New Method of Designing Controller for Uncertain Differential-Difference Systems and Application to Time-Delay Operational Amplifier System

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.

Correction of traditional incorrect oscillation formula for the Wien‐Bridge Oscillator

“…An important particularity of CEUA is the utilisation of R CCC = ∞ ( R CCC = 0) to effectively reduce the solving load. The invented equivalent circuits of significant electronic devices including Figures 4–13 are shown as follows. Ideal transformer device [21]: Mutual inductance device [21]: Quiescent DC BJT transistor device [9]: First‐order delay device [20]: Complex operational amplifier device [23]: …”

“…Utilise the invented matrix algebraic properties of CEUA [20] to reduce Equation (55) in the simple form.…”

“…The dependent variables will be converted to be mesh‐current or node‐voltage variables and move the dependent item to the other side of the equation. Using our invented matrix operations reduces the matrix equation to be a simple form [20].…”

“…Utilise the invented matrix algebraic properties of CEUA [20] to reduce Equation () in the simple form. …”

“…To derive the oscillation condition and frequency of the Wien-Bridge oscillator in this study, we will apply our series research CEUA [18][19][20][21][22][23][24] to overcome the serious shortcomings of the traditional Barkhausen method. Moreover, another important feature of our method is that the oscillation condition is effective for a range, not a single value, and it can solve the impact caused by the change in environmental factors.…”