Senior Project GuidelinesY(s)[1 + KG(s) H(s)] = R(s) KG(s) H(s)
1+KGH: Characteristics Equation and KGH is the open loop transfer function
System stability depends on Roots of the Characteristic Equation
11-Initial Value Theorem
12-Final Value Theorem
1- Maximum Overshoot Mp = ymax – yss where ymax >> yss
% Max overshoot = max overshoot / yss * 100
2- Delay time td= time required for y(s) to reach ½ yss
3- Rise time tr =time required to rise from 10 to 90% of yss
4- Settling time: ts= time required for step response to decrease and stay within 5% of yss
SS error
Transient state
Steady state
Response Analysis
The first step in analyzing a control system is to derive a mathematical model of the system.
Test signals: step, ramp, acceleration, impulse, sinusoidal …
Transient response and steady-state response
- First order systems
First- order systems
1/ (Ts+1)
- T is the torque
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Roots:
3- over-damped (ξ>1)
Quiz2
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