Steady-state error & PID control worksheet with answers

Free printable Steady-state error & PID control worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A proportional controller K = 4 drives the plant G(s) = 2/(s + 10) in a unity-feedback loop. A step of size 10 is applied. Find the final value of the output y(∞).

G(s) = 2/(s + 10)K = 4r = 10

y(∞) =

2.Easy

A proportional controller K = 3 drives the plant G(s) = 2/(s + 10) in a unity-feedback loop. A step of size 5 is applied. Find the final value of the output y(∞).

G(s) = 2/(s + 10)K = 3r = 5

y(∞) =

3.Medium

The input r(t) = 1 + 1t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 2(s + 1)/(s(s + 1)(s + 4)). Find the steady-state error e_ss.

G(s) = 2(s + 1)/(s(s + 1)(s + 4))r(t) = 1 + 1t

e_ss =

4.Medium

A process G(s) = 2/(10s + 1) is controlled by a proportional gain K = 9 in a unity-feedback loop. Find the steady-state error e_ss for a step, as a percentage of the step size.

G(s) = 2/(10s + 1)K = 9

e_ss = %

5.Hard

A proportional controller K = 40 drives the plant G(s) = 5/(s(s + 6)) in a unity-feedback loop. Find the peak time t_p of the step response.

G(s) = 5/(s(s + 6))K = 40

t_p = s

6.Hard

A proportional controller K = 25 drives the plant G(s) = 2/(s(s + 10)) in a unity-feedback loop. Find the peak time t_p of the step response.

G(s) = 2/(s(s + 10))K = 25

t_p = s

Answer key

1. y(∞) = 4.444
2. y(∞) = 1.875
3. e_ss = 2
4. e_ss = 5.263 %
5. t_p = 0.2273 s
6. t_p = 0.6283 s

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