# Continuous stirred-tank reactor system

## Model description:

The following CSTR system developed by Liu(1967). The reaction is exothermic first-order, $A \rightarrow B$, and is given by the following mass and energy balances. One should notice that the energy balance includes cooling water jacket dynamics. The following model was identified using regression techniques on the energy balance equations:

$$\begin{align*} y(k) &= 1.3187y(k-1) - 0.2214y(k-2) - 0.1474y(k-3) \\ &- 8.6337u(k-1) + 2.9234u(k-2) + 1.2493u(k-3) \\ &- 0.0858y(k-1)u(k-1) + 0.0050y(k-2)u(k-1) \\ &+ 0.0602y(k-2)u(k-2) + 0.0035y(k-3)u(k-1) \\ &- 0.0281y(k-3)u(k-2) + 0.0107y(k-3)u(k-3). \end{align*}$$

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## Publication details:

Title | Identification and Control of Bilinear Systems |

Publication Type | Conference Paper |

Year of Publication | 1992 |

Authors | Bartee, James F., and Georgakis Christos |

Conference Name | American Control Conference, 1992 |

Date Published | 06/1992 |

Publisher | IEEE |

Conference Location | Chicago, Illinois |

ISBN Number | 0-7803-0210-9 |

Keywords | Algorithm design and analysis, Chemical processes, Continuous-stirred tank reactor, control system synthesis, Control systems, Control theory, linear systems, nonlinear control systems, nonlinear systems, process control |

Abstract | The research presented in this paper combines the problem of identifiction and control of nonlinear processes. This is done by approximating the process with a bilinear model and designing model-based control structures (Reference System Controllers) based on the bilinear approximation. The identification of the bilinear model and the construction of the controller are described below. An example of the identification and control of an exothermic CSTR is also presented. |

URL | http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=4792606&queryText%3DIdentification+and+Control+of+Bilinear+Systems |