Multivariable Control of a Simulated Industrial Gas-Phase Polyethylene Reactor

Esrafili, Ali; Alhumaizi, Khalid; Ajbar, Abdelhamid

doi:10.1021/ie020386h

Cited by 20 publications

(9 citation statements)

References 24 publications

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“…In the operating range of industrial interest, the fluidized‐bed reactor in Figure can be modeled as a single‐phase, well‐mixed continuous stirred‐tank reactor . For simplicity, it is assumed that there is only one type of active catalyst sites . A mathematical model for this reactor has the form

\begin{matrix} lefttrue \\ \frac{italicdY}{italicdt} = F_{c} a_{c} - k_{d} Y - \frac{(R_{M_{1}} M_{W_{1}} + R_{M_{2}} M_{W_{2}}) Y}{B_{w}} \\ \frac{italicdT}{italicdt} = \frac{H_{f} + H_{g} - H_{italictop} - H_{r} - H_{italicpol}}{M_{r} C_{italicpr} + B_{w} C_{italicppol}} \\ \frac{d [italicIn]}{italicdt} = \frac{F_{italicIn} - x_{italicIn} b_{t}}{V_{g}} \\ \frac{d [M_{1}]}{italicdt} = \frac{F_{M_{1}} - x_{M_{1}} b_{t} - R_{M_{1}}}{V_{g}} \\ \frac{d [M_{2}]}{italicdt} = \frac{F_{M_{2}} - x_{M_{2}} b_{t} - R_{M_{2}}}{V_{g}} \\ \frac{d [H]}{italicdt} = \frac{F_{H} - x_{H} b_{t}}{V_{g}} \\ \frac{{italicdMI}_{c}^{- \frac{1}{3.5}}}{dt} = \frac{1}{τ_{r}} {italicMI}_{i}^{- \frac{1}{3.5}} - \frac{1}{τ_{r}} {italicMI}_{c}^{- \frac{1}{3.5}} \\ \frac{{dD}_{c}^{- 1}}{italicdt} = \frac{1}{τ_{r}} \end{matrix}

…”

Section: Case Studiesmentioning

confidence: 99%

A dead time compensation approach for multirate observer design with large measurement delays

Ling¹,

Kravaris

2018

AIChE Journal

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In our previous work, we developed a multirate observer design method in linear systems with asynchronous sampling based on a Luenberger observer design coupled with inter‐sample predictors. In this article, the problem of multirate multidelay observer design is addressed where both asynchronous sampling and possible measurement delays are accounted for. The proposed observer adopts an available multirate observer design in the time interval between two consecutive delayed measurements. A dead time compensation approach is developed to compensate for the effect of delay and update past estimates when a delayed measurement arrives. The stability and robustness properties of the multirate observer will be preserved under nonconstant, arbitrarily large measurement delays. A mathematical example and a gas‐phase polyethylene reactor example demonstrate good performance of the proposed observer in the presence of nonuniform sampling and nonconstant measurement delays. © 2018 American Institute of Chemical Engineers AIChE J, 65: 562–570, 2019

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\begin{matrix} lefttrue \\ \frac{italicdY}{italicdt} = F_{c} a_{c} - k_{d} Y - \frac{(R_{M_{1}} M_{W_{1}} + R_{M_{2}} M_{W_{2}}) Y}{B_{w}} \\ \frac{italicdT}{italicdt} = \frac{H_{f} + H_{g} - H_{italictop} - H_{r} - H_{italicpol}}{M_{r} C_{italicpr} + B_{w} C_{italicppol}} \\ \frac{d [italicIn]}{italicdt} = \frac{F_{italicIn} - x_{italicIn} b_{t}}{V_{g}} \\ \frac{d [M_{1}]}{italicdt} = \frac{F_{M_{1}} - x_{M_{1}} b_{t} - R_{M_{1}}}{V_{g}} \\ \frac{d [M_{2}]}{italicdt} = \frac{F_{M_{2}} - x_{M_{2}} b_{t} - R_{M_{2}}}{V_{g}} \\ \frac{d [H]}{italicdt} = \frac{F_{H} - x_{H} b_{t}}{V_{g}} \\ \frac{{italicdMI}_{c}^{- \frac{1}{3.5}}}{dt} = \frac{1}{τ_{r}} {italicMI}_{i}^{- \frac{1}{3.5}} - \frac{1}{τ_{r}} {italicMI}_{c}^{- \frac{1}{3.5}} \\ \frac{{dD}_{c}^{- 1}}{italicdt} = \frac{1}{τ_{r}} \end{matrix}

…”

Section: Case Studiesmentioning

confidence: 99%

A dead time compensation approach for multirate observer design with large measurement delays

Ling¹,

Kravaris

2018

AIChE Journal

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“…The steady state operating conditions for the plant are given in Tables 2 and 3. These operating conditions were found by optimization and were discussed elsewhere [26].…”

Section: Process Modelmentioning

confidence: 99%

“…For nonlinear MPC, the predicted output, y over the prediction horizon P is obtained by the numerical integration of: (26) y=g(x) (27) from t k up to t k+P where x and y represent the states and the output of the model, respectively. The symbol ||.|| denotes the Euclidean norm, k is the sampling instant, Γ and Λ are diagonal weight matrices and R=[r(k+1) … r(k+P)] T is a vector of the desired output trajectory.…”

Section: The On-line Nlmpc Algorithmmentioning

confidence: 99%

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Control of molecular weight distribution of polyethylene in gas-phase fluidized bed reactors

Ali

Ajbar

Alhumaizi

2010

Korean J. Chem. Eng.

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This paper presents a feasibility study of the broadening of polyethylene molecular weight distribution produced using a multisite Ziegler-Natta catalyst in a fluidized-bed reactor. A nonlinear model predictive control algorithm, applied to a validated model of the reactor, is used for the on-line control of the entire molecular weight distribution of the produced polymer. Control of a target chain-length distribution is achieved by selecting a collection of points in the distribution and using them as set points for the control algorithm. An on-line Kalman filter is used to incorporate infrequent and delayed off-line molecular weight measurements. Through simulation the control algorithm is evaluated, under tracking conditions as well as plant-model mismatch. The results demonstrate that the control algorithm can regulate the entire molecular weight distribution with minimum steady state error. However, the efficiency of this approach is highly dependent on the dynamics of hydrogen inside the reactor.

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“…The controller exhibited greater performance and was able to maintain the stability over a wide range of operating conditions compared to optimally tuned PID controller. E. Ali et al (2003) [8] presented two control schemes in the paper to study the multivariable control of polyethylene in fluidized bed reactor where both nonlinear and linear MPC are used and compared. It was found that non-linear MPC was better than the latter in the sense providing a good performance even in the presence of moderate modeling error.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy-GMC Control of Gas-Phase Propylene Copolymerization in Fluidized Bed Reactor

et al. 2018

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A modified two-phase model for gas phase propylene and ethylene copolymerization was chosen to represent the process in a fluidized bed reactor. This model considered the entrainment of solid particles in the reactor, as a modification to the original two-phase model assumptions. The non-linearity of this process makes it difficult to control just by using conventional controller such as PID. A hybrid control strategy (a simple designed fuzzy logic controller (FLC) integrated with generic model control (GMC)) is designed to control the temperature of the reactor. This advanced control system was compared with the GMC and conventional PID controller. The simulation results showed that the hybrid controller (Fuzzy-GMC) performed better than both GMC and PID in terms of both servo and regulatory control.

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Multivariable Control of a Simulated Industrial Gas-Phase Polyethylene Reactor

Cited by 20 publications

References 24 publications

A dead time compensation approach for multirate observer design with large measurement delays

A dead time compensation approach for multirate observer design with large measurement delays

Control of molecular weight distribution of polyethylene in gas-phase fluidized bed reactors

Fuzzy-GMC Control of Gas-Phase Propylene Copolymerization in Fluidized Bed Reactor

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