Non-Linear Control System and Motor synchronization

dt2611

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.

dingpud

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

what do you mean by two linear models?

dingpud

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

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]