Worst Case of Relative Disturbance Gain Array for Uncertain Distillation System

Authors

Rudy Agustriyanto, Chemical Engineering, Surabaya University, Surabaya 60292, IndonesiaFollow
Jie Zhang, School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK

Abstract

This article discusses the constrained nonlinear optimization formulation for calculating the worst case of lower and upper bounds of relative disturbance gain array (RDGA) for uncertain process models. The proposed approach seeks the minimum and maximum values of the relative disturbance gains subject to the constraints in which the process and disturbance gains are within their uncertainty ranges. RDGA ranges are useful for control structure determination and the related robustness, as they provide information regarding the sensitivity to gain uncertainties. The proposed method is demonstrated by ternary distillation column case study. Closed loop simulation results support the analysis based on the proposed method. It is shown that for a particular degree of uncertainties, the range of process gain determinant should not include zero to ensure the successfulness of the calculation. For the distillation system being studied, the maximum allowable α is 0.339 to avoid the singularity of matrix K.

Bahasa Abstract

Kondisi Terburuk Harga Relative Disturbance Gain Array untuk Sistem Distilasi Tak Pasti. Artikel ini mempresentasikan formulasi optimisasi nonlinear berbatas untuk menghitung kondisi terburuk batas bawah dan batas atas harga relative disturbance gain array (RDGA) untuk suatu model proses yang mengandung ketidakpastian. Pendekatan yang diusulkan adalah untuk mencari harga relative disturbance gain minimum dan maksimum sesuai batasan kisaran ketidakpastian yang terdapat baik pada gain proses maupun gain gangguan. Kisaran RDGA berguna untuk penentuan struktur pengendali dan ketegarannya (robustness) karena menyediakan informasi terkait sensitivitasnya terhadap ketidakpastian harga gain. Metode yang diusulkan kemudian diaplikasikan pada studi kasus kolom distilasi. Hasil simulasi lintas tertutup mendukung analisis yang didasarkan pada metode yang diusulkan. Pada kasus yang dipelajari, ditunjukkan bahwa untuk suatu derajat ketidakpastian tertentu, kisaran determinan gain tidak boleh mencakup titik nol untuk menjamin keberhasilan perhitungan. Untuk kasus sistem distilasi yang dipelajari, harga maksimum ketidakpastian, α adalah 0.339 untuk menghindari singularitas matrix K (gain).

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Recommended Citation

Agustriyanto, Rudy and Zhang, Jie (2012) "Worst Case of Relative Disturbance Gain Array for Uncertain Distillation System," Makara Journal of Technology: Vol. 16: Iss. 2, Article 7.
DOI: 10.7454/mst.v16i2.1512
Available at: https://scholarhub.ui.ac.id/mjt/vol16/iss2/7