Galil DMC-2X00 user manual 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
A/V	Current amplifier gain
	Digital filter gain
	Digital filter zero
	No integrator
Counts/rev	Encoder line density
ms	Sample period

The transfer function of the system elements are: Motor

M(s) = P/I = Kt/Js2 = 500/s2 [rad/A]

Amp

Ka = 4 [Amp/V]

DAC

Kd = 0.0003 [V/count]

Encoder

Kf = 4N/2π = 318 [count/rad]

ZOH

2000/(s+2000) Digital Filter

KP = 12.5, KD = 245, T = 0.001 Therefore,

D(z) = 1030 (z-0.95)/Z

Accordingly, the coefficients of the continuous filter are: P = 50

D = 0.98

The filter equation may be written in the continuous equivalent form: G(s) = 50 + 0.98s = .098 (s+51)

The system elements are shown in Fig. 10.7.

DMC-2X00 Chapter 10 Theory of Operation y 141