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Identifiability of fractional order systems using input output frequency contents
Peyman Nazarian1, Mohammad Haeri, Mohammad Saleh Tavazoei
1Electrical Engineering Department, Islamic Azad University, Science and Research Branch, Tehran, Iran. pay_naz@yahoo.com
ISA Transactions
|December 17, 2009
Summary
This study shows that fractional order systems become less identifiable with smaller fractional orders (alpha), even with rich inputs. This identifiability issue is exacerbated by noise and small alpha values.
Area of Science:
- Control Systems Engineering
- Signal Processing
- Mathematical Modeling
Background:
- Fractional order systems are increasingly used in modeling complex dynamics.
- System identifiability is crucial for accurate model development and control.
- Understanding the limitations of identifiability in fractional order systems is essential.
Purpose of the Study:
- To investigate the identifiability of fractional order systems based on input and output frequency content.
- To analytically study the impact of the commensurate order (alpha) on model structure and parameter identifiability.
- To identify the conditions under which identifiability is compromised.
Main Methods:
- Analytical study of fractional order system identifiability.
- Frequency domain analysis of input and output signals.
- Investigation of the influence of the fractional order (alpha) on identifiability metrics.
Main Results:
- Identifiability of both model structure and parameters significantly decreases for smaller values of alpha.
- This reduction in identifiability persists even with rich input signals and when the system belongs to the model set.
- The problem is more pronounced with smaller alpha and noisy measurements.
Conclusions:
- The reduced identifiability stems from the inability to distinguish between model set members due to precision limitations.
- Smaller fractional orders (alpha) present significant challenges for system identification.
- Robust identification methods are needed for fractional order systems, especially in noisy conditions.
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