Galil DMC-3425 Manual De Usuario

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1

4

0.1

50

200

2000

W (rad/s)

Magnitude

 

For the given example, the crossover frequency was computed numerically resulting in 200 rad/s. 

Next, we determine the phase of A(s) at the crossover frequency. 

 

A(j200) = 390,000 (j200+51)/[(j200)2 . (j200 + 2000)] 

 

α = Arg[A(j200)] = tan-1(200/51)-180° -tan-1(200/2000) 

 

α  = 76° - 180° - 6° =  -110° 

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. 

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 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: