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Questions and Answers
What is the time response of a control system typically divided into?
What is the mathematical representation of a ramp function?
What is the parabolic function in terms of the ramp function?
What is the maximum overshoot used to measure in a control system?
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What is the steady-state error in a control system?
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What are the three terms in the denominator that are taken to the limit to determine the steady-state error?
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How can the steady-state error be found for nonunity feedback systems?
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What is the system type, and the appropriate error constant associated with it, for a unit step input?
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Study Notes
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.
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Description
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.
