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Questions and Answers
What is the time response of a control system typically divided into?
What is the time response of a control system typically divided into?
What is the mathematical representation of a ramp function?
What is the mathematical representation of a ramp function?
What is the parabolic function in terms of the 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?
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?
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?
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?
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?
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.
