You've built a model for a large damped servo system with dynamics Jj = -by+T where...

  

Transcribed Image Text:

You've built a model for a large damped servo system with dynamics Jj = -by+T where J is the servo motor inertia of a large servo, b is a damping constant for a damping system, and T is the torque applied upstream of the servo as a control signal. We suppose that the torque signal T(t)= Kru(t) is an amplified signal of an input signal u(t) coming from an upstream controller. (a) You now wire the system with a proportional controller u(t)= Kpe(t) in unity feedback configuration. In the process of doing so, suppose that you accidentally leave an inverting amplifier in between your input signal and torque signal so that T(t) = -Kru(t). Is it possible to stabilize the system? Use a root locus argument to justify your answer. What if you change the sign? You've built a model for a large damped servo system with dynamics Jj = -by+T where J is the servo motor inertia of a large servo, b is a damping constant for a damping system, and T is the torque applied upstream of the servo as a control signal. We suppose that the torque signal T(t)= Kru(t) is an amplified signal of an input signal u(t) coming from an upstream controller. (a) You now wire the system with a proportional controller u(t)= Kpe(t) in unity feedback configuration. In the process of doing so, suppose that you accidentally leave an inverting amplifier in between your input signal and torque signal so that T(t) = -Kru(t). Is it possible to stabilize the system? Use a root locus argument to justify your answer. What if you change the sign?