reducing the total number of calculation steps required and decreasing computational time while maintaining stability.
3Ease of operation
If the explicit Euler method is used, then the algorithm is simple to implement, but computational capacity of the engine control unit is tied down
Solution Approach 1:
The patent changes the computational method parameter from explicit to implicit Euler method. Although the implicit method requires solving equations iteratively, it allows larger time steps that reduce the total number of calculations needed. This parameter change balances implementation complexity with reduced computational capacity requirements by performing fewer, more efficient calculation cycles.
4Measurement precision
If additional filtering of air mass signal is applied to reduce noise, then the signal quality is improved, but the achievable dynamics are impaired
Solution Approach 1:
The patent changes the fundamental calculation method parameter to implicit Euler method, which inherently provides more accurate and stable results without requiring additional filtering. This parameter change improves signal quality through better numerical accuracy while preserving dynamics by avoiding the smoothing effect that filtering introduces, thus resolving the contradiction between signal quality and dynamic response.
Data Source
AI summary
A method for determining at least one air system variable in an air supply system of an internal combustion engine in successive, discrete calculation steps, a differential equation being provided with respect to the air system variable based on measured and/or modeled variables, which describe conditions in the air supply system, a difference equation being formed for the quantization of the differential equation according to an implicit method, and the difference equation being solved in each discrete calculation step, in order to obtain the air system variable.