The time-domain specifications when the pendulum is balanced and tracking a rotary arm setpoint are: PO...

 

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The time-domain specifications when the pendulum is balanced and tracking a rotary arm setpoint are: PO < 6.81% ts 1.54 s Thus, as the rotary arm goes back and forth to track the reference (while balancing the pendulum) it should have a percent overshoot and settling time matching these requirements. 1. The open-loop poles of the inverted pendulum are located at {0, -22.03, 13.58, -4.672). Note that the system is unstable. Find the characteristic equation of A. 2. Find the companion matrices (Ã, B). 3. The percent overshoot and settling time specifications given in Equation 2.1 translates into the following natural frequency and damping ratio requirements: = 0.65 Wn = 4 rad/s Based on these specifications, find the location of the two dominant poles pi and P2. 4. Find the desired characteristic equation if the other poles are placed at p3 = -40 and p4 = -45. 5. Applying the companion-based control u = - Kx to (Ã, B) results in the closed-loop system (Ã – KB). Find the gain K that assigns the poles to their new desired location. The time-domain specifications when the pendulum is balanced and tracking a rotary arm setpoint are: PO < 6.81% ts 1.54 s Thus, as the rotary arm goes back and forth to track the reference (while balancing the pendulum) it should have a percent overshoot and settling time matching these requirements. 1. The open-loop poles of the inverted pendulum are located at {0, -22.03, 13.58, -4.672). Note that the system is unstable. Find the characteristic equation of A. 2. Find the companion matrices (Ã, B). 3. The percent overshoot and settling time specifications given in Equation 2.1 translates into the following natural frequency and damping ratio requirements: = 0.65 Wn = 4 rad/s Based on these specifications, find the location of the two dominant poles pi and P2. 4. Find the desired characteristic equation if the other poles are placed at p3 = -40 and p4 = -45. 5. Applying the companion-based control u = - Kx to (Ã, B) results in the closed-loop system (Ã – KB). Find the gain K that assigns the poles to their new desired location.

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1 The characteristic equation of A can be found by multiplying the factors corresponding to the open... View the full answer