Draft:Clegg integrator

Submission declined on 27 May 2026 by MSK (talk).

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Declined by MSK 5 months ago. Last edited by MSK 5 months ago. Reviewer: Inform author.

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Comment: Currently relies on only one source, which is primary. m s k 18:27, 27 May 2026 (UTC)

The Clegg integrator is a nonlinear analog integrator equipped with a reset mechanism, used in feedback control systems. It was proposed by J. C. Clegg in 1958 as a modification of the conventional linear integrator.^[1]

Description

The Clegg integrator behaves like an ordinary linear integrator, except that it resets its output to zero whenever its input crosses zero.

The circuit of a Clegg integrator consists of resistors $R$ , $R_{d}$ , and $R_{s}$ , two capacitors $C$ , four diodes, and two operational amplifiers. It is assumed that $R_{d} ≪ R$ . Let $V_{i n}$ denote the input voltage of the circuit and $V_{o u t}$ the output voltage. As long as $V_{i n}$ does not cross zero, the output $V_{o u t}$ is proportional to the integral of $V_{i n}$ . However, the integral is reset as soon as $V_{i n} = 0$ . Denoting by $t_{i}$ the most recent instant at which $V_{i n} = 0$ , we then have:

$V_{o u t} (t) = - \frac{1}{2 R C} \int_{t_{i}}^{t} V_{i n} (s) d s$

Use

In control theory, controllers with an integral action on the control error (for example PID controllers) suffer from windup phenomena when the actuator saturates (a valve at its limit, maximum voltage, etc.). This is known as the windup problem. By replacing the conventional linear integrator with a Clegg integrator, the integral term is reset to zero at each zero-crossing of the error, which improves the performance of the controller.

References

↑ Clegg, J. C. (March 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. Retrieved 2026-05-26.

[1] Clegg, J. C. (March 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. Retrieved 2026-05-26.

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