Stepping motor lifting speed mathematical model

In order to
rotating joint make the stepping motor in the operation of the don't appear out of step phenomenon, general requirements of the maximum operating frequency should be less than or

equal to) step response frequency fs. In the frequency, the stepper motor can be arbitrary start and stop or reverse turn not happen step out of phenomenon. Stepping motor

lifting speed have two kinds of driving mode, namely triangle and trapezoidal driving mode (see chart 1), and the triangle driving mode is a special case of the trapezoidal

drive, so we as long as the research keystone way. Motor of acceleration and deceleration is through the computer continually modify timer initial value to
rotary union achieve. In the motor

accelerating phase, from starting instantaneous start, each produce a pulse, the timer initial value decrease a certain value, the corresponding pulse cycle reduced, namely

pulse frequency increase; In reduction phase, the timer initial value unceasingly increases, the corresponding pulse cycle increases, the pulse frequency decreases, and the

corresponding trapezoidal pulse frequency characteristics of the deceleration phase. This design is the key to determine the pulse timing tn, pulse interval namely pulse cycle

tn and pulse frequency fn. Hypothesis from starting instantaneous start counting pulse number, accelerate the phase of the pulse number for n, and set starting instantaneous for

timing starting point, the timer initial value for D1, the timer initial value reduction for train. From the physical process of accelerating stage, it is known that the first

pulse cycle, that is activated when the pulse cycle T1 = D1 / f0, T1 = 0. Due to fiber optic rotary joint the initial value of timer revision, the second pulse cycle T2 = (D1 - train) / f0 = T1 -

train/f0, pulse timing T2 = T1, then the first n pulse cycle for:
Pulse timing for:
Pulse frequency for:
The type respectively show the pulse number n and pulse frequency fn and time tn relationship. To train/f0 = δ, namely accelerating stage adjacent two pulse cycle reduction,

the above formula simplified to:
Simultaneous (4), (5), and simplify the relationship between fn and tn, it is concluded that accelerate stage of the mathematical model for:
Among them, is constant, the value and timer initial value and timer change related, A = - δ, B = (2 t1 + δ) 2, C = 8 δ.