Lecture 7 ME 176 2 Time Response
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The document discusses underdamped second-order systems and defines key terms used to characterize their time response including: rise time, peak time, settling time, and percent overshoot. It provides examples of calculating these terms from plots of system response as well as determining system parameters like damping ratio to achieve a desired response. The document contains content on underdamped second-order systems and examples for determining time response specifications and system parameters from diagrams.
Lecture 7 ME 176 2 Time Response
- 1. ME 176 Control Systems Engineering Department of Mechanical Engineering Time Response
- 2. Underdamped Second-Order Systems: Review Department of Mechanical Engineering
- 3. Underdamped Second-Order Systems: Department of Mechanical Engineering
- 4. Underdamped Second-Order Systems: Department of Mechanical Engineering Rise Time: Time required for wave form to go from 0.1 of the final value to 0.9 of the final value. Peak Time: The time required to reach the first, or maximum peak. Settling Time: Time required for the transient damped oscillations to reach and stay within ~2% of the steady state value. Percent Overshoot : Amount that the waveform overshoots the steady-state, or final, value at the peak time, expressed as a percentage of the steady- state value.
- 5. Underdamped Second-Order Systems: Peak Time: Settling Time: Percent Overshot : Rise Time: Department of Mechanical Engineering
- 6. Underdamped Second-Order Systems: Review = Damped Frequency of Oscillation = Exponential Damping Frequency = Natural Frequency = Damping Ratio Department of Mechanical Engineering
- 7. Underdamped Second-Order Systems: Department of Mechanical Engineering
- 8. Examples: 1. Given the plot shown on right, find , , , , and 2. Given diagram below, find J and D to yield overshoot of 20% and a settling time of 2 seconds for a step input of torque T(t): Department of Mechanical Engineering
- 9. Quiz: 1.For the system shown or the right, a. Find the transfer function G(s) = X(s) / F(s). b. Find , , , , and . Department of Mechanical Engineering