Interaction Analysis And Decentralzied PID Controller Design For Multivariable Processes

Most of the large and complex industrial processes are multivariable systems. Compared with the single-input single-output systems, multivariable systems are more difficult to control due to interactions among input and output variables. There are two kinds of controller structures for multivariable systems, i.e. a multivariable or centralized multivariable controller and a set of decentralized single-input single-output controllers. The stronger the interactions among loops are, the more complex the controllers are and the more difficult it is to select the parameters of controllers. Therefore, how to measure the interactions among variables and pair the manipulated variables with output variables based on the interaction analysis has become an important task in designing controllers for multivariable systems. As for this problem, this thesis makes some research from three aspects as follows:(1) The interactions among loops are embodied by discrepancies of the static open-loop gains of the same loop when the other loops are closed one by one. A larger change of the static gain of a certain loop means stronger interactions it is affected by. In this thesis, relative gain table and relative gain graph are proposed to analyze interactions between two random loops vividly. Based on the analysis, a new criterion is defined to measure interactions among loops, and a pairing method is brought forward correspondingly.(2) Interactions among loops are analyzed in terms of the dynamic characteristics of the system. The Effective Open-loop Process (EOP) is used to calculate the equivalent transmission from a manipulated variable to a controlled variable with the interactions from other loops being taken into consideration. The frequency responses of one loop are compared under two following circumstances: (1) all the other loops are open; (2) all the other loops are closed. The Effective Relative Gain Array (ERGA) which denotes the change of effect gains is used to measure the dynamic interactions. The method of calculating ERGA is proposed.(3) The design of decentralized PID controllers for multivariable processes are studied based on the EOP proposed in (2). Variables are paired in accordance with the index which contains the dynamic features of interactions as mentioned in (2), and then the original multivariable system is equivalent to a set of SISO systems with the EOP between a couple of paired variables being the controlled plant for an SISO system. Independent controllers are designed individually for the simplified EOPs and the stability condition for the decentralized control system is also presented.