Assessment of predictive control performance using fractal measures

Paweł D Domański,Maciej Ławryńczuk

doi:10.1007/s11071-017-3484-3

Paweł D Domański, Maciej Ławryńczuk

Open Access

https://doi.org/10.1007/s11071-017-3484-3

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Journal: Nonlinear Dynamics	Publication Date: Mar 24, 2017
Citations: 20	License type: open-access

Affiliation: Warsaw University of Technology

Abstract

This paper presents novel approach to the task of control performance assessment. Proposed approach does not require any a priori knowledge on process model and uses control error time series data using nonlinear dynamical fractal persistence measures. Notion of the rescaled range R/S plots with estimation of Hurst exponent is applied. Crossover phenomenon is observed in data being investigated and discussed. Paper starts with industrial engineering rationale. Review of the control error histogram is followed by statistical analysis of probabilistic distribution functions (PDFs). Lévy alpha -stable PDF parameters seem to be best fitted. They directly lead to the fractal analysis using Hurst exponents and R/S plot crossover points. The evaluation aims at performance of the generalized predictive control (GPC) and discusses freshly introduced loop performance quality sensitivity against design parameters of the GPC controller.

Highlights

Presented work combines observations from different contexts: CPA [24], model predictive control (MPC) [6], non-Gaussian statistics [19] and fractal nonlinear analysis [36]
The main research interests focus on the subject of control quality for SISO loop using predictive controller (GPC)
(H2) Can we identify whether generalized predictive control (GPC) model gain is appropriate?

Summary

Introduction

Presented work combines observations from different contexts: CPA [24], model predictive control (MPC) [6], non-Gaussian statistics [19] and fractal nonlinear analysis [36]. The main research interests focus on the subject of control quality for SISO loop using predictive controller (GPC). Predictive MPC algorithms gain popularity in industrial process control. They are more complicated and require specific knowledge, they allow to address issues that are unattained by PID loops. Application of MPC may significantly improve control quality. It is compensated with more extensive tuning effort due to the larger number of parameters. System sensitivity to unmodeled dynamics or internal model misfit increases. Improper or inexistent maintenance may significantly deteriorate any positive results [39]

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Conclusion