Eigenvalue for DC motor convergence rate

AI Thread Summary
The discussion centers on finding the control voltage for a DC motor to ensure that the speed converges to a constant reference input while determining the convergence rate through specified eigenvalues L1 and L2. The user shares the governing equations for the DC motor, which include parameters like inertia, load torque, resistance, and input voltage. They express confidence in calculating the control voltage but seek guidance on how to derive the convergence rate linked to the eigenvalues. The conversation highlights the need for clarity on the relationship between the motor's dynamics and the eigenvalues. Understanding this connection is crucial for achieving the desired speed control and convergence behavior.
pcming
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Hi,
I have troubles solving this question:
Given the general DC motor governed equation, find the control voltage such that the speed w tends to constand reference input w* and the convergence rate is determined by the desired eigenvalues L1 and L2.
I think it's easy to find the control voltage to the speed w. However I don't know how to find "convergence rate" which is determined by the desired eigenvalues. Can anyone give me some suggestions? Thanks.
 
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pcming said:
Hi,
I have troubles solving this question:
Given the general DC motor governed equation, find the control voltage such that the speed w tends to constand reference input w* and the convergence rate is determined by the desired eigenvalues L1 and L2.
I think it's easy to find the control voltage to the speed w. However I don't know how to find "convergence rate" which is determined by the desired eigenvalues. Can anyone give me some suggestions? Thanks.
Can you give us the "general DC motor governed equation"?

AM
 
Hi Andrew,
here it is:

J(dw/dt)=K1*i-T
L(di/dt)=-R*i-K2*w+u

where J is the inertial moment, w is motor speed, T is load torque, R is resistance, i is current, K1 and K2 are constant, and u is the input voltage.

Thank for your reply! Hope you know how to do it.
 

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