摘要
绝大部分化工过程本质上都是复杂的多变量、多时滞系统,输入变量与输出变量之间的相互关联,以及各回路不同滞后时间的存在,给多变量PID控制系统的研究工作带来较大的困难。本文针对典型的化工过程多变量FOPTD(一阶加纯滞后)、SOPTD(二阶加纯滞后)对象,在有效传递函数法的基础上进行改进,系统地研究了多变量PID控制器的整定和优化问题。主要内容如下:
1.介绍一种基于有效相对增益矩阵(ERGA)的回路配对准则,它同时考虑对象的静态和动态信息,且不依赖控制器的设计。将其与两种常见的配对准则:传统的基于RGA和NI的回路配对准则,及新的基于DRGA的回路配对准则相比较,通过理论分析和实例仿真,说明ERGA方法是一种更为直接有效的配对方法。
2.求导了针对多变量、多时滞对象的传递函数矩阵和状态空间表达式的转换通式,利用添加辅助变量的方式解决多时滞问题;然后基于多变量PID控制系统的结构统一性,进一步推导了其闭环状态空间表达通式,以便于在时域上分析整个控制系统的性能特征,求取各类综合性能指标。
3.对有效传递函数法进行改进,提出了一种基于完整性分析的鲁棒分散PID控制器的设计方法,即改进的有效传递函数法METF。利用有效相对增益矩阵ERGA,计算对象各回路的有效传递函数,并引入综合性能指标——李亚普诺夫二次型指标和复实比率指标,对分散PID参数式中的幅值裕度进行多约束、多目标NLJ寻优,同时利用完整性定理分析分散控制系统的完整性。通过五个实例仿真,验证了这种设计方法对于典型的多变量化工过程对象有很好的通用性和良好的控制效果。4.将有效传递函数法扩展到多变量解耦PID控制系统的设计。基于理想解耦控制和动态相对增益矩阵,推导出控制器非对角解耦参数的计算公式,同时利用列占优指标和不确定因子判断控制的解耦效果和鲁棒性。仿真实例的结果说明,这种方法能够有效削减回路间的耦合,且控制效果良好。
5.最后针对模型非精确辨识的情况,研究了基于继电反馈试验的多变量解耦PID控制器的设计方法,研究结果和实例仿真表明,它对于全交叉耦合的多变量对象具有很好的控制效果。
Most chemical processes are essentially complicated multivariable systems with time-delay; the interactions between input and output variables, and the existence of different time-delay in the loops, make the research on multivariable PID control system become a difficult task.. Aiming at typical multivariable FOPTD (first order plus time delay) and SOPTD (second order plus time delay) plants in chemical processes, and with some improvements of the effective transfer function method, this paper deals with the tuning and optimization problems of multivariable PID controllers systemically. The main contributions of the paper are as follows:
1. A practical loop pairing criterion based on effective relative gain matrix (ERGA) is introduced; it takes both static and dynamic information of plants into account, and does not rely on the controller's design. Compared with two common criterion: the traditional RGA and NI based loop pairing criterion, and the new DRGA based loop pairing criterion, the ERGA rule is more useful and effective, through theoretical analysis and example simulations.
2. The formulas transferred from multivariable time-delay processes' transfer function matrix to state space representation is obtained, in which we solve the problem of time-delay by adding auxiliary variables; and then according to the unified structure of multivariable PID control system, the close-loop's state space representation of the whole system is obtained, which is quite useful to analyze the control system's performance characteristics in time domain, and calculate various kinds of integrative performance index.
3. Based on some improvements of the effective transfer function method, a multivariable decentralized PID controller's design method with high robustness and integrity analysis is proposed, which is called METF(modified effective transfer function method). Use the effective relative gain matrix (ERGA) to calculate the effective transfer function of loops, and employ theintegrative performance index------Lyapunov quadratic index andcomplex/real ratio to do the multi-objective NLJ optimizing of gain margin in PID parameter tuning formula, and then check up the tuning results' reliability by the integrality criterion. Five simulation examples demonstrate the effectiveness, robustness and universality of the modified method.
4. Effective transfer function method is extended to the multivariable decoupling PID control system's design. Based on the ideal decoupling control and dynamic relative gain matrix, the calculating formulas of non-diagonal controller's parameters are obtained, and also employ the column dominance index and uncertainty factor to measure the decoupling effect and robustness of the control system. Simulation results show that, this method reduces the coupling between loops effectively, and makes a good control performance.
5. Lastly, aiming at the model with non-accurate identification, a research of multivariable decoupling PID controllers' design method based on decentralized relay feedback test is provided. The study results and examples simulation show that, the method makes good control performance for those fully cross-coupled multivariable plants.
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