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# PSoC Creator & Designer Software

New Contributor II

## Discrete math question - derivatives, integrals, and real time motor control applications

Greetings all!  This is a general question that involves engineering judgement (which I don't have a lot of in the field of motor controls).

1. In discrete math for a real time application, I might code a time derivative as:

y = (x - x[n - 1]) / T     Where x is the current ADC sample, x[n-1] is the previous ADC sample, T is the sampling period, and y is the "derivative"

Similar equation for an integral:

y = y[n-1] + T*x

2. There are more "accurate" equations than the ones above, for instance:

More accurate derivative:

y =    (4 / 3) * (x[n+1] - x[n-1]) / (2*T)   -   (1 / 3) * (x[n+2] - x[n-2]) / (4*T)

QUESTION:

Let's say I want to use the "more accurate" derivative equation in a 100kHz PWM control loop application (for instance, a dc-dc converter, or a motor control application).

The "more accurate" derivative uses an x[n+2] term, which means that whenever I use the equation, I'm always 2 samples "behind".  In the world of 100kHz real time applications, is this 2 sample delay a "big deal", or can I get away with it?

2 Replies
Employee

## Re: Discrete math question - derivatives, integrals, and real time motor control applications

Hi,

Are you trying to implement PID loop for motor speed control. These delays have effect and also the motor/circuit lag will introduce more delay in the system. A proper tuned PID can overcome this.

Thanks

Jobin GT

Honored Contributor II

## Re: Discrete math question - derivatives, integrals, and real time motor control applications

In my experience with PID control, the derivative term is usually unnecessary or diminished. In discrete math it is mostly a noise maker, for that it is not worth improving it with 4-point approximation. Furthermore, increasing sampling rate worsens derivative term accuracy to practically a noise level. I think that 10kHz sampling rate should suffice for a motor control, while 100kHz is not enough for DC-DC converter application.

/odissey1