Axial Torque Control with Cayley-Mapped Spring Rigidity Fluctuations
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Solution Overview
Problem
Existing shaft torque control apparatuses in engine bench systems have low control responsiveness due to conservative design methods that set gain parameters based on low spring rigidity, failing to account for significant fluctuations in spring rigidity, leading to unstable control.
Innovation Solution
A control apparatus design method that uses a fluctuation unit with a Cayley transform to map unbounded complex fluctuations to a bounded range, allowing for the design of a shaft torque control apparatus that can handle fluctuations in spring rigidity, achieving stable and high-response control by setting a phase adjustment transfer function as a positive real function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If gain parameters are set based on low spring rigidity to ensure stability, then control stability is improved, but control responsiveness deteriorates
Solution Approach 1:
The invention applies dynamic parameter adjustment by switching between different gain parameters (Kp1, Ki1 for low rigidity; Kp2, Ki2 for high rigidity) based on the detected spring rigidity state. This allows the control system to adapt its characteristics in real-time, achieving both stability when rigidity is low and responsiveness when rigidity is high, rather than being constrained to a single conservative setting.
Solution Approach 2:
The invention changes control parameters (gain values Kp and Ki) based on the detected spring rigidity condition. By detecting whether spring rigidity is below or above a threshold and selecting corresponding gain parameters, the system optimizes control performance for each operating condition, resolving the contradiction between stability and responsiveness.
2Reliability
If gain parameters are set based on low spring rigidity to ensure stability, then control stability is improved, but control performance deteriorates
Solution Approach 1:
The control system dynamically selects gain parameters based on detected spring rigidity, switching between conservative settings (low rigidity) and aggressive settings (high rigidity). This dynamic adaptation enables the system to achieve both stability and high control performance across varying operating conditions, rather than being limited to conservative performance.
Solution Approach 2:
By changing gain parameters (Kp, Ki) according to spring rigidity detection results, the system optimizes control performance for each rigidity condition. This parameter adaptation resolves the contradiction by enabling high performance when rigidity allows while maintaining stability when rigidity is low.
3Speed
If spring rigidity fluctuations are not accounted for in design, then control responsiveness is improved, but control stability deteriorates
Solution Approach 1:
The invention implements feedback by detecting spring rigidity in real-time and using this information to adjust gain parameters. This closed-loop approach ensures that control responsiveness is optimized for current rigidity conditions while maintaining stability through adaptive parameter selection, rather than relying on fixed conservative design assumptions.
Solution Approach 2:
The system changes control parameters based on detected spring rigidity fluctuations, adapting to actual operating conditions. This resolves the contradiction by enabling high responsiveness when rigidity is favorable while maintaining stability through parameter adjustment when rigidity changes, rather than being constrained by worst-case design assumptions.
Data Source
AI summary
In this control apparatus design method, a feedback control system comprises a generalization plant including a nominal plant N representing the input/output characteristic of an object to be controlled and a fluctuation unit Δ for making at least one model parameter included in the nominal plant N fluctuate, and a controller for applying input to the generalization plant P on the basis of output from the generalization plant P. The controller is designed so as to satisfy a prescribed design condition. The nominal plant N comprises a nominal value multiplication unit for multiplying an input signal η by a nominal value for the model parameter and an addition unit for adding a fluctuation output signal ξ from the fluctuation unit Δ and an output signal from the nominal value multiplication unit. Further, the fluctuation unit Δ generates the fluctuation output signal ξ using a mapping Δp obtained from a Cayley transform of unbounded complex fluctuation Δg.