A novel algorithm for linear parameter varying identification of Hammerstein systems with time-varying nonlinearities
Summary
This study introduces a new method to identify Hammerstein systems with time-varying nonlinearities. The technique provides accurate component estimates for complex systems, validated in biomechanical models.
Area of Science:
- Systems Engineering
- Control Theory
- Biomedical Engineering
Background:
- Hammerstein systems, characterized by a static nonlinearity followed by a linear time-invariant element, are common in control engineering.
- Accurate identification of systems with time-varying (TV) nonlinearities is challenging but crucial for effective modeling and control.
- Existing methods often struggle to deconvolve the static and dynamic components in TV Hammerstein systems.
Purpose of the Study:
- To develop and validate a novel subspace identification method for Hammerstein systems featuring time-varying static nonlinearities.
- To enable the separate estimation of the time-invariant linear dynamics and the time-varying static nonlinear components.
- To demonstrate the applicability of the proposed method in biomechanical contexts.
Main Methods:
- Development of a linear parameter varying (LPV) state-space representation for the target Hammerstein systems.
- Application of a subspace identification technique to estimate the individual Hammerstein system components.
- Validation using simulated data from a time-varying ankle joint reflex stiffness model.
Main Results:
- The proposed subspace identification technique successfully estimated the individual Hammerstein components.
- Simulated data validation confirmed the method's ability to handle time-varying nonlinearities.
- Pilot experiments on ankle joint reflex EMG responses during walking showed systematic changes in nonlinearity with joint position trajectory.
Conclusions:
- The novel LPV-based subspace identification method effectively characterizes Hammerstein systems with time-varying nonlinearities.
- The technique offers a robust approach for dissecting complex nonlinear dynamic systems.
- This method has potential applications in understanding and modeling biological systems with changing physiological parameters.
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