Galil DMC-3425 user manual System Analysis, Zoh

K = 160

A = 0.9

C = 1

a = 250 rad/s

and the equivalent continuous filter, G(s), is

G(s) = [16 + 0.144s + 1000/s} ∗ 250/ (s+250)

The notch filter has two complex zeros, Z and z, and two complex poles, P and p.

The effect of the notch filter is to cancel the resonance affect by placing the complex zeros on top of the resonance poles. The notch poles, P and p, are programmable and are selected to have sufficient damping. It is best to select the notch parameters by the frequency terms. The poles and zeros have a frequency in Hz, selected by the command NF. The real part of the poles is set by NB and the real part of the zeros is set by NZ.

The simplest procedure for setting the notch filter is to identify the resonance frequency and set NF to the same value. Set NB to about one half of NF and set NZ to a low value between zero and 5.

ZOH

The ZOH, or zero-order-hold, represents the effect of the sampling process, where the motor command is updated once per sampling period. The effect of the ZOH can be modeled by the transfer function

H(s) = 1/(1+sT/2)

If the sampling period is T = 0.001, for example, H(s) becomes: H(s) = 2000/(s+2000)

However, in most applications, H(s) may be approximated as one.

This completes the modeling of the system elements. Next, we discuss the system analysis.

System Analysis

To analyze the system, we start with a block diagram model of the system elements. The analysis procedure is illustrated in terms of the following example.

Consider a position control system with the DMC-2x00 controller and the following parameters:

Kt = 0.1

J= 2.10-4R = 2 Ka = 4

KP = 12.5 KD = 245 KI = 0 N = 500 T = 1

Nm/A	Torque constant
kg.m2	System moment of inertia
Ω	Motor resistance
Amp/Volt	Current amplifier gain
	Digital filter gain
	Digital filter zero
	No integrator
Counts/rev	Encoder line density
ms	Sample period

The transfer functions of the system elements are:

DMC-3425 Chapter 10 Theory of Operation• 165