Control Systems

Use this for “Find ωₙ, ζ and the DC gain of G(s) = 1/(2s² + 8s + 50) for a 2 kg mass.”

Use this for “G(s) = 4/(s + 1) has unity feedback. Find the closed-loop pole, the DC gain and the time constant.”

Use this for “A loop must overshoot 10% and settle in 2 s. Find ζ and ωₙ.”

Use this for “Find the DC gain of G(s) = 5(s + 2)/((s + 1)(s + 4)).”

Use this for “Find the steady-state step error of G(s) = 30/((s + 1)(s + 5)) under unity feedback.”

Use this for “How many roots of s³ + s² + 2s + 8 = 0 lie in the right half-plane?”

Use this for “Sketch the root locus of K/(s(s + 2)(s + 4)): find the centroid and the breakaway point.”

Use this for “Sketch the Bode gain of 100 ÷ (s + 10) and find the exact gain at 50 rad/s.”

Use this for “Find the gain margin of G(s) = 2 ÷ (s(s + 1)(s + 2)) in unity feedback.”

Use this for “Find the closed-loop bandwidth of a system with ζ = 0.4 and ωₙ = 5 rad/s.”

Use this for “A plant 1/(s + 1) under PI control with Kₚ = 3 and Kᵢ = 8: find ωₙ and ζ of the closed loop.”

Use this for “A loop oscillates steadily at Kᵤ = 48 with period Tᵤ = 2.22 s. Find the Ziegler–Nichols PID gains.”

Use this for “Which PID term removes the steady-state error to a step?”