Running discrete Fourier transform and its applications in control loop performance assessment

Abstract

Control loop performance assessment (CLPA) techniques are crucial for optimizing any plant or machine. They can bring huge energy and material savings and increase product quality. In this paper, the employment of running discrete Fourier transform (RDFT) in CLPA field is discussed. The first part of the paper documents the development of new RDFT function block which is suitable for CLPA. The paper focuses on implementation aspects whose aim is to minimize the number of arithmetic operations and to avoid numerical errors which are cumulated in many algorithms when running over longer time period. Then three RDFT applications are introduced. They are mostly dedicated to CLPA area: The changes in RDFT output help to detect increasing valve stiction or reveal a cause of oscillations in the loop. RDFT can be also used for continuous monitoring of process changes at particular frequencies. The most advanced problem presented is the estimation of special performance indices. More specifically, key samples of sensitivity function are gained and compared to the reference ones. Inspired by the model free design techniques, only a minimum a priori information about the process is assumed. The authors believe that the presented ideas will be suitable for both academic and industrial sphere.

Statistical measures for proportional–integral–derivative control quality: Simulations and industrial data

“…Time measures-mean square error (MSE), integral absolute error (IAE), amplitude index (AMP); 3. Frequency domain methods, like with the use of the Fourier transform, 13 sensitivity function 14 or the reference to disturbance ratio (RDR) index; 15 4. Minimum variance indexes, 5.…”

“…Frequency domain methods, like with the use of the Fourier transform, 13 sensitivity function 14 or the reference to disturbance ratio (RDR) index; 15…”

Performance Assessment of Predictive Control—A Survey

“…• minimum variance and normalized Harris index [75], Control Performance Index [76], and other variance benchmarking methods [77]; • all types of the model-based measures [78], derived from close loop identification, such as aggressive/oscillatory and sluggishness indexes [79]; • frequency methods starting from classical Bode, Nyquist and Nichols charts with phase and gain margins [69] followed by deeper investigations, such as with the use of Fourier transform [80], sensitivity function [81], reference to disturbance ratio index [82], and singular spectrum analysis [83]; and • alternative indexes using neural networks [84] or support vector machines [85].…”

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“…where |A(u,v)|, |B(u,v)| is a spectral amplitude, ș(u,v) is phase, is Fourier transform (Schlegel et al, 2013).…”