Pseudo-random binary sequence closed-loop system identification error with integration control

This paper studies the closed-loop system identification (ID) error when a dynamic integral controller is used. Pseudo-random binary sequence (PRBS) q-Markov covariance equivalent realization (Cover) is used to identify the closed-loop model, and the open-loop model is obtained based upon the identified closed-loop model. Accurate open-loop models were obtained using PRBS q-Markov Cover system ID directly. For closed-loop system ID, accurate open-loop identified models were obtained with a proportional controller, but when a dynamic controller was used, low-frequency system ID error was found. This study suggests that extra caution is required when a dynamic integral controller is used for closed-loop system identification. The closed-loop identification framework also has significant effects on closed-loop identification error. Both first- and second-order examples are provided in this paper.

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Closed-Loop System Identification Based on Data Correlation

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4025158 ◽

2013 ◽

Vol 136 (1) ◽

Cited By ~ 7

Author(s):

Hassene Jammoussi ◽

Matthew Franchek ◽

Karolos Grigoriadis ◽

Martin Books

Keyword(s):

System Identification ◽

Instrumental Variables ◽

Closed Loop ◽

Linear Time ◽

Open Loop ◽

Loop System ◽

Loop Model ◽

Closed Loop System ◽

Engine Operation ◽

Single Input Single Output

A closed-loop system identification method is developed to estimate the parameters of a single input single output (SISO) linear time invariant system (LTI) operating within a feedback loop. The method uses the reference command in addition to the input–output data and establishes a correlation framework to structure the system. The correlation-based method is capable of delivering consistent estimates provided that the specific conditions on the signals are met. The method parallels the instrumental variables four step algorithm (IV4) and is comprised of three steps. First a model is estimated using cross correlation calculations between the reference input signal and the control and measured output signals. In the second step, a prefilter is identified to reduce estimation bias. In the final step, the prefilter, the instrumental variables and the measured signals are employed to estimate the final model. A consistency proof is provided for the proposed estimation process. The method is demonstrated on two examples. The first uses data collected from a diesel engine operation, and an open-loop model relating fueling to engine speed is sought. The identification process is complicated by the presence of nonmeasurable external torque disturbances and stochastic sensor noise. The second example uses data obtained from a time domain simulation of a closed-loop system where high levels of nonmeasured noise and disturbances were considered and a comparison with existing methods is made.

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Discrete-Time Closed-Loop Model Identification of Fixed-Structure Unstable Multivariable Systems

Volume 9: Mechanical Systems and Control, Parts A, B, and C ◽

10.1115/imece2007-41834 ◽

2007 ◽

Author(s):

Huzefa Shakir ◽

Won-Jong Kim

Keyword(s):

System Identification ◽

Discrete Time ◽

Closed Loop ◽

Model Identification ◽

Order Reduction ◽

Loop System ◽

Loop Model ◽

Frequency Range ◽

Closed Loop System ◽

Closed Loop Identification

This paper presents improved empirical representations of a general class of open-loop unstable systems using closed-loop system identification. A multi-axis magnetic-levitation (maglev) nanopositioning system with an extended translational travel range is used as a test bed to verify the closed-loop system-identification method proposed in this paper. A closed-loop identification technique employing the Box-Jenkins (BJ) method and a known controller structure is developed for model identification and validation. Direct and coupling transfer functions (TFs) are then derived from the experimental input-output time sequences and the knowledge of controller dynamics. A persistently excited signal with a frequency range of [0, 2500] Hz is used as a reference input. An order-reduction algorithm is applied to obtain TFs with predefined orders, which give a close match in the frequency range of interest without missing any significant plant dynamics. The entire analysis is performed in the discrete-time domain in order to avoid any errors due to continuous-to-discrete-time conversion and vice versa. Continuous-time TFs are used only for order-reduction and performance analysis of the identified plant TFs. Experimental results in the time as well as frequency domains verified the accuracy of the plant TFs and demonstrated the effectiveness of the closed-loop identification and order-reduction methods.

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Algorithm for Closed Loop System Identification Based on Data Correlation

ASME 2008 Dynamic Systems and Control Conference, Parts A and B ◽

10.1115/dscc2008-2162 ◽

2008 ◽

Author(s):

H. Jammoussi ◽

M. A. Franchek ◽

K. Grigoriadis ◽

M. Books

Keyword(s):

System Identification ◽

Instrumental Variables ◽

Closed Loop ◽

Open Loop ◽

Loop System ◽

Loop Model ◽

Closed Loop System ◽

Final Model ◽

Cross Covariance ◽

Step Algorithm

A closed loop system identification method is developed in which estimation bias from sensor noise and external disturbances is minimized. The method, based on the instrumental variables four step algorithm (IV4), uses three steps. The first step estimates a model using cross covariance calculations between the reference input signal and the control and measured output signals. The second step employs the prefilter identification process from the IV4 process. The third and final step uses the prefilter, the instrumental variables and the reference, control and output signals to estimate the final model. The method is demonstrated on a diesel engine where an open loop model relating fueling to engine speed is sought. The identification example is complicated by the presence of nonmeasurable external torque disturbances due to vehicle accessories.

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