Exercise 1.5#
Analysis ∙ Linear dynamical systems
Assume that the DC motor described in Exercise 1.1 is controlled by a Proportional (P) controller.
Sketch the block diagram of the control system. Determine how the poles of the closed-loop depend on the proportional gain \(K\), and discuss what this means for the behavior of the closed-loop.
Consider two reference signals, a step \(\theta_{ref}(t) = \textrm{step}(t)\) and a ramp \(\theta_{ref}(t) = \textrm{ramp}(t)\). What is the steady-state controll error (or output tracking error) in these two cases?
Consider now a Proportional Integral (PI) controller. What will the steady-state error be if the reference signal is a ramp?