Desired dynamic equational proportional‐integral‐derivative controller design based on probabilistic robustness

• Published in: International journal of robust and nonlinear control Vol. 32; no. 18; pp. 9556 - 9592
• Main Authors: Shi, Gengjin, Li, Donghai, Ding, Yanjun, Chen, Yang Quan
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.12.2022; Wiley Subscription Services, Inc
• Subjects: Combustion chambers; Control systems design; Controllers; Design; desired dynamic equational; Flow charts; Fluidized bed combustion; fluidized bed combustor unit; Fluidized beds; level system; Parameterization; probabilistic robustness; Probability theory; Proportional integral derivative; proportional‐integral‐derivative controller; Robustness (mathematics); Statistical analysis; Uncertainty; Water tanks
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5667

Uncertainties existing in industrial processes always result in many challenges for controller design. To enhance the ability of the closed‐loop system to handle the uncertainties, a desired dynamic equational (DDE) proportional‐integral‐derivative (PID) controller is designed based on probabilistic robustness (PR) in this article. The necessity of the proposed design method is demonstrated by introducing the problem formulation. Based on its fundamentals, DDE PID designed based on PR (DDE‐PR PID) is proposed for uncertain systems and corresponding design procedure is summarized as a flow chart. Then the proposed DDE‐PR PID is designed for several typical processes and simulation results indicate that the proposed DDE‐PR PID cannot only achieve satisfactory control performance for nominal systems, but also satisfy control requirements for all uncertain systems with the maximum probability. Finally, the proposed DDE‐PR PID is applied to the nonlinear model of a fluidized bed combustor unit and the level system of a water tank. Its superiority in robustness is validated by both simulations and experiments, which shows the promising prospect of DDE‐PR PID in future power industry. On the other hand, the DDE method is extended to the generalized two‐degree‐of‐freedom PID controller and its bandwidth‐parameterization is proposed in this article as well.