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Input multiplied by one of the states-State Space Representation

Input multiplied by one of the states-State Space Representation

Input multiplied by one of the states-State Space Representation

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?

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

Your equations do not look right to me. Angular momentum is angular velocity x inertia. You are dividing by inertia. Perhaps you mean angular acceleration. In this case the numerator should be torque. This way your states are angle and angular velocity and you are computing the derivative angular velocity and angular acceleration.

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

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