1. By applying second-order approximation, the closed-loop bandwidth is determined i.e. required to meet the requirements of settling time, peak time, or rise time.
2. The gain, K, is set to the value that is required by the steady-state error specification.
3. Then, the Bode magnitude and phase diagrams for this gain value are plotted.
4. By applying second-order approximation, the phase margin is calculated to meet the damping ratio or the requirements of percent overshoot.
5. A new phase-margin frequency near ωBW is selected.
6. At the new phase-margin frequency, the additional amount of phase lead required to meet the phase-margin requirement is determined. Then, a small contribution is added that will be required after the lag compensator is added.
7. The lag compensator is designed by opting for higher break frequency one decade below the new phase-margin frequency. The lag compensator design is not critical, and any of the proper phase margin design will be demoted to the lead compensator. The lag compensator provides stability to the system with the gain needed for the steady-state error specification. The value of É£ from the lead compensator's requisites is found. By using the phase required from the lead compensator, the phase response curve of the Figure can be used to determine the value of É£ = 1/β. This value, and the previously found lag's upper break frequency, permits us to determine the lag's lower break frequency.
8. The lead compensator is designed. Using y value from the lag compensator design and that assumed for the new phase-margin frequency, the lower and upper break frequency for the lead compensator is found, after solving for T.
9. The bandwidth is to be checked to be ascertained that the speed requirement given in Step 1 is met.
10. Redesign it, if transient or phase-margin specifications are not met, as revealed by simulation or analysis.
2. The gain, K, is set to the value that is required by the steady-state error specification.
3. Then, the Bode magnitude and phase diagrams for this gain value are plotted.
4. By applying second-order approximation, the phase margin is calculated to meet the damping ratio or the requirements of percent overshoot.
5. A new phase-margin frequency near ωBW is selected.
6. At the new phase-margin frequency, the additional amount of phase lead required to meet the phase-margin requirement is determined. Then, a small contribution is added that will be required after the lag compensator is added.
7. The lag compensator is designed by opting for higher break frequency one decade below the new phase-margin frequency. The lag compensator design is not critical, and any of the proper phase margin design will be demoted to the lead compensator. The lag compensator provides stability to the system with the gain needed for the steady-state error specification. The value of É£ from the lead compensator's requisites is found. By using the phase required from the lead compensator, the phase response curve of the Figure can be used to determine the value of É£ = 1/β. This value, and the previously found lag's upper break frequency, permits us to determine the lag's lower break frequency.
8. The lead compensator is designed. Using y value from the lag compensator design and that assumed for the new phase-margin frequency, the lower and upper break frequency for the lead compensator is found, after solving for T.
9. The bandwidth is to be checked to be ascertained that the speed requirement given in Step 1 is met.
10. Redesign it, if transient or phase-margin specifications are not met, as revealed by simulation or analysis.
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