AC Phase Control

See AC Phase Control
Input, gate, output voltage for one period of signals.

T2 = will be constant determined by a minimum requirement of the traic.
T3 = (1/60Hz)/2 = 8.3(3)ms constant is the "Zero crossing" signal.

T1 = 0ms(100%) сorresponds to 110 Vac
T1 = 1 ms сorresponds to 105.9 Vac
T1 = 2 ms сorresponds to 94.6 Vac
T1 = 3 ms сorresponds to 77.8 Vac
T1 = 4 ms сorresponds to 57.8 Vac
T1 = 4.2ms(50%) сorresponds to 55 Vac
T1 = 5 ms сorresponds to 37.3 Vac
T1 = 6 ms сorresponds to 19.4 Vac
T1 = 7 ms сorresponds to 6.5 Vac

T1 = 2.05ms(75%) сorresponds to 93.9 Vac

T1 = 6.22(25%) сorresponds to 16.1 Vac

Discretization of the time and quantization the voltage by level.


The required acceleration (deceleration) time T0 is 1 second.

Time discretization depend on "Zero crossing" signal. Nz = 1 s / 8.3(3) = 120.
Required Step level is 0.1ms. PLC cycle time is equal to Step level = 0.1ms.
Required quantization time is 7ms and less than 8.3ms "Zero crossing" signal.
Quantization by level depend on required Step level 0.1ms. Nl = 7ms / 0.1ms = 70.
Actual number of quantization steps N = min(Nz, Nl) = min(120, 70) = 70.

Multiplier K = round( T0 / (N * 8.3) ) = round( 1s / (70 * 8.3ms) ) = 2
Actual acceleration (deceleration) time T0 is
T0 = N * K * 8.3ms = 70 * 2 * 8.3ms = 1.16s

Version 1

Proteus

Start Btn->Acceleration->Work->Stop Btn->Deceleration->OFF softstart1.avi
LD, hex, Proteus8.4 in SOFTSTART.ZIP

Note 1
There is jitter near 1 time PLC cycle since the external "Zero crossing" and internal "PLC cycle" signals are not synchronous. Compliance with the condition Duration of "Zero crossing" signal > "PLC cycle time" is required to detect "Zero crossing" signal in each PLC cycle.

"Jitter" softstart2.avi

Note 2
The problem is very short PLC cycle = 0.1ms, duty of PLC cycle near 40%. Big LD program can't fit in 0.1ms.

Version 2

You can change N from 70 down to 49 without any other changes in softstart.ld to adjust the minimum speed after deceleration.
T1 = 5 ms сorresponds to 37.3 Vac (N = 50)
T1 = 6 ms сorresponds to 19.4 Vac (N = 60)
T1 = 7 ms сorresponds to 6.5 Vac (N = 70)

Start Btn->Acceleration->Work->Deceleration Limit->Deceleration->Low voltage work->Stop Limit->OFF softstart3.avi
LD, asm, hex, Proteus8.4 in SOFTSTART2.ZIP

If PLC cycle = 0.1ms is too short you can set:
PLC cycle = 0.2ms, N = 35, K = 3, CK = 2
PLC cycle = 0.3ms, N = 23, K = 5, CK = 4
PLC cycle = 0.4ms, N = 17, K = 7, CK = 6
PLC cycle = 0.5ms, N = 14, K = 9, CK = 8

You can increase acceleration (deceleration) time T0 by increase CK multiplier.

Any questions to LDmicro.GitHub@gmail.com.