New Method of Designing Controller for Uncertain Differential-Difference Systems and Application to Time-Delay Operation
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ORIGINAL ARTICLE
New Method of Designing Controller for Uncertain Differential‑Difference Systems and Application to Time‑Delay Operational Amplifier System Ke Jian1 · Chung‑Cheng Chen1 · Yen‑Ting Chen2 · Gui‑hong Lin1 Received: 20 June 2020 / Revised: 20 August 2020 / Accepted: 17 September 2020 / Published online: 30 September 2020 © The Korean Institute of Electrical Engineers 2020
Abstract This study combines the feedback linearization method and our recent researches of Chen electrical unifying approach to propose a global tracking controller design for nonlinear uncertain differential-difference systems with time delay. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is presented in this study to show the essential points that the tracking performance is easily solved by the proposed approach. The study applies Chen electrical unifying approach to take the place of using the disorganized virtual ground technique and the Kirchhoff’s law for those traditional approaches. In order to show its significant practicability, the study has firstly designed an easy-to-implement adder and a time-delay circuit, and an unstable time-delay operational amplifier control system based on the Chen electrical unifying approach, and then has proposed a stable controller. Keywords Uncertain differential-difference systems · Time-delay operational amplifier system · Feedback linearization approach · Differential geometry approach · Chen electrical unifying approach
1 Introduction Differential geometry method has proved that it is an important method for nonlinear control systems, and its importance is just like the Laplace transformation in the linear control system [2, 40]. Differential geometry method converts the original nonlinear system into an equivalent linear system, then the linear method can be used [18]. Many nonlinear control methods are used to solve the tracking control * Chung‑Cheng Chen [email protected] Ke Jian [email protected] Yen‑Ting Chen [email protected] Gui‑hong Lin [email protected] 1
City College of Dongguan University of Technology, No. 1, Wenchang Road, Liaobu Town, Dongguan, Guangdong, China
Department of Electrical Engineering, Graduate School, National Chung Hsing University, 145, Xingda Rd., South Dist., Taichung City 402, Taiwan, ROC
2
problems, including sliding mode control methods [15, 57] and nonlinear control methods [27]. The sliding-mode control approach has been applied to solve nonlinear control system [39]. However, the inherent chattering characteristics of unmodeled high-frequency signals due to discontinuous switching operations are destructive shortcomings [9, 12, 59]. Designing sliding mode controllers for electrical systems is not easy because the chattering characteristics can damage the actuator. Nonlinear control methods usually have to solve the difficult Hamilton–Jacobi equation, which is a complex partial differential equation with many computational operations [16, 46, 58]. In addition, we can onl
