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Shankar P. Bhattacharyya - One of the best experts on this subject based on the ideXlab platform.
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Gain–Phase Margin-Based Design of Discrete-Time Controllers
Analytical Design of PID Controllers, 2019Co-Authors: Iván D. Díaz-rodríguez, Sangjin Han, Shankar P. BhattacharyyaAbstract:In this chapter, we develop design procedures for digital PI and PID controllers based on gain and Phase Margin specifications using magnitude and Phase loci.
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Gain and Phase Margin-Based Design for Continuous-Time Plants
Analytical Design of PID Controllers, 2019Co-Authors: Iván D. Díaz-rodríguez, Sangjin Han, Shankar P. BhattacharyyaAbstract:In this chapter, we introduce an approach to the robust design of PID controllers for continuous-time plants based on gain and Phase Margin specifications. This design is based on a simple parametrization of constant magnitude and constant Phase loci of the PID controller. This parametrization produces ellipses and straight lines for first-order and PI controllers and cylinder and plane for PID controllers. These geometric figures are computed by considering a prescribed but arbitrary gain crossover frequency and prescribed but arbitrary Phase Margin for the closed-loop system with the given plant. These graphical representations enable the retrieval of PI, PID, and first-order controller designs with simultaneous specifications on gain and Phase Margins.
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CDC - Stabilizing Set and Phase Margin Computation for Resonant Controllers
2019 IEEE 58th Conference on Decision and Control (CDC), 2019Co-Authors: Rafael Fernando Quirino Magossi, Vilma Alves De Oliveira, Ricardo Q. Machado, Shankar P. BhattacharyyaAbstract:In this work, we present the computation of the complete stabilizing set for a general three-terms resonant controller which includes the proportional-resonant (PR) controller commonly used in grid-connected voltage source inverter solutions. The stabilizing set is based on the generalization of the Hermite-Biehler theorem which provides the concept of signature for polynomials. Using the signature concept, the stabilizing set can be computed by linear programming methods. Phase Margin and gain crossover frequency specifications are commonly used in the design of PR controllers. Therefore, we also present a procedure to find the controller which provides the prescribed Phase Margin and gain crossover frequency, as well a prediction for the corresponding gain Margin. In order to illustrate the design, numerical examples are presented.
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CDC - PI controller design in the achievable gain-Phase Margin plane
2016 IEEE 55th Conference on Decision and Control (CDC), 2016Co-Authors: Iván D. Díaz-rodríguez, Shankar P. BhattacharyyaAbstract:In this paper, we present a new approach to the design of Proportional-Integral (PI) controllers. The focus is on a simultaneous achievement of the design specifications most often required in applications. These are a) gain Margin, b) Phase Margin, and c) gain crossover frequency. To accomplish this, we develop a set of design curves in the gain and Phase Margin plane, indexed by gain crossover frequencies. These curves are constructed from the stabilizing set of PI controllers corresponding to the given plant. Each point in this space represents a prescribed gain Margin, Phase Margin, and crossover frequency, achievable by some PI controller in the stabilizing set. The specific and unique PI achieving these specifications can be found from the intersection of constant magnitude and constant Phase loci in the space of controller gains, which consist of ellipses and straight lines. Illustrative examples are presented.
Oliver W. W. Yang - One of the best experts on this subject based on the ideXlab platform.
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Using interval Phase Margin assignment to self-tune a PI AQM controller for TCP traffic
Telecommunication Systems, 2007Co-Authors: Yang Hong, Oliver W. W. YangAbstract:We propose a self-tuning PI (Proportional-Integral) controller for an AQM (Active Queue Management) router supporting TCP traffic in the Internet. Classical control theory is applied in the controller design to meet the Phase Margin specification in the frequency domain. By assigning a proper interval of the Phase Margin, we can achieve good AQM performance by making the control system adapt to dramatic load changes. Our self-tuning PI controller self-tunes only when there is a great change in the network environment that would cause the Phase Margin of the AQM control system to drift outside the specified interval. Based on the knowledge of the queue size, our PI controller can regulate the TCP source window size by adjusting the packet drop probability, thus clamping the steady queue size around a desirable target buffer occupancy. We demonstrate by OPNET^® simulations that with our self-tuning PI controller applied, the network exhibits a good transient behavior. A simple PID (Proportional-Integral-Derivative) controller design method is also provided.
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design of adaptive pi rate controller for best effort traffic in the internet based on Phase Margin
IEEE Transactions on Parallel and Distributed Systems, 2007Co-Authors: Yang Hong, Oliver W. W. YangAbstract:In this paper, we propose an adaptive PI (proportional-integral) rate controller for the AQM (active queue management) router that would support best-effort traffic in the Internet. Unlike most window-based controllers, our rate-based controller design is derived from the classical control theory and it would allow the users to achieve good stability robustness of the AQM control system by specifying a proper Phase Margin. We also make our controller adaptive by selecting a simple heuristic parameter to monitor the network environment real-time so that the controller would self-tune only when a dramatic change of the network traffic has drifted the monitoring parameter outside its specified interval. Located in the router, the adaptive PI rate controller calculates desirable source window sizes (i.e., source sending rates) based on the instantaneous queue length of the buffer and advertises it to the sources. Our simulations demonstrate that our AQM control system can adapt very well to sudden changes in network environment, thus providing the network with good transient behavior. By making the source sending rate relatively smooth, our adaptive PI rate controller becomes quite suitable for streaming media traffic control in the Internet
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adaptive multiloop pi rate based controller design for a mimo ip router based on Phase Margin
Global Communications Conference, 2005Co-Authors: Yang Hong, Oliver W. W. YangAbstract:We design an adaptive multiloop PI (proportional-integral) rate-based controller for the MIMO (multiple-input multiple-output) AQM (active queue management) router to support best-effort streaming media traffic in the Internet. Our controller design employs the DNA (direct Nyquist array) method by shaping the Gershgorin band analytically, thus allowing users to achieve good stability robustness of the MIMO AQM control system through specifying a proper Phase Margin.
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Design of TCP traffic controllers for AQM routers based on Phase Margin specification
2004 Workshop on High Performance Switching and Routing 2004. HPSR., 1Co-Authors: Yang Hong, Oliver W. W. YangAbstract:We propose proportional and proportional-integral (PI) controllers for active queue management (AQM) in the Internet. Classical control theory is applied in the design to meet the frequency domain specification - Phase Margin. The user can specify the Phase Margin to achieve good performance of AQM. The PI controller can regulate the source window size based on the knowledge of the queue size to clamp the steady state value of queue size to the specified reference queue size. Our controllers are verified by OPNET simulation and our PI controller is shown to outperform RED significantly.
Yuanjay Wang - One of the best experts on this subject based on the ideXlab platform.
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determination of all feasible robust pid controllers for open loop unstable plus time delay processes with gain Margin and Phase Margin specifications
Isa Transactions, 2014Co-Authors: Yuanjay WangAbstract:Abstract This paper proposes a novel alternative method to graphically compute all feasible gain and Phase Margin specifications-oriented robust PID controllers for open-loop unstable plus time delay (OLUPTD) processes. This method is applicable to general OLUPTD processes without constraint on system order. To retain robustness for OLUPTD processes subject to positive or negative gain variations, the downward gain Margin (GM down ), upward gain Margin (GM up ), and Phase Margin (PM) are considered. A virtual gain-Phase Margin tester compensator is incorporated to guarantee the concerned system satisfies certain robust safety Margins. In addition, the stability equation method and the parameter plane method are exploited to portray the stability boundary and the constant gain Margin (GM) boundary as well as the constant PM boundary. The overlapping region of these boundaries is graphically determined and denotes the GM and PM specifications-oriented region (GPMSOR). Alternatively, the GPMSOR characterizes all feasible robust PID controllers which achieve the pre-specified safety Margins. In particular, to achieve optimal gain tuning, the controller gains are searched within the GPMSOR to minimize the integral of the absolute error (IAE) or the integral of the squared error (ISE) performance criterion. Thus, an optimal PID controller gain set is successfully found within the GPMSOR and guarantees the OLUPTD processes with a pre-specified GM and PM as well as a minimum IAE or ISE. Consequently, both robustness and performance can be simultaneously assured. Further, the design procedures are summarized as an algorithm to help rapidly locate the GPMSOR and search an optimal PID gain set. Finally, three highly cited examples are provided to illustrate the design process and to demonstrate the effectiveness of the proposed method.
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graphical computation of gain and Phase Margin specifications oriented robust pid controllers for uncertain systems with time varying delay
Journal of Process Control, 2011Co-Authors: Yuanjay WangAbstract:Abstract This paper proposes a novel graphical method to compute all feasible gain and Phase Margin specifications-oriented robust PID controllers to stabilize uncertain control systems with time-varying delay. A virtual gain-Phase Margin tester compensator is incorporated to guarantee the concerned system with certain robust safety Margins. The complex Kharitonov theorem is used to characterize the parametric uncertainties of the considered system and is exploited as a stability criterion for the Hurwitz property of a family of polynomials with complex coefficients varying within given intervals. The coefficients of the characteristic equation are overbounded and eight vertex Kharitonov polynomials are derived to perform stability analysis. The stability equation method and the parameter plane method are exploited to portray constant gain Margin and Phase Margin boundaries. The feasible controllers stabilizing every one of the eight vertex polynomials are identified in the parameter plane by taking the overlapped region of the plotted boundaries. The overlapped region of the useful region of each vertex polynomial is the Kharitonov region, which represents all the feasible specifications-oriented robust PID controller gain sets. Variations of the Kharitonov region with respect to variations of the derivative gain are extensively studied. The way to select representative points from the Kharitonov region for designing robust controllers is suggested. Finally, three illustrative examples with computer simulations are provided to demonstrate the effectiveness and confirm the validity of the proposed methodology. Based on the pre-specified gain and Phase Margin specifications, a non-conservative Kharitonov region can be graphically identified directly in the parameter plane for designing robust PID controllers.
Yang Hong - One of the best experts on this subject based on the ideXlab platform.
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Using interval Phase Margin assignment to self-tune a PI AQM controller for TCP traffic
Telecommunication Systems, 2007Co-Authors: Yang Hong, Oliver W. W. YangAbstract:We propose a self-tuning PI (Proportional-Integral) controller for an AQM (Active Queue Management) router supporting TCP traffic in the Internet. Classical control theory is applied in the controller design to meet the Phase Margin specification in the frequency domain. By assigning a proper interval of the Phase Margin, we can achieve good AQM performance by making the control system adapt to dramatic load changes. Our self-tuning PI controller self-tunes only when there is a great change in the network environment that would cause the Phase Margin of the AQM control system to drift outside the specified interval. Based on the knowledge of the queue size, our PI controller can regulate the TCP source window size by adjusting the packet drop probability, thus clamping the steady queue size around a desirable target buffer occupancy. We demonstrate by OPNET^® simulations that with our self-tuning PI controller applied, the network exhibits a good transient behavior. A simple PID (Proportional-Integral-Derivative) controller design method is also provided.
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design of adaptive pi rate controller for best effort traffic in the internet based on Phase Margin
IEEE Transactions on Parallel and Distributed Systems, 2007Co-Authors: Yang Hong, Oliver W. W. YangAbstract:In this paper, we propose an adaptive PI (proportional-integral) rate controller for the AQM (active queue management) router that would support best-effort traffic in the Internet. Unlike most window-based controllers, our rate-based controller design is derived from the classical control theory and it would allow the users to achieve good stability robustness of the AQM control system by specifying a proper Phase Margin. We also make our controller adaptive by selecting a simple heuristic parameter to monitor the network environment real-time so that the controller would self-tune only when a dramatic change of the network traffic has drifted the monitoring parameter outside its specified interval. Located in the router, the adaptive PI rate controller calculates desirable source window sizes (i.e., source sending rates) based on the instantaneous queue length of the buffer and advertises it to the sources. Our simulations demonstrate that our AQM control system can adapt very well to sudden changes in network environment, thus providing the network with good transient behavior. By making the source sending rate relatively smooth, our adaptive PI rate controller becomes quite suitable for streaming media traffic control in the Internet
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adaptive multiloop pi rate based controller design for a mimo ip router based on Phase Margin
Global Communications Conference, 2005Co-Authors: Yang Hong, Oliver W. W. YangAbstract:We design an adaptive multiloop PI (proportional-integral) rate-based controller for the MIMO (multiple-input multiple-output) AQM (active queue management) router to support best-effort streaming media traffic in the Internet. Our controller design employs the DNA (direct Nyquist array) method by shaping the Gershgorin band analytically, thus allowing users to achieve good stability robustness of the MIMO AQM control system through specifying a proper Phase Margin.
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Design of TCP traffic controllers for AQM routers based on Phase Margin specification
2004 Workshop on High Performance Switching and Routing 2004. HPSR., 1Co-Authors: Yang Hong, Oliver W. W. YangAbstract:We propose proportional and proportional-integral (PI) controllers for active queue management (AQM) in the Internet. Classical control theory is applied in the design to meet the frequency domain specification - Phase Margin. The user can specify the Phase Margin to achieve good performance of AQM. The PI controller can regulate the source window size based on the knowledge of the queue size to clamp the steady state value of queue size to the specified reference queue size. Our controllers are verified by OPNET simulation and our PI controller is shown to outperform RED significantly.
Dragan Maksimovic - One of the best experts on this subject based on the ideXlab platform.
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design and implementation of an adaptive tuning system based on desired Phase Margin for digitally controlled dc dc converters
IEEE Transactions on Power Electronics, 2009Co-Authors: J. Morroni, Regan Zane, Dragan MaksimovicAbstract:This letter presents an online adaptive tuning technique for digitally controlled switched-mode power supplies (SMPS). The approach is based on continuous monitoring of the system crossover frequency and Phase Margin, followed by a multi-input-multi-output (MIMO) control loop that continuously and concurrently tunes the compensator parameters to meet crossover frequency and Phase Margin targets. Continuous stability Margin monitoring is achieved by injecting a small digital square-wave signal between the digital compensator and the digital pulsewidth modulator. The MIMO loop adaptively adjusts the compensator parameters to minimize the error between the desired and measured crossover frequency and Phase Margin. Small-signal models are derived, and the MIMO control loop is designed to achieve stability and performance over a wide range of operating conditions. Using modest hardware resources, the proposed approach enables adaptive tuning during normal SMPS operation. Experimental results demonstrating system functionality are presented for a synchronous buck SMPS.
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adaptive tuning of digitally controlled switched mode power supplies based on desired Phase Margin
Power Electronics Specialists Conference, 2008Co-Authors: J. Morroni, Regan Zane, Dragan MaksimovicAbstract:This paper presents an online adaptive tuning technique for digitally controlled switched-mode power supplies (SMPS). The approach is based on continuous monitoring of the system crossover frequency and Phase Margin, followed by a multi-input multi-output (MIMO) control loop that continuously and concurrently tunes the compensator parameters to meet crossover frequency and Phase Margin targets. Small-signal models are derived and the MIMO control loop is designed to achieve stability and performance over a wide range of operating conditions. Using modest hardware resources, the proposed approach enables adaptive tuning during normal closed-loop SMPS operation. Experimental results demonstrating system functionality are presented for a synchronous buck SMPS.
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An online Phase Margin monitor for digitally controlled switched-mode power supplies
2008 IEEE Power Electronics Specialists Conference, 2008Co-Authors: J. Morroni, Regan Zane, Dragan MaksimovicAbstract:This paper presents a practical injection-based method for continuous monitoring of the crossover frequency and Phase Margin in digitally controlled switched-mode power supplies (SMPS). The proposed approach is based on Middlebrook's loop-gain measurement technique, adapted to digital controller implementation. A digital square-wave signal is injected in the loop, and the injection signal frequency is adjusted while monitoring loop signals to obtain the system crossover frequency and Phase Margin online, i.e., during normal SMPS operation. The approach does not require open loop or steady-state SMPS operation and is capable of convergence in the presence of load transients or other disturbances. Experimental results are presented for various power stage configurations demonstrating close matches between monitored and expected crossover frequencies and Phase Margins.
