Integral-cycle control (on–off control) of AC regulators For integral-cycle control of an AC regulator, the control period (m + n)T should be chosen how, relative to the mechanical or thermal time constant of the load/system, to ensure smooth output?

Introduction / Context:
Integral-cycle control (also called on–off or burst firing) applies whole cycles of AC to a load followed by whole cycles of no power. The average power is controlled by the duty ratio m/(m+n). To obtain a smooth process variable (speed, temperature), the modulation period must be short compared with the system’s response time.

Given Data / Assumptions:

• (m + n)T is the burst period, with T = cycle time of mains.
• Load has a dominant mechanical or thermal time constant τ.
• Goal is to minimise ripple in the controlled variable.

Concept / Approach:

If the burst period is much shorter than τ, the load integrates (averages) the on/off power, yielding a nearly steady output. If the period is long compared with τ, the process variable will oscillate noticeably (hunting), which is undesirable for quality and component stress.

Step-by-Step Solution:

Verification / Alternative check:

Control engineering practice recommends carrier (modulation) frequency high enough that the plant cannot respond cycle-by-cycle; the same principle applies to burst firing on heaters and some motors.

Why Other Options Are Wrong:

Periods longer than τ cause visible cycling; “does not matter” is incorrect; exact equality is not a design requirement; “very high” in the sense of much larger than τ is the wrong direction.

Common Pitfalls:

Confusing electrical ripple with process ripple; assuming more cycles on at once is always better regardless of τ.

Final Answer:

Less than the mechanical or thermal time constant