Time Domain Analysis of Control Systems Chapter 5

Time Response of Control Systems

• The time response of a control system is divided into two parts: the transient response and the steady-state response.
• The time response, y(t), can be written as the sum of the transient response, Yi(t), and the steady-state response, Yss(t).

Typical Test Signals

Step-Function Input

• A step function has a constant magnitude, R.
• The mathematical representation of a step function is R.

Ramp Function Input

• A ramp function changes constantly with time.
• The mathematical representation of a ramp function is Rt.

Parabolic-Function Input

• A parabolic function represents a signal that is one order faster than the ramp function.
• The mathematical representation of a parabolic function is (R/2)t².

Steady-State Error

• The steady-state error is the difference between the output and the reference in the steady state.
• The steady-state error is determined by the limits of the three terms in the denominator, known as static error constants.
• The names of the static error constants are:
  • Position error constant (Kp)
  • Velocity error constant (Kv)
  • Acceleration error constant (Ka)

Evaluating Static Error Constants

• Example: evaluate the static error constants and find the expected error for standard step, ramp, and parabolic inputs.

Steady-State Error for Nonunity Feedback Systems

• Steady-state error can be found from the state space.

System Type and Steady-State Error

• The system type, error constant, and steady-state error can be determined for a unit step input.
• Example: find the system type, the appropriate error constant associated with the system type, and the steady-state error for a unit step input.

This quiz covers the time response of a control system, including transient and steady-state responses, based on Chapter 5 of Automatic Control System by Kuo.