Review Quiz: Basic Control Systems
The following linear system of differential equations represents a physical system.
𝑑2 𝑦
𝑑𝑦
𝑑𝑢
+5
+ 4𝑦 =
+ 2𝑢
2
𝑑𝑡
𝑑𝑡
𝑑𝑡
Part 1: Determine the Transfer Function 𝐻(𝑠) of the system
Part 2: Determine the system’s State Equations
Part 3: Draw the all-integrator block diagram representation of the system.
Part 4: Determine the state space representation of the system in the controllable canonical form.
𝒙̇ = 𝐴𝒙 + 𝑩𝑢
𝑦 = 𝐶𝒙 + 𝑫𝑢
Part 5: Calculate the system poles. Plot them on the complex plane provided below. Is the system stable? Does it
exhibit any oscillatory behavior?
𝑗𝜔
𝜎