Galil DMC-13X8 user manual Kd = 10/32768 = Encoder Kf = 4N/2π =

Consider a system with the following parameters:

Kt	Nm/A
J = 2.10-4	kg.m2
R = 2	Ω
Ka = 2	Amp/Volt
N = 1000	Counts/rev

Torque constant

System moment of inertia

Motor resistance Current amplifier gain

Encoder line density

The DAC of theDMC-13X8 outputs +/-10V for a 16-bit command of +/-32768 counts.

The design objective is to select the filter parameters in order to close a position loop with a crossover frequency of ωc = 500 rad/s and a phase margin of 45 degrees.

The first step is to develop a mathematical model of the system, as discussed in the previous system. Motor

M(s) = P/I = Kt/Js2 = 1000/s2

Amp

Ka = 2 [Amp/V]

DAC

Kd = 10/32768 = .0003

Encoder

Kf = 4N/2π = 636

ZOH

H(s) = 2000/(s+2000) Compensation Filter

G(s) = P + sD

The next step is to combine all the system elements, with the exception of G(s), into one function, L(s). L(s) = M(s) Ka Kd Kf H(s) =3.17∗106/[s2(s+2000)]

Then the open loop transfer function, A(s), is A(s) = L(s) G(s)

Now, determine the magnitude and phase of L(s) at the frequency ωc = 500.

L(j500) = 3.17∗106/[(j500)2 (j500+2000)] This function has a magnitude of

L(j500) = 0.00625 and a phase

Arg[L(j500)] = -180°- tan-1(500/2000) = -194°

G(s) is selected so that A(s) has a crossover frequency of 500 rad/s and a phase margin of 45 degrees. This requires that

A(j500) = 1

Arg [A(j500)] = -135°

Chapter 10 Theory of Operation • 168 USER MANUAL