PI controller design in the achievable gain-phase margin plane

Díaz-Rodríguez, Iván D.; Bhattacharyya, S.P.

doi:10.1109/cdc.2016.7799021

Cited by 14 publications

(5 citation statements)

References 10 publications

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“…Furthermore, an existing controller tuning method was applied in which the P and PI controller values were determined based on the intended phase margins of the measured Bode plots [41]. This measured model is further denoted as G. The controller tuning method was applied to obtain P acceleration controllers with intended phase margins φ PM equal to 30 • , 60 • , and 90 • .…”

Section: Comparison To Existing Controller Tuning Methodsmentioning

confidence: 99%

Optimal Hardware and Control Co-Design Applied to an Active Car Suspension Setup

et al. 2021

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For complex systems, it is not easy to obtain optimal designs for the hardware architecture and control configurations. Every design aspect influences the final performance, and often the interactions of the different components cannot be clearly determined in advance. In this work, a novel co-design optimization method was applied that allows the optimal placement and selection of actuators and sensors to be performed simultaneously with the determination of the control architecture and associated controller tuning parameters. This novel co-design method was applied to a state-space model of a downscaled active car suspension laboratory setup. This setup mimics a car driving over a specific road surface while active components in the suspension have to increase the driver’s comfort by counteracting unwanted vibrations. The result of this co-design optimization methodology is a Pareto front that graphically represents the trade-off between the maximum performance and the total implementation cost; the co-design results were validated with measurements of the physical active car suspension setup. The obtained controller tuning parameters are compared herein with existing controller tuning methods to demonstrate that the co-design method is able to determine optimal controller tuning parameters.

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Section: Comparison To Existing Controller Tuning Methodsmentioning

confidence: 99%

Optimal Hardware and Control Co-Design Applied to an Active Car Suspension Setup

et al. 2021

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“…In order to show the effectiveness of the proposed method, we performed a classic tuning based on the concepts of bandwidth and phase margin [27]. As

ω_{1_{d_{1}}} = 5

rad/s, for a fair comparison, we selected the bandwidth as half of this value and we obtained the controller (filled triangle) of Table 1 with the same phase margin of filled lozenge using the tuning strategy of [18].…”

Section: Examplesmentioning

confidence: 99%

“…On the other hand, current analytical design of PID controllers offers the possibility to consider the stabilising set and performance constraints at the same time. As a matter of fact, in [18], a method to tune PI controllers achieving prescribed gain and phase margins was developed. The method used the stabilising set of PI controllers given in [5, 19].…”

Section: Introductionmentioning

confidence: 99%

Geometric‐based PID control design with selective harmonic mitigation for DC–DC converters by imposing a norm bound on the sensitivity function

Magossi

Han

Machado

et al. 2020

IET Control Theory & Appl

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The DC-DC converters usually interfaces renewable energy sources in DC microgrids which may be contaminated by harmonic perturbations that adversely affect performance, creates stability and protection problems in a DC grid system. In this paper, the authors propose the use of the popular proportional-integral-derivative (PID) controller to mitigate selected harmonics. The solution is obtained by computing the complete set of stabilising controllers and imposing a bound on the sensitivity function. Using matrix representation of conic sections, the geometric-based PID controller is derived in the controller parameter space. The main result finds a subset of the stabilising set in which the controller mitigate harmonics with prescribed levels of attenuation which are constructively determined for each frequency of the selected harmonics. Simulation and experimental results using a boost converter are provided for validation.

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“…Nominal stabilization of the plants for the specified GMs and PMs by means of the stability boundary locus method was published in [19], [38]. Further, the design of PI controllers for simultaneous achievement of the specified GM, PM, and Gain Crossover Frequency (GCF) by means of the curves in the GM-PM plane was presented in [39]. For some alternative techniques for mapping the performance requirements into the parameter space, see, e.g., [40]- [43].…”

Section: Introductionmentioning

confidence: 99%

Design of Robust PI Controllers for Interval Plants With Worst-Case Gain and Phase Margin Specifications in Presence of Multiple Crossover Frequencies

et al. 2022

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This article deals with the computation of robustly performing Proportional-Integral (PI) controllers for interval plants, where the performance measures are represented by the worst-case Gain Margin (GM) and Phase Margin (PM) specifications, in the event of multiple Phase Crossover Frequencies (PCFs) and/or Gain Crossover Frequencies (GCFs). The multiplicity of PCFs and GCFs poses a considerable complication in frequency-domain control design methods. The paper is a continuation of the authors' previous work that applied the robust PI controller design approach to a Continuous Stirred Tank Reactor (CSTR). This preceding application represented the system with a single PCF and a single GCF, but the current article focuses on a case of multiple PCFs and GCFs. The determination of a robust performance region in the P-I plane is based on the stability/performance boundary locus method and the sixteen plant theorem. In the illustrative example, a robust performance region is obtained for an experimental oblique wing aircraft that is mathematically modeled as the unstable interval plant. The direct application of the method results in the (pseudo-)GM and (pseudo-)PM regions that ''illogically'' protrude from the stability region. Consequently, a deeper analysis of the selected points in the P-I plane shows that the calculated GM and PM boundary loci are related to the numerically correct values, but that the results may be misleading, especially for the loci outside the stability region, due to the multiplicity of the PCFs and GCFs. Nevertheless, the example eventually shows that the important parts of the GM and PM regions, i.e., the parts that have an impact on the final robust performance region, are valid. Thus, the method is applicable even to unstable interval plants and to the control loops with multiple PCFs and GCFs.

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PI controller design in the achievable gain-phase margin plane

Cited by 14 publications

References 10 publications

Optimal Hardware and Control Co-Design Applied to an Active Car Suspension Setup

Optimal Hardware and Control Co-Design Applied to an Active Car Suspension Setup

Geometric‐based PID control design with selective harmonic mitigation for DC–DC converters by imposing a norm bound on the sensitivity function

Design of Robust PI Controllers for Interval Plants With Worst-Case Gain and Phase Margin Specifications in Presence of Multiple Crossover Frequencies

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