# Non-Linear Control System and Motor synchronization

1. Feb 6, 2008

### 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
p = air density
S =Surface Area
C_d = Drag coeeficient
T_t = transient 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.

2. Feb 6, 2008

### 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?

3. Feb 6, 2008

### dt2611

what do you mean by two linear models?

4. Feb 6, 2008

### 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.

5. Feb 7, 2008

### 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 $$\dot{x} = Ax + Bu$$