IMC-PID tuning method based on maximum sensitivity for uncertain multivariable systems

A controller design method based on effective open-loop transfer function (EOTF) and internal model control (IMC) is proposed for square multivariable systems with uncertain parameters. In this paper, two equivalent substitutions are used to deal with the multivariable system with uncertain parameters. In the first equivalent substitution, the EOTF method is used to solve the coupling problem of the system. In order to prevent the interval explosion problem of parameters, the affine algorithm is adopted in the decoupling process to determine the value region of system parameters. Then, the multivariable system with uncertain parameters is transformed into a set of single-variable system with uncertain parameters. The second equivalent substitution is based on Kharitonov's theorem to process every single variable system with uncertain parameters and replace it by a set of boundary models. Meanwhile, in order to ensure that the tuning controller can not only make the system stable but also meet a certain degree of robustness, based on the idea of IMC, the maximum sensitivity is introduced to design the PID controller. Finally, numerical simulation results are given to verify the effectiveness of the proposed method.