Question

4. We set up the model for the cart-pendulum system in class, and linearized it around the operating point, $(x, \theta, u) = (0, 0, 0)$. Now linearize the system around $(x, \theta, u) = (0, \pi, 0)$, and obtain the transfer function $\Delta u \to \Delta \theta$.

Name: 4. We set up the model for the cart-pendulum system in class, and linearized it around the operating point, (x, θ, u) = (0, 0, 0). Now linearize the system around (x, θ, u) = (0, π, 0), and obtain the transfer function Δ u →Δθ.
Uploaded: 2023-08-21T09:36:29-08:00
Duration: 5 min 32 s
Channel: Madhur L
Description: 4. We set up the model for the cart-pendulum system in class, and linearized it around the operating point, (x, θ, u) = (0, 0, 0). Now linearize the system around (x, θ, u) = (0, π, 0), and obtain the transfer function Δ u →Δθ.

          4. We set up the model for the cart-pendulum system in class, and linearized it around the operating point, $(x, \theta, u) = (0, 0, 0)$. Now linearize the system around $(x, \theta, u) = (0, \pi, 0)$, and obtain the transfer function $\Delta u \to \Delta \theta$.

4. We set up the model for the cart-pendulum system in class, and linearized it around the operating point, (x, θ, u) = (0, 0, 0). Now linearize the system around (x, θ, u) = (0, π, 0), and obtain the transfer function Δ u →Δθ.

Added by Juan Carlos H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

08/21/2023

Step 1

Step 1: Linearize the system around the new operating point (x, θ, u) = (0, π, 0) by finding the Jacobian matrices A, B, C, and D. Show more…

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We set up the model for the cart-pendulum system in class, and linearized it around the operating point, (x, θ, u) = (0, 0, 0). Now linearize the system around (x, θ, u) = (0, π, 0), and obtain the transfer function Δu -> Δθ. 4. We set up the model for the cart-pendulum system in class, and linearized it around the operating point, x, u = 0, 0. Now linearize the system around, u = 0, π, 0 and obtain the transfer function u.