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Non-Linear Control System and Motor synchronization

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dt2611
#1
Feb6-08, 11:13 AM
P: 2
Hello,
I am currently trying to design a system that will sychronize two propellor motors, and I must design using the following equation:
w'*I + (w^2*r^2*p*S*C_d)/(2) = T_t + T_ss
w' = Angular acceleration
I = moment of inertia
w = angular velocity
r = radius of blade
p = air density
S =Surface Area
C_d = Drag coeeficient
T_t = transient torque
T_ss = Steady state torque

The problem is this is a non-linear system, and I do not know how to 'linearize' the system to use general linear control system theory. Any help would be greatly appreciated. Thanks.
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dingpud
#2
Feb6-08, 11:19 AM
P: 202
this is just a shot in the dark, but can you break the problem up into 2 linear models? Will that help at all?
dt2611
#3
Feb6-08, 11:24 AM
P: 2
what do you mean by two linear models?

dingpud
#4
Feb6-08, 07:31 PM
P: 202
Non-Linear Control System and Motor synchronization

sorry, probably worded that wrong.

Is there anyway to break the problem up into pieces? Other than that, I don't have much to offer, sorry.
trambolin
#5
Feb7-08, 05:28 PM
P: 341
For linearization, follow the procedure in http://en.wikipedia.org/wiki/Jacobian

and evaluate at the operating point that you want. It will clear out the nonlinear terms in the Jacobian and give you a linear system at that point in the form of [tex]\dot{x} = Ax + Bu[/tex]


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