System Dynamics Describability Testing for Sensor-Based Control
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Solution Overview
Problem
Existing control systems for complex technical systems struggle to accurately predict and control dynamics due to incomplete description of system behavior by sensor data and differential equations, leading to potential chaotic deviations.
Innovation Solution
A method is developed to test the completeness of the description of system dynamics using multiple sensors and differential equations, involving the establishment of a dynamics function, initial and boundary conditions, and analytical solvability testing to determine if the equations fully describe the system's behavior.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If complex technical systems are controlled using sensor data and differential equations, then control functionality is provided, but the system behavior may not be completely described leading to unpredictable chaotic deviations
Solution Approach 1:
The invention performs preliminary testing of analytical solvability before actual control operations. By establishing differential equations from sensor data and testing whether they can be solved analytically, the system proactively identifies situations where the sensor configuration and model completely describe system dynamics, preventing unpredictable behavior before it occurs.
Solution Approach 2:
The invention replaces physical trial-and-error testing with mathematical analysis. Instead of relying on extensive physical experiments to verify system predictability, the method uses analytical solvability testing of differential equations to determine whether sensor data and models completely describe system behavior, substituting mechanical testing with computational verification.
2Reliability
If extensive physical testing is performed to verify complete describability of system dynamics, then reliability is improved, but time consumption and energy usage increase
Solution Approach 1:
The invention replaces extensive physical testing with mathematical analytical solvability testing. By determining whether differential equations derived from sensor data can be solved analytically, the method verifies complete describability of system dynamics through computational analysis rather than time-consuming physical experiments.
Solution Approach 2:
The invention creates a mathematical model (differential equations) that copies and represents the physical system's behavior. By testing the solvability of this mathematical representation, the system verifies whether sensor data and models completely describe actual system dynamics without needing to physically test every scenario.
3Measurement precision
If analytical solvability testing is performed to determine complete describability, then measurement precision is improved, but computational complexity increases
Solution Approach 1:
The invention segments the verification process into distinct steps: establishing sensor data acquisition, forming differential equations, and testing analytical solvability. This segmentation allows the computational complexity to be managed as a structured sequence of operations rather than a monolithic complex process.
Data Source
AI summary
A method for testing to what extent the dynamics of a technical system starting from a predetermined operation situation are completely described through the acquisition of the state of the technical system with multiple sensors in combination with at least one differential equation. The method includes establishing a dynamics function describing the predetermined operation situation and dynamics of the technical system; forming the at least one differential equation from the dynamics function; ascertaining initial conditions, boundary conditions and/or regional conditions based on the predetermined operation situation for solving the at least one differential equation; testing whether the differential equation is analytically solvable; and in response to a positive determination, determining that the acquisition with the sensors and the at least one differential equation completely describe the dynamics of the system.