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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

A unity-feedback loop has the open-loop transfer function G(s) = 10/((s + 2)(s + 4)). Find the position error constant K_p.

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

K_p =

2.Easy

A unity-feedback loop has the open-loop transfer function G(s) = 20/(s(s + 2)(s + 5)). Find the velocity error constant K_v.

G(s) = 20/(s(s + 2)(s + 5))

K_v =

3.Medium

The parabolic input r(t) = 5·t²/2 is applied to a unity-feedback loop with G(s) = 4(s + 4)/(s²(s + 4)). Find the steady-state error e_ss.

G(s) = 4(s + 4)/(s²(s + 4))r(t) = 5·t²/2

e_ss =

4.Medium

The input r(t) = 10 + 2t (a step plus a ramp) is applied to a unity-feedback loop with G(s) = 4/(s(s + 4)(s + 10)). Find the steady-state error e_ss.

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

e_ss =

5.Hard

A PI controller C(s) = 5 + 10/s drives the plant G(s) = 10/((s + 1)(s + 10)) in a unity-feedback loop. Find the steady-state error e_ss for the ramp input r(t) = 2t.

C(s) = 5 + 10/sG(s) = 10/((s + 1)(s + 10))r(t) = 2t

e_ss =

6.Hard

A PI controller C(s) = 1 + 1/s drives the plant G(s) = 4/((s + 1)(s + 2)) in a unity-feedback loop. Find the steady-state error e_ss for the ramp input r(t) = 5t.

C(s) = 1 + 1/sG(s) = 4/((s + 1)(s + 2))r(t) = 5t

e_ss =

Answer key

1. K_p = 1.25
2. K_v = 2
3. e_ss = 1.25
4. e_ss = 20
5. e_ss = 0.2
6. e_ss = 2.5

Full step-by-step solutions: practise this topic on examproblems.com.