Bifurcation, Quasi-Periodicity, Chaos, and Co-Existence of Different Behaviors in the Controlled H-Bridge Inverter

2015 ◽  
pp. 301-332 ◽  
Author(s):  
Yosra Miladi ◽  
Moez Feki
Keyword(s):  
Fixed Point ◽  
Stability Region ◽  
Feedback Controller ◽  
Proportional Integral ◽  
Linear Controller ◽  
Delayed Feedback Controller ◽  
Integral Controller ◽  
Proportional Integral Controller ◽  
The Stability ◽  
Time Delayed Feedback

This chapter deals with the analysis of the dynamic behavior of a controlled single-phase H-bridge inverter. The authors show that in addition to border collision bifurcation, when it is controlled with a time-delayed controller or with a dynamic controller that increases the system dimension, the H-bridge inverter can exhibit several other types of behaviors such as Neimark-Sacker bifurcation, quasi-periodicity, and coexistence of different periodic behaviors, as well as coexistence between periodic and chaotic behaviors. The proposed controllers are of different types. In addition to the Fixed-Point Induced Controller (FPIC), the authors also present the Time-Delayed Feedback Controller (TDFC) and the dynamic linear controller, such as the proportional-integral controller. The main issue of this chapter is to perform analysis within and beyond the stability region. Analytic calculation and numerical simulations are presented to confirm the obtained results.

scholarly journals Control theory for scanning probe microscopy revisited

2014 ◽  
Vol 5 ◽  
pp. 337-345 ◽  
Author(s):  
Julian Stirling
Keyword(s):  
Control Theory ◽  
Feedback Environment ◽  
Proportional Integral ◽  
Mechanical Responses ◽  
Wide Range ◽  
Integral Controller ◽  
Proportional Integral Controller ◽  
Standard Models ◽  
The Stability ◽  
Insight Into

We derive a theoretical model for studying SPM feedback in the context of control theory. Previous models presented in the literature that apply standard models for proportional-integral-derivative controllers predict a highly unstable feedback environment. This model uses features specific to the SPM implementation of the proportional-integral controller to give realistic feedback behaviour. As such the stability of SPM feedback for a wide range of feedback gains can be understood. Further consideration of mechanical responses of the SPM system gives insight into the causes of exciting mechanical resonances of the scanner during feedback operation.

Robustly stabilizing proportional integral controller for uncertain system under computational delay

2020 ◽  
pp. 107754632095792
Author(s):  
Sahaj Saxena ◽  
Yogesh V Hote
Keyword(s):  
Stability Boundary ◽  
Parametric Uncertainty ◽  
Uncertain System ◽  
Regulatory Control ◽  
Integral Control ◽  
Proportional Integral ◽  
Integral Controller ◽  
Proportional Integral Controller ◽  
Proportional Integral Control ◽  
The Stability

In a feedback control loop, when there exists a delay in processing the control signal (often called computational delay), it is difficult to stabilize the system, particularly when the system exhibits uncertainty. To solve this problem, we proposed a new robust proportional integral control strategy for a class of uncertain systems exhibiting parametric uncertainty. A two-stage scheme is proposed in which the first stage identifies the worst plant that has the highest chance of facing instability; and in the second stage, based on the worst plant, the tuning parameters of the proportional integral controller are determined using the stability boundary locus approach under the desired closed-loop specifications of gain and phase margins. The efficiency of the proposed scheme is verified for servo and regulatory control problems.

Proportional-Integral Controller Assisted by GPI Observer for Microalgal Continuous Culture

2020 ◽  
Author(s):  
Viyils Sangregorio-Soto ◽  
Claudia L. Garzon-Castro ◽  
Gianfranco Mazzanti ◽  
Manuel Figueredo ◽  
John A. Cortes-Romero
Keyword(s):  
Continuous Culture ◽  
Proportional Integral ◽  
Integral Controller ◽  
Proportional Integral Controller

Limits of a simplified controller design based on integral plus dead time models

2018 ◽  
Vol 232 (6) ◽  
pp. 728-741 ◽  
Author(s):  
Mikuláš Huba ◽  
Igor Bélai
Keyword(s):  
Dead Time ◽  
Controller Design ◽  
Absolute Error ◽  
Higher Order ◽  
Smith Predictor ◽  
Proportional Integral ◽  
Overall Design ◽  
Error Measures ◽  
Integral Controller ◽  
Proportional Integral Controller

This article presents design and evaluation of filtered proportional–integral controllers and filtered Smith predictor–inspired constrained dead time compensators. Both are based on the integral plus dead time and on the first-order time delayed plant models. They are compared as for tuning simplicity, robustness and noise attenuation. Such a comparison, which presents a robustness test regarding the importance of the internal plant feedback approximation, may be carried out by performance measures built on deviations of the input and output transient responses from their ideal shapes. When combined with integral of absolute error measures of both solution types with the disturbance responses set as nearly equivalent, we can see that the filtered Smith predictor setpoint responses may be significantly faster than the filtered proportional–integral controller responses, more robust and, using higher-order filters, also sufficiently smooth. Furthermore, tuning of the possibly higher-order filters for filtered Smith predictor is simpler. Its overall design is more transparent and straightforward with respect to the control constraints, where the filtered Smith predictor requires some additional anti-windup measures.

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