基于非线性微分几何理论的半间歇聚合釜温度控制器设计

Design of Temperature Controller Based on Nonlinear Differential Geometric for a Semi-batch Polymerization Reactor

半间歇聚合反应具有强非线性、时滞、时变的特点,反应机理复杂,其温度控制一直是难点。应用传统的串级PID控制结构,无法保证温度控制在允许的误差范围内。为保证产品质量,设计了一个非线性控制器来提高温度控制精度。根据Chylla-Haase反应器模型,利用非线性微分几何理论,通过微分同胚和状态反馈,实现输入-输出精确线性化,在此基础上引入误差渐近跟踪项和积分器,设计出温度渐近跟踪控制器,通过调整控制器参数,可达到误差快速指数衰减。仿真结果表明该控制器在设定值跟踪和抗干扰方面明显优于串级PID控制器及模糊串级PID。

It is a difficult task to control the temperature of semi-batch polymerization processes, due to its strong nonlinearity, long delay, time varying, and complex mechanism. Moreover, the traditional cascade control structure cannot ensure that the temperature is controlled within the allowed error range. In this paper, a nonlinear controller is designed to improve the control accuracy of temperature. According to the model of Chylla-Haase reactor, the differential geometry is utilized to achieve the exact linearization of input and output via diffeomorphism and state feedback. And then, by introducing an error tracking term and an integral term, this paper designs an asymptotic tracking controller with adjustable parameters to achieve the exponential decay of errors. The simulation results show that the proposed controller is superior to the cascade PID controller and fuzzy cascade PID in the tracking of set point and the anti- interference.