## Input multiplied by one of the states-State Space Representation

## Input multiplied by one of the states-State Space Representation

(OP)

Hello. I want to represent a mechanical system in state space form. It is a see-saw like device with a motor and propeller attached to the longer end, and a counterweight attached to the shorter end. When the motor spins the propeller the longer end rises. I have to control the position (height). When writing the equations I end up with:

theta=angular position

(angular momentum)=Sin(theta)(-90.8621+1.4797 u -fg+fc)/(moment of inertia)

(angular velocity)=d(angular position)/dt

My states are angular position and angular velocity.

My problem is my input is multiplied by one of my states(angular position) and when writing it in matrix form I don't know how to separate u and the state theta(angular position). What is the best solution to solve this problem?

theta=angular position

(angular momentum)=Sin(theta)(-90.8621+1.4797 u -fg+fc)/(moment of inertia)

(angular velocity)=d(angular position)/dt

My states are angular position and angular velocity.

My problem is my input is multiplied by one of my states(angular position) and when writing it in matrix form I don't know how to separate u and the state theta(angular position). What is the best solution to solve this problem?

## RE: Input multiplied by one of the states-State Space Representation

BTW, the sin() function is non-linear. You really should use differential equations and integrate them using Runge-Kutta. State space will work only if you continuously update your transition matrix as theta or angular position changes. In this case it is easier to use Runge-Kutta.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/