User:Saung Tadashi/Clegg integrator

Clegg integrator or reset integrator^[1] is an analog integrator used in the design of controllers for control systems. It was proposed by J. C. Clegg in 1958.^[2]

Definition

The Clegg integrator can be described by the following equations:

$\left\{{\begin{array}{ll}{{\dot {u}}(t)=e(t)}&{{\text{ when }}e(t)\neq 0}\\{u\left(t^{+}\right)=0}&{{\text{ when }}e(t)=0}\end{array}}\right.$

where e is the error input to the integrator and u is the output. The reset happens exactly at the time $t^{+}$ when there is a zero crossing of the input.

TODO

Add circuit implementation^[3]^[4]
Add describing function analysis

References

^ Baños, Alfonso, 1965- (2012). Reset control systems. Barreiro, Antonio. London: Springer. ISBN 9781447122500. OCLC 758652894.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
^ Clegg, J. C. (1958). "A nonlinear integrator for servomechanisms". Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry. 77 (1): 41–42. doi:10.1109/TAI.1958.6367399. ISSN 0097-2185.
^ Zaccarian, L.; Nesic, D.; Teel, A.R. (2005). "First order reset elements and the Clegg integrator revisited". Proceedings of the 2005, American Control Conference, 2005. Portland, OR, USA: IEEE: 563–568. doi:10.1109/ACC.2005.1470016. ISBN 9780780390980.
^ Prieur, Christophe; Queinnec, Isabelle; Tarbouriech, Sophie; Zaccarian, Luca (2018). "Analysis and Synthesis of Reset Control Systems". Foundations and Trends® in Systems and Control. 6 (2–3): 117–338. doi:10.1561/2600000017. ISSN 2325-6818.

[1] Baños, Alfonso, 1965- (2012). Reset control systems. Barreiro, Antonio. London: Springer. ISBN 9781447122500. OCLC 758652894.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)

[2] Clegg, J. C. (1958). "A nonlinear integrator for servomechanisms". Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry. 77 (1): 41–42. doi:10.1109/TAI.1958.6367399. ISSN 0097-2185.

[3] Zaccarian, L.; Nesic, D.; Teel, A.R. (2005). "First order reset elements and the Clegg integrator revisited". Proceedings of the 2005, American Control Conference, 2005. Portland, OR, USA: IEEE: 563–568. doi:10.1109/ACC.2005.1470016. ISBN 9780780390980.

[4] Prieur, Christophe; Queinnec, Isabelle; Tarbouriech, Sophie; Zaccarian, Luca (2018). "Analysis and Synthesis of Reset Control Systems". Foundations and Trends® in Systems and Control. 6 (2–3): 117–338. doi:10.1561/2600000017. ISSN 2325-6818.

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Definition

TODO

See also

References