The characteristic equation is a polynomial equation derived from the transfer function of the system. It helps determine the stability and behavior of the system.

The term "computed torque diagram" does not typically have a direct connection to a characteristic equation. The computed torque method is a control strategy used in robotic systems to achieve desired trajectories and improve tracking performance.

Here is characteristic equation, let's consider a simple second-order control system with a transfer function:

G(s) = K / (s^2 + 2ζωn s + ωn^2)

Where:

- K is the system gain

- ζ is the damping ratio

- ωn is the natural frequency

The characteristic equation is obtained by setting the denominator of the transfer function equal to zero:

s^2 + 2ζωn s + ωn^2 = 0

This is a second-order polynomial equation in the Laplace domain, and its roots (solutions) define the system's poles. The characteristic equation allows us to analyze the stability and transient response of the system.

For example, if we have ζ > 1 (overdamped system), the characteristic equation will have two distinct real roots. If ζ = 1 (critically damped system), the characteristic equation will have two equal real roots. And if ζ < 1 (underdamped system), the characteristic equation will have a pair of complex conjugate roots.

Good luck

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