Tiebiao Zhao MESA (Mechatronics, Embedded Systems and Automation)Lab

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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: tzhao3@ucmerced.edu Phone: 209-2015212 June 30, 2014. Monday 4:00-6:00 PM Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

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 Series @ MESALAB @ UCMerced

Identifying a closed-loop SISO Indirect approach Direct approach Joint input/output approach 06/16/2014 AFC Workshop Series @ MESALAB @ UCMerced

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 Series @ MESALAB @ UCMerced

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 Series @ MESALAB @ UCMerced

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 Series @ MESALAB @ UCMerced

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

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

Open-loop Parameter Calculation 06/16/2014 AFC Workshop Series @ MESALAB @ UCMerced

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 Series @ MESALAB @ UCMerced

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 Series @ MESALAB @ UCMerced

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: tzhao3@ucmerced.edu Phone: 209-2015212 June 30, 2014. Monday 4:00-6:00 PM Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

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

Position and speed control of DC-motor 06/16/2014 AFC Workshop Series @ MESALAB @ UCMerced

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

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 Series @ MESALAB @ UCMerced