The Research Of Multivariable System's PID Control On Chemical Process

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.