PID controller design with an  H∞  criterion

Han, Sangjin; Keel, L.H.; Bhattacharyya, S.P.

doi:10.1016/j.ifacol.2018.06.127

Cited by 11 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Accordingly with [25], given a bound

γ > 0

for the

H_{\infty}

norm on the sensitivity function, we can write

true2.470em2.470emtrue∥ \frac{1}{1 + P_{u} false(s false) C false(s false)} ∥_{\infty} < γ

which is equivalent to

| 1 + P_{u} false(j ω false) C false(j ω false) | > \frac{1}{γ}, normal∀ ω \in false[0, normal∞ false) .

…”

Section: Preliminariesmentioning

confidence: 99%

“…In this paper, we use the stabilising set for PID controllers [5, 19] and results to synthesise a PI/PID controller with an

H_{\infty}

norm [25] to design a PI/PID controller which tracks step reference signals and mitigates selective harmonics disturbances present in DC microgrids systems. Preliminary results for a PI controller with a single disturbance signal were presented in [26] and summarised in [27].…”

Section: Introductionmentioning

confidence: 99%

“…The paper is organised as follows. Section 2, following this introduction, summarises the design constraint approach of [25] and in Section 3, a design procedure of PI/PID controllers is proposed. In Section 4, a numerical example is presented in order to illustrate the construction of the stabilising sets along with performance specifications.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Accordingly with [25], given a bound

γ > 0

for the

H_{\infty}

norm on the sensitivity function, we can write

true2.470em2.470emtrue∥ \frac{1}{1 + P_{u} false(s false) C false(s false)} ∥_{\infty} < γ

which is equivalent to

| 1 + P_{u} false(j ω false) C false(j ω false) | > \frac{1}{γ}, normal∀ ω \in false[0, normal∞ false) .

…”

Section: Preliminariesmentioning

confidence: 99%

“…In this paper, we use the stabilising set for PID controllers [5, 19] and results to synthesise a PI/PID controller with an

H_{\infty}

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…Em geral, as normas H ∞ e H 2 são usados para avaliar a robustez do controlador e os critérios de desempenho em níveis de atenuação de perturbações para várias classes de perturbações determinísticas e estocásticas Balandin and Kogan (2019); Díaz-Rodríguez et al (2019). Em consonância com os trabalhos apresentados em Ho et al (1999) e Díaz-Rodríguez and Bhattacharyya (2016), em Han et al (2018) os autores desenvolveram uma abordagem geométrica para limitar a norma H ∞ e consequentemente fornecer garantias estabilidade relativa.…”

Section: Introductionunclassified

“…Han et al (2018)é demonstrado comoé possível obter garantia de margem de fase e ganho para o sistema sem distúrbio mostrado na Figura 1 a partir da limitação da função de transferência do erro. Para fácil referência o resultadoé apresentado a seguir.Teorema 4.…”

unclassified

Projeto de controlador de ordem fixa via LMI com limitação da norma H-infinito e garantias de margens de estabilidade

Magossi

Araújo

Elias

et al. 2020

Anais Do Congresso Brasileiro De Automática 2020

View full text Add to dashboard Cite

Controladores de ordem fixa, como os controladores Proporcional+Integral+Derivativo (PID), são amplamente utilizados na indústria e a norma H-infinito pode ser utilizada para avaliar critérios de robustez e desempenho do controlador. Neste trabalho é proposta uma estratégia de ajuste para controladores de ordem fixa usando um limite superior na norma H-infinito e garantia da margem de estabilidade. A estratégia de sintonia utiliza uma realização canônica controlável associada à uma representação do produto de polinômios na forma matricial, sem busca iterativa ou necessidade de utilizar métodos geométricos, através de desigualdades matriciais lineares. Exemplos numéricos são apresentados para validar o método de sintonia proposto.

show abstract