The PI Controller Design For Multivariable Non-square Systems

There exist amounts of multivariable systems in industry, which can be classified into the multivariable square systems and the multivariable non-square systems according to the relationship between the number of input variables and output variables. With the high requirements of control and the change of operating conditions, etc., the multivariable square systems are transformed into the non-square one frequently. Therefore, the control of multivariable non-square system gradually caused the attention by the scholars. The control strategies of industrial processes are common used by decentralized control structure and centralized control structure. For the weak coupling process, decentralized control can meet control performance need and has been widely used on account of the convenience in industrials. However, for the strong coupling process, centralized control is more appropriate. Whether one of them used, the crucial problem is to design the controller parameters by considering the interactions of each loop. It is becoming the hot topic how to deal with the coupling problem. With regarding to the common multivariable non-square system, this paper analyzes the non-square system specifically based on the equivalent transfer function of the system(ETF). The specific content is as follows:(1) This paper proposes a new parameterization method of equivalent transfer function for non-square system. By exploiting the relationship between the ETF and generalized inverse of transfer function of the non-square systems, a higher accuracy analytical expression of ETF is derived, which enriches the parameterization method theory for the non-square system.(2) According to the extent of coupling in multivariable non-square systems, the decentralized PI controller and centralized PI controller are designed respectively based on the ETF method. For the weak coupling systems, decentralized controller structure can be adopt to meet the most of the requirements. Three steps are developed for multi-loop controller design: pairing the controlled variables and manipulated variables, obtaining the ETF, using the IMC-PID method to design the corresponding single loop controller parameters. If the system coupling is strong, the other one, centralized controller structure, should be counted. The required closed-loop transfer functions are cited to design the controller parameter. Simultaneously, in order to avoid calculating the generalized inverse of the transfer function, it can be obtained based on the relationship of the ETF and the generalized inverse. Then the PI controller is designed for each loop by the ETF transfer function matrix, respectively.(3) Considering the external disturbance, the double controllers structure are designed for non-square multivariable systems with good set point tracking and disturbance rejection. By exploiting the relationship between the ETF and generalized inverse of transfer function of the non-square multivariable systems, the multivariable system is transformed into a set of single-loop systems by above ETF. Then, two independent PI controllers, set-point controller and disturbance controller, are designed respectively. So the set-point response of closed-loop system is separated from the disturbance response.This paper considers designing controller for the non-square systems with time delays and disturbance rejection based on the equivalent transfer function theory, and the PI controller method in this paper is easy to be designed. Finally, examples are employed to demonstrate the effectiveness and simplicity of the proposed method.