1. Indirect Approach for Closed-loop System Identification with Fractional Models
Tiebiao Zhao
MESA (Mechatronics, Embedded Systems and Automation)Lab
School of Engineering,
University of California, Merced
E: Phone:
June 30, Monday 4:00-6:00 PM
Applied Fractional Calculus Workshop MESA UCMerced

2. Limitations of Open-loop System Identification
Unstable open-loop system
Subject to significant drift in open-loop operation
The production recommendation do not allow the regulators to be removed
06/16/2014
AFC Workshop UCMerced

3. Identifying a closed-loop SISO
Indirect approach
Direct approach
Joint input/output approach
06/16/2014
AFC Workshop UCMerced

4. AFC Workshop Series @ MESALAB @ UCMerced
Assumption
All differentiation orders are supposed known a priori.
Only the coefficients of the closed-loop fractional transfer function are estimated.
06/16/2014
AFC Workshop UCMerced

5. AFC Workshop Series @ MESALAB @ UCMerced
Proposed Method
Indirect approach
A linear transformation is applied to the input and output signals to avoid the noise amplification.
06/16/2014
AFC Workshop UCMerced

6. Closed-loop parameter estimation
Discretization and linearization
Parameter estimation using ordinary least squares
algorithm (OLS)
Parameter estimation using recursive least squares
algorithm (RLS)
The Iterative Least Squares (IOLS and IRLS)
06/16/2014
AFC Workshop UCMerced

7. AFC Workshop Series @ MESALAB @ UCMerced
06/16/2014
AFC Workshop UCMerced

8. AFC Workshop Series @ MESALAB @ UCMerced
06/16/2014
AFC Workshop UCMerced

9. Open-loop Parameter Calculation
06/16/2014
AFC Workshop UCMerced

10. AFC Workshop Series @ MESALAB @ UCMerced
Results
Pseudo random binary sequence (PRBS) applied to the closed-loop system
Output corrupted by an additive gaussien white noise
06/16/2014
AFC Workshop UCMerced

11. AFC Workshop Series @ MESALAB @ UCMerced
Remarks
The results are biased at high levels of SNR. Future method like instrumental variable method.
How to identify fractional orders in closed-loop systems?
Is it possible to apply this method to obtain the parameters for online-tuning of the controllers?
06/16/2014
AFC Workshop UCMerced

12. Combined Fractional Feedback-Feedforward Controller Design for Electrical Drives
Tiebiao Zhao
MESA (Mechatronics, Embedded Systems and Automation)Lab
School of Engineering,
University of California, Merced
E: Phone:
June 30, Monday 4:00-6:00 PM
Applied Fractional Calculus Workshop MESA UCMerced

13. Scheme of the Speed Control System
Fractional PI
Set-point filter
Decoupling network
06/16/2014
AFC Workshop UCMerced

14. Position and speed control of DC-motor
06/16/2014
AFC Workshop UCMerced

15. AFC Workshop Series @ MESALAB @ UCMerced
Unfiltered response
Response with integer filters
Fractional filters
06/16/2014
AFC Workshop UCMerced

16. AFC Workshop Series @ MESALAB @ UCMerced
Remarks
Apply this method in UAV including fractional PID and fractional feed-forward set-point filter
06/16/2014
AFC Workshop UCMerced