Galil DMC-2X00 user manual System Design and Compensation, Analytical Method

Finally, the phase margin, PM, equals PM = 180° + α = 70°

As long as PM is positive, the system is stable. However, for a well damped system, PM should be between 30 degrees and 45 degrees. The phase margin of 70 degrees given above indicated overdamped response.

Next, we discuss the design of control systems.

System Design and Compensation

The closed-loop control system can be stabilized by a digital filter, which is preprogrammed in the DMC-2x00 controller. The filter parameters can be selected by the user for the best compensation. The following discussion presents an analytical design method.

The Analytical Method

The analytical design method is aimed at closing the loop at a crossover frequency, ωc, with a phase margin PM. The system parameters are assumed known. The design procedure is best illustrated by a design example.

Consider a system with the following parameters:

Kt

J= 2.10-4R = 2

Ka = 2 N = 1000

Nm/A	Torque constant
kg.m2	System moment of inertia
Ω	Motor resistance
A/V	Current amplifier gain
Counts/rev	Encoder line density

The DAC of the DMC-2x00 outputs +/-10V for a 14-bit command of +/-8192 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

DMC-2X00 Chapter 10 Theory of Operation y 143