Graphical tuning method of PID controller for systems with uncertain parameters based on affine algorithm

For systems with uncertain parameters, it is very important to find a controller that can satisfy the preset robustness. The traditional method often ignores the influence of parameter coupling on the set boundary system when substituting the original system with the boundary system group, resulting in the calculated controller value region being too conservative. In this article, noise information is introduced based on affine algorithm to describe uncertain system parameters. Then, based on Kharitonov theorem, a new grouping method for boundary systems is proposed. This method takes the parameter coupling information into account when determining the boundary system, and avoids the problem of interval conservation. On this basis, a virtual phase margin tester is introduced to ensure that the obtained controller parameter range can make the system meet the specific robustness requirements. The results obtained in this article are general and strictly proved. Finally, examples are provided to illustrate the design process and verify the feasibility and efficacy of the proposed approach.