Consider the cascade control system shown in the figure below and answer the following questions.

Consider the cascade control system shown in the figure below. 1. (20 points) Find the value of the gain of the inner loop P controller, Kc2, that provides a decay ratio of 1/4 (I.e., find the Ziegler Nichols settings for this controller). Note that you should approximate the behavior of the system as a FOPTD transfer function. 2. (10 points) Find the settings of the PI primary controller using direct synthesis (the tuning rules in table 12.1 SEMD) 3. (20 points) compare the gain of the primary controller with the gain of a PI controller that would be implemented in a single-loop (non-cascade) configuration. To this end, assume that KcC=1, and that the sensor transfer function circled in blue is zero. What can you conclude about the benefits of cascade control