Control - 5 - Steady state response

Question 1

What does the system class tell us?

Answer 1

System class reflects the response to steps and ramp inputs.

Question 2

Class one system

Answer 2

• has an integrator in the forward path
• Steady state error is not zero in a class zero system.
• Class zero systems can function adequately despite the steady state error.

Question 3

Class two system

Answer 3

• Class two system has two integrators in the forward path.
• If U(s) is a unit step or a unit ramp then e_ss = 0.
• A class two system is often unstable because each integrator gives a phase lag of -π/2.
• The forward path inverts the error signal. Subtraction at the summing junction inverts it again so the loop gain can easily become >1.

Question 4

Classification of systems: Stability considerations

Answer 4

• K
  
  • Increasing gain K improves steady-state errors;
  • But increasing K can make the CL system unstable:
• Integrators
  
  • Adding integrators eliminates steady-state errors;
  • But adding integrators can make the CL system unstable because each integrator contributes phase lag of -π/2.